Abstract
The study of rotor-bearing vibration is crucial across various fields, encompassing applications such as rotating machinery, wind turbines, washing machines, and elevators. However, operational challenges can arise from these machines’ propensity to vibrate under specific conditions. To address this issue, the current research investigates the utilization of shape memory alloy (SMA) springs as intelligent materials in the rotor suspension system. SMA’s unique property of changing stiffness with temperature-induced phase shifts is harnessed, leading to the construction of a test rig for validating vibration characteristics. A novel hybrid bearing is devised to effectively manage vibrations, particularly in resonance zones. To the authors’ knowledge, this new model is never reported in the literature. Then, an accelerometer is employed to measure the rotor shaft response corresponding to disc position vibration signals. Furthermore, a numerical model is developed to validate experimental results, taking into account the phase change of SMA springs and the disc’s influence on the rotor bearing’s natural frequency. Temperature variations from 20 to 80°C resulted in a 13% change in natural frequency for the hybrid spring configuration. The experimental findings align closely with ANSYS simulations, displaying an acceptable error ratio, with the highest error remaining within 20% thresholds.
1 Introduction
Rotor-bearing vibration may be incredibly dangerous and expensive. It may result in equipment failure, property damage, and safety issues. It is important to control vibration levels in rotating equipment to minimize its effects. One may achieve this through a variety of approaches. Using smart materials is one of these methods. These materials can alter their phase due to temperature changes, which affects their characteristics, particularly the modulus elasticity [1,2,3,4]. The use of shape memory alloys (SMAs) for this purpose has attracted many researchers in recent years. When heated over a given temperature, SMAs can change from the martensite phase, which has a certain shape, to the austenite phase, which has a different shape. Therefore, the rotor of a rotating machine can be suspended at the correct place using SMA wires that carry electric current for heating to alter their phase [5,6,7]. Several studies have thoroughly investigated how SMAs affect the vibration behavior of rotating bearings. For example, Yogaraju et al. [8] developed a novel semi-active experimentally and numerically journal bearing using SMAs to provide needed force. Their experimental results found that the ovality ratio can impact the dynamic response, where when it increased, this would increase dynamic stiffness and damping. Garafolo and McHugh [9] studied the effect of SMA wire on the reduced vibration of flexible clamped–free beams embedded by SMA wire, where the accelerometer sensor was connected at the tip of the beam, and the natural frequency was determined using a frequency response function at various temperatures. According to their experimental findings, the natural frequency shift was 44.7%, and the amplitude at the beam’s tip dropped by 34%. Likewise, the unactivated SMA had a 44.6% amplitude reduction and a 160% frequency shift, whereas the activated SMA had a 258% amplitude reduction and a 63.6% frequency shift. Borges et al. [10] investigated that the first natural frequency, which is based on spring stiffness increasing as temperature increases and was empirically measured, might be reduced by utilizing helical SMA springs. A fuzzy controller is used to raise the temperature from 30 to 70°C in 25 s. Their results showed that the resonance zone’s amplitudes decreased by up to 60%. Xu et al. [11] utilized, experimentally and theoretically, the rotor seal system and the dynamic vibration absorber to reduce unbalanced or critical vibration. Their findings demonstrated that the dynamic vibration absorber alters the instability threshold and instability vibration frequency. Atiyah et al. [12] looked into the effect of the SMA wire number on the composite cantilever beam’s inherent frequency. According to their findings, increasing the number and diameter of SMA wires in the martensite phase caused a drop in the beam’s natural frequency, but increasing them in the austenite phase caused an increase. Also, it was discovered that a decrease in the beam’s inherent frequency might have occurred due to lengthening the beam. Braga et al. [13], utilizing a passive controller, examined numerically and experimentally the effect of SMA wire at different temperatures (30, 45, and 60°C) on the dynamic response of spinning. The results supported computational predictions that the SMA may reduce vibration amplitudes. Oliveira et al. [14] employed the Jeffcott modified approach, which operates at frequency across the resonance area, to examine the effect of stiffness change brought on by temperature rise on the performance of helical SMA springs of smart bearings. With a response time of 12–15 s, an amplitude reduction of 63% (RMS) and a maximum reduction of 73% were achieved. Rahmana et al. [15] investigated the whirling effect of the Jeffcott rotor formed from an SMA theoretically and experimentally. Based on the findings, they concluded that more damping greatly lowers the whirling amplitude (r/e). The maximum r/e for synchronous whirls occurs at unity spin ratios due to resonance. Yet, at high spin ratio values, the value of r/e approaches unity. It is noteworthy that the shaft reaction is notably different for a certain spin ratio of 1.414, all Pd/mg vs on both sides of the crossing point. Abdulkadhim et al. [16] used a proportional–integral–derivative controller on the two-dimensional rotor system suspended by helical SMA springs, and it was discovered that the controller had a high tracking and set point precision. Senko et al. [17] used experiments to analyze the mechanical performance of a unique bending spring shape composed of superelastic SMA (SMA-SE). The findings showed that, compared to cases without and with 1.5 mm of preload, employing the innovative M-shape spring of SMA-SE might reduce vibration by up to 23 dB. It has been demonstrated how well the M-shape device works to reduce mechanical vibration in rotor systems. Tuaib et al. [18] studied the effect of adding active magnetic bearings on rotating machines to minimize vibration and vibration behavior in traditional bearing systems. Their article uses simulation tools to analyze the vibrations in the rotary bearing system to determine their natural frequencies and performance-affecting factors. As a result of adding active magnetic bearings to rotating bearing shafts, vibration amplitude was reduced by around 60%. According to their study, the spinning bearing shaft is more solid and stable with the active magnetic bearing attached. Furthermore, the natural frequency was inversely proportional to the shaft length. The research was done on the effects of adding active magnetic bearings to rotating machines to reduce vibration and the vibration behavior in conventional bearing systems. They analyzed theoretically and analytically the vibrations in the rotary bearing system using simulation tools to identify the natural frequencies and performance-influencing elements. According to their results, adding active magnetic bearings to the rotating bearing shafts reduced vibration amplitude by almost 60%. This research suggests that adding the active magnetic bearing to the spinning bearing shaft makes the system more robust and solid. The natural frequency was also inversely related to the diameter of the spinning shaft, as seen in previous studies [19,20,21].
Different from the mentioned literature, this research fills many gaps. The main objective of this work is to monitor the variation and the natural frequency of the rotor system using SMA suspensions and compare the experimental with numerical results. A hybrid spring that combines helical and leaf springs is used to study rotor-bearing dynamics. To the authors’ knowledge, utilizing helical spring has never reported in the literature before in similar studies. Also, the effect of disc location on the dynamic reaction of the rotor bearings, as well as their dynamic behavior at the second, third, and fourth critical speeds, is investigated. The general objectives can be summarized as follows:
The dynamic response of a new design of support consisting of the combination of the leaf and helical springs of rotor bearings (hybrid type) is studied.
Designing and manufacturing molds for the SMA springs.
Manufacturing an experimental rig with a flexible rotor shaft and bearings with supports.
Implementing the controller of vibration and heating.
Designing and implementing electrical circuits for heat generation.
Develop an analytical model and compare it with the experimental and numerical by using the ANSYS 18.1 in simulation.
The research methodology is summarized in Figure 1.

Research methodology flowchart.
The article is organized as follows: Section 2 presents the theoretical investigation. The experimental part is presented in Section 3. Section 4 discusses the results. Finally, Section 5 concludes the article.
2 Theoretical investigation
The built-in rig was numerically modeled using the ANSYS tool in the majority of earlier works that could be found in the literature in order to analyze the natural frequency behavior at martensite and austinite phases. Different from other literature, utilizing SMA suspensions, track the rotor system’s variation in natural frequency and contrast the experimental and numerical results. To analyze rotor-bearing dynamics, helical and leaf springs are coupled to create a hybrid spring. Noting that, this novel design is never reported in the literature. Additionally, the dynamic behavior of the rotor bearings at the second, third, and fourth critical speeds is examined, as well as the impact of disc position on these factors. This study utilizes the ANSYS workbench version 18.1 software. In this section, creating the geometry using the AUTOCAD 2021 program, which is interoperable with various simulation modeling tools, the geometry for each module was drawn. Then, as shown in Figure 2, it was loaded into the ANSYS program. Then, the identical instances explored experimentally are modeled and numerically resolved. This study uses an eight-node SOLID186 element to mesh a 3D rotor system model, as illustrated in Figure 3. The default mesh size is also chosen. To conduct a free vibration analysis, finite-element quantities are compared to test ones. To keep the layers from growing genetically related to one another, requirements link layers and skins of the rotor plate at their contact points. Drawing the structure after choosing the element types, adding the mechanical properties of the materials for the design, supporting the system following the supported type for the rotor structure, and finally using modal analysis to determine the free vibration characteristics for the rotor were all part of the numerical solution. Note that in this work, the properties of the shaft are assumed to be constant such as cross section, Young’s modulus, and moment of inertia. These assumptions do not affect the current study. On the other side, the internal and the external damping of the shaft are neglected. Since the study is involved in studying and investigating the damping effect of the hybrid spring, the boundary conditions are assumed firm and articulated for the clamped side (no spring side) and the hanged side (the spring side) (Figure 4).

The SMA springs with shaft and disc modeled in AutoCAD.

Boundary conditions used.

Demonstration of the first mode shape.
3 Experimental work
In this article, a test rig is built to conduct an experiment on which the dynamics of an asymmetric journal-bearing supported rotor system is to be examined. The base for the experiment is a stiff cylindrical shaft supported by an antifriction bearing. On the shaft side, a single disc is attached at various distances from the bearing and spring arrangement. The translational vibrations of the pedestal were measured using the accelerometer sensor, which was mounted on the end of the rotating shaft. When the shaft rotates at a slow rotational speed, a continuous synchronous vibration with a small amplitude is observed. The system reaches the initial resonance with a significant vibration amplitude at the first natural frequency as the rotational speed rises. The vibration resumes its regular state after the resonance. As the shaft emerges, the vibration gets stronger and faster.
Results for the chemical composition of the rotor shaft are shown in Table 1, while the mechanical properties of the shaft are shown in Table 2. Tables 3 and 4 show the mechanical characteristics of springs, while Table 5 shows the chemical components of springs (SMAs) (Figures 5 and 6).
Chemical composition of the steel shaft
| Sample | C% | Si% | Mn% | P% | S% | Cr% | Mo% | Ni% | Al% | Cu% | Fe% |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Diameter (8 mm) | 0.128 | 0.364 | 12.53 | 0.0369 | 0.0056 | 13.24 | 0.0162 | 1.35 | 0.0057 | 0.593 | Bal. |
Steel shaft specifications (experimentally)
| Density (kg/m3) | Yield strength (MPa) | Ultimate strength (MPa) | Elongation (%) | Modulus of elasticity (GPa) |
|---|---|---|---|---|
| 7,850 | 812.31 | 1067.9 | 40 | 204 |
Specification of SMA helical spring wire
| IT. | Properties | Values |
|---|---|---|
| 1 | Melting point (°C) | 1,300 |
| 2 | Density (kg/m3) | 6,450 |
| 3 | Modulus of elasticity (GPa) (martensite) | 36 |
| Modulus of elasticity (GPa) (austenite) | 87 | |
| 4 | Poisson’s ratio | 0.33 |
| 5 | Yield strength (MPa) (martensite) | 392 |
| Yield strength (MPa) (austenite) | 759 | |
| 6 | Austenite start temperature (A s) (°C) | 34.5 |
| 7 | Austenite finish temperature (A f) (°C) | 66.8 |
| 8 | Wire diameter (mm) | 2 |
| 9 | Inner diameter (mm) | 25 |
| 10 | No. of coils | 3 |
| 11 | Pitch length (mm) | 20 |
| 12 | Exp. spring constant (N/m) (martensite) | 553 |
| 13 | Exp. spring constant (N/m) (austenite) | 1,331 |
Specification of SMA leaf spring
| IT. | Properties | Values |
|---|---|---|
| 1 | Melting point (°C) | 1,300 |
| 2 | Density (kg/m3) | 6,450 |
| 3 | Modulus of elasticity (GPa) (martensite) | 36 |
| Modulus of elasticity (GPa) (austenite) | 87 | |
| 4 | Poisson’s ratio | 0.33 |
| 5 | Yield strength (MPa) (martensite) | 392 |
| Yield strength (MPa) (austenite) | 759 | |
| 6 | Austenite start temperature (As) (°C) | 34.5 |
| 7 | Austenite finish temperature (Af) (°C) | 66.8 |
| 8 | Thickness (mm) | 2 |
| 9 | Width (mm) | 5 |
| 10 | R1 (mm) | 35 |
| 11 | R2 (mm) | 70 |
| 12 | Exp. spring constant (N/m) (martensite) | 1,189 |
| 13 | Exp. spring constant (N/m) (austenite) | 2,560 |
Chemical composition of SMA
| C% | Co% | Cu% | Cr% | H% | Fe% | No% | Nb% | Ni% | Ti% |
|---|---|---|---|---|---|---|---|---|---|
| 0.05 | 0.05 | 0.01 | 0.01 | 0.005 | 0.05 | 0.0162 | 0.025 | 55 | Bal. |

Experiment setup.

Vibration rig.
4 Results
In this work, the experimental investigation is carried out to analyze the free vibration problem of the rotor system with SMA metal. The evaluated results include the amplitude, natural frequency, and temperature profile of the clamped hanged supported rotor journal bearings with various parameters, temperature, and geometrical properties. Numerical investigation using ANSYS software for verification purposes is also employed. The obtained results are tabulated and drawn with multiple curves. Figures 7–10 show the critical speed relationship in the X–Y directions for free vibration analysis with springs only and with the disc, and mass at 20 and 80°C, where we note that:
The areas of increasing amplitudes along the ascending frequency line, where these points represent the critical speed, as within the used range, more than one essential point appeared, and this was previously planned when choosing the length and diameter of the rotating shaft.
The increase in stiffness caused by the modules of elasticity increasing as a result of phase transfer resulted in an increase in natural frequencies. Due to the increased gravity impact, progress is primarily seen on the frequencies in the Y-direction rather than the other axis (X-direction).
When operating at critical speeds, natural frequencies are displayed within the applied speed range. It was noted that the amplitudes of the two axes for the same crucial velocity were not the same. As a consequence of the stiffness asymmetry in the two axes (orientation of leaf spring installation), the critical speed in the Y-axis was determined earlier than in the X-axis. Gravitational effects also contribute to the speed along the vertical axis (Y-axis). As a result of the lack of symmetry, the increased stiffness resulted in a delay in the crucial time on the horizontal axis (X-axis). In addition, there is a slight difference between the first and second critical speeds, but it is evident at the third and fourth necessary speeds, where the speed has been higher due to the different mode shapes.

Vibration amplitudes of hybrid springs SMA at 20°C.

Vibration amplitudes of hybrid springs SMA at 80°C.

Experimental dynamic response hybrid springs SMA in X–Y directions at temperature 20°C, when disc position at 40 cm.

Experimental dynamic response of hybrid springs SMA in X–Y directions at temperature 80°C, when disc position at 40 cm.
The initial natural frequency of leaf and helical springs is compared in Table 6 using computational (by ANSYS software) and experimental results. Results showed that the Austinite phase is more important than the Martensite phase, and the natural frequencies drop with increasing disc distance. The rotor’s high rigidity in the Austinite alloy is thought to be the cause. The Second Natural Frequency of Leaf and Helical Springs data are shown in Table 7, with the largest disparity (24%) occurring at a disc distance of 60 mm. The third and fourth frequency findings for the identical rotor system are displayed in Tables 8 and 9. Regarding disc distance and alloy, the system behaves identically in all cases. The difference between the experimental and numerical solutions is within acceptable bounds, with the third and fourth frequencies experiencing the largest divergence (26%) overall (Figures 11–14).
First critical speed (RPM) of hybrid springs
| Disc position (cm) | Martensite ANSYS | Martensite exp. | Error% | Austinite exp. | Austinite ANSYS | Error% |
|---|---|---|---|---|---|---|
| Without disc | 997.74 | 1,500 | 33 | 1579.00 | 1484.04 | 6 |
| 10 | 995.73 | 1,412 | 29 | 1478.00 | 1378.12 | 7 |
| 20 | 983.31 | 1,348 | 27 | 1428.00 | 1350.90 | 5 |
| 30 | 948.25 | 1,207 | 21 | 1280.00 | 1290.83 | 1 |
| 40 | 894.36 | 1,102 | 19 | 1150.00 | 1229.33 | 6 |
| 50 | 841.27 | 1,024 | 18 | 1100.00 | 1158.34 | 5 |
| 60 | 800.62 | 1,101 | 27 | 1158.00 | 1129.78 | 2 |
| 70 | 773.19 | 1,138 | 32 | 1208.00 | 1136.94 | 6 |
Second critical speed (RPM) of hybrid springs
| Disc position (cm) | Martensite ANSYS | Martensite exp. | Error% | Austinite exp. | Austinite ANSYS | Error% |
|---|---|---|---|---|---|---|
| Without disc | 1241.01 | 1,554 | 20 | 1,636 | 1328.12 | 19 |
| 10 | 1241.57 | 1,441 | 14 | 1,550 | 1326.21 | 14 |
| 20 | 1231.74 | 1,400 | 12 | 1,444 | 1290.38 | 11 |
| 30 | 1114.93 | 1,251 | 11 | 1,290 | 1192.64 | 8 |
| 40 | 979.96 | 1,134 | 14 | 1,152 | 1077.04 | 7 |
| 50 | 923.27 | 1,098 | 16 | 1,110 | 1001.46 | 10 |
| 60 | 875.35 | 1,196 | 27 | 1,280 | 972.99 | 24 |
| 70 | 1081.95 | 1,245 | 15 | 1,315 | 1154.33 | 12 |
Third critical speed (RPM) of hybrid springs
| Disc position (cm) | Martensite ANSYS | Martensite exp. | Error% | Austinite exp. | Austinite ANSYS | Error% |
|---|---|---|---|---|---|---|
| Without disc | 2622.90 | 2116.00 | 19 | 2280.00 | 2722.93 | 16 |
| 10 | 2513.79 | 1978.00 | 21 | 2195.00 | 2675.16 | 18 |
| 20 | 2382.42 | 1732.00 | 27 | 1846.00 | 2502.80 | 26 |
| 30 | 2066.37 | 1655.00 | 20 | 1790.00 | 2233.85 | 20 |
| 40 | 1998.63 | 1697.00 | 15 | 1800.00 | 2224.97 | 19 |
| 50 | 2139.94 | 1770.00 | 17 | 1900.00 | 2381.94 | 20 |
| 60 | 2431.05 | 1850.00 | 24 | 2085.00 | 2646.78 | 21 |
| 70 | 2511.97 | 1947.00 | 22 | 2178.00 | 2665.61 | 18 |
Fourth critical speed (RPM) of hybrid springs
| Disc position (cm) | Martensite ANSYS | Martensite exp. | Error% | Austinite exp. | Austinite ANSYS | Error% |
|---|---|---|---|---|---|---|
| Without disc | 2904.01 | 2190.00 | 25 | 2228.00 | 2967.99 | 25 |
| 10 | 2806.24 | 2055.00 | 27 | 2162.00 | 2927.29 | 26 |
| 20 | 2472.71 | 1892.00 | 23 | 1990.00 | 2602.64 | 24 |
| 30 | 2094.17 | 1788.00 | 15 | 1900.00 | 2330.45 | 18 |
| 40 | 2034.36 | 1820.00 | 11 | 1920.00 | 2344.39 | 18 |
| 50 | 2192.10 | 1917.00 | 13 | 2024.00 | 2511.50 | 19 |
| 60 | 2559.36 | 1988.00 | 22 | 2088.00 | 2704.39 | 23 |
| 70 | 2736.69 | 2115.00 | 23 | 2312.00 | 2870.35 | 19 |

First natural frequency behavior due to disc position variation at different temperatures for hybrid springs SMA.

Second natural frequency behavior due to disc position variation at different temperatures hybrid springs SMA.

Third natural frequency behavior due to disc position variation at different temperatures hybrid springs SMA.

Fourth natural frequency behavior due to disc position variation at different temperatures for hybrid springs SMA.
The Campbell diagram is examined at various parameters in Figures 15–22. One can infer from the graphics that an operating system’s Campbell diagram illustrates the vibration excitation zone that takes place across the rotor system. Additionally, Campbell diagrams may be produced using the machine’s design criteria or operational information. The frequency responsiveness decreases with temperature, as seen by the link between the engine’s rotating speed along the X-axis and the system’s frequency on the Y-axis. Furthermore, as disc distance increases, the same pattern can be seen. When deciding if a running frequency, its harmonics, or subharmonics are to blame for the excitation of a natural frequency, the rotor system must perform this design analysis (Tables 10–13).

Campbell diagram of the system at 20°C without disc.

Campbell diagram of the system at 80°C without disc.

Campbell diagram of the system at 20°C with disc position 20 cm.

Campbell diagram of the system at 80°C with disc position 20 cm.

Campbell diagram of the system at 20°C with disc position 40 cm.

Campbell diagram of the system at 80°C with disc position 40 cm.

Campbell diagram of the system at 20°C with disc position 70 cm.

Campbell diagram of the system at 80°C with disc position 70 cm.
First critical speed (RPM) of hybrid springs at different disc positions and temperatures
| Disc position (cm) | 20°C | 40°C | 50°C | 60°C | 80°C | Increasing RPM | Increasing% |
|---|---|---|---|---|---|---|---|
| Without disc | 1,500 | 1,520 | 1,530 | 1,540 | 1,579 | 79 | 5 |
| 10 | 1,412 | 1,400 | 1,434 | 1,465 | 1,478 | 66 | 5 |
| 20 | 1,348 | 1,340 | 1,350 | 1,411 | 1,428 | 80 | 6 |
| 30 | 1,207 | 1,240 | 1,268 | 1,274 | 1,280 | 73 | 6 |
| 40 | 1,102 | 1,118 | 1,141 | 1,145 | 1,150 | 48 | 4 |
| 50 | 1,024 | 1,033 | 1,042 | 1,069 | 1,100 | 76 | 7 |
| 60 | 1,101 | 1,110 | 1,115 | 1,129 | 1,158 | 57 | 5 |
| 70 | 1,138 | 1,140 | 1,174 | 1,195 | 1,208 | 70 | 6 |
Second critical speed (RPM) of hybrid springs at different disc positions and temperatures
| Disc position (cm) | 20°C | 40°C | 50°C | 60°C | 80°C | Increasing RPM | Increasing% |
|---|---|---|---|---|---|---|---|
| Without disc | 1,554 | 1,572 | 1,585 | 1,591 | 1,636 | 82 | 5 |
| 10 | 1,441 | 1,475 | 1,520 | 1,542 | 1,550 | 109 | 8 |
| 20 | 1,400 | 1,410 | 1,420 | 1,434 | 1,444 | 44 | 3 |
| 30 | 1,251 | 1,271 | 1,277 | 1,286 | 1,290 | 39 | 3 |
| 40 | 1,134 | 1,137 | 1,144 | 1,146 | 1,152 | 18 | 2 |
| 50 | 1,098 | 1,090 | 1,100 | 1,104 | 1,110 | 12 | 1 |
| 60 | 1,196 | 1,200 | 1,255 | 1,275 | 1,280 | 84 | 7 |
| 70 | 1,245 | 1,261 | 1,291 | 1,309 | 1,315 | 70 | 6 |
Third critical speed (RPM) of hybrid springs at different disc positions and temperatures
| Disc position (cm) | 20°C | 40°C | 50°C | 60°C | 80°C | Increasing RPM | Increasing% |
|---|---|---|---|---|---|---|---|
| Without disc | 2,116 | 2,243 | 2,272 | 2,275 | 2,280 | 164 | 8 |
| 10 | 1,978 | 2,070 | 2,100 | 2,154 | 2,195 | 217 | 11 |
| 20 | 1,732 | 1,765 | 1,780 | 1,810 | 1,846 | 114 | 7 |
| 30 | 1,655 | 1,665 | 1,695 | 1,730 | 1,790 | 135 | 8 |
| 40 | 1,697 | 1,690 | 1,750 | 1,772 | 1,800 | 103 | 6 |
| 50 | 1,770 | 1,794 | 1,838 | 1,872 | 1,900 | 130 | 7 |
| 60 | 1,850 | 1,960 | 2,000 | 2,075 | 2,085 | 235 | 13 |
| 70 | 1,947 | 2,016 | 2,056 | 2,105 | 2,178 | 231 | 12 |
Fourth critical speed (RPM) of hybrid springs at different disc positions and temperatures
| Disc position (cm) | 20°C | 40°C | 50°C | 60°C | 80°C | Increasing RPM | Increasing% |
|---|---|---|---|---|---|---|---|
| Without disc | 2,190 | 2,206 | 2,285 | 2,292 | 2,328 | 138 | 6 |
| 10 | 2,055 | 2,066 | 2,095 | 2,100 | 2,162 | 107 | 5 |
| 20 | 1,892 | 1,892 | 1,900 | 1,948 | 1,990 | 98 | 5 |
| 30 | 1,820 | 1,832 | 1,841 | 1,904 | 1,920 | 100 | 5 |
| 40 | 1,788 | 1,797 | 1,800 | 1,875 | 1,900 | 112 | 6 |
| 50 | 1,917 | 1,920 | 1,937 | 2,000 | 2,024 | 107 | 6 |
| 60 | 1,988 | 2,000 | 2,056 | 2,070 | 2,088 | 100 | 5 |
| 70 | 2,115 | 2,139 | 2,213 | 2,272 | 2,312 | 197 | 9 |
It can be noticed that the gravitational acceleration is assumed to be constant, and it is equal to 9.81 m/s.
5 Conclusions
The most significant findings and observations from this work are presented in this section, where it is revealed that the apparent impact of temperature on the dynamic response was caused by a phase transition that altered the SMA springs’ elasticity modulus. Additionally, there was a clear mass effect, which peaked when the disc was positioned in the center of the revolving shaft (proving the Jeffcott approach). Additionally, increasing the stiffness led to an increase in the system’s natural frequencies. The suspension system’s natural frequency changed by 235 RPM (13%), which was the largest change as a result of temperature changes from 20 to 80°C. Additionally, the experimental results supported the ANSYS results with a tolerable error ratio. For future work, the authors intend to use optimization methods to predict the properties of SMA springs and natural frequencies.
Acknowledgment
The authors thank the head and staff members of the Mechanical Engineering Department at the University of Technology for their efforts in solving the difficulties that they faced during this work.
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Funding information: This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
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Author contributions: All authors contributed equally to this work.
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Conflict of interest: The authors declare no conflict of interest.
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Data availability statement: The data supporting this study’s findings are available on request from the corresponding author.
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© 2024 the author(s), published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.
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Artikel in diesem Heft
- Regular Articles
- Methodology of automated quality management
- Influence of vibratory conveyor design parameters on the trough motion and the self-synchronization of inertial vibrators
- Application of finite element method in industrial design, example of an electric motorcycle design project
- Correlative evaluation of the corrosion resilience and passivation properties of zinc and aluminum alloys in neutral chloride and acid-chloride solutions
- Will COVID “encourage” B2B and data exchange engineering in logistic firms?
- Influence of unsupported sleepers on flange climb derailment of two freight wagons
- A hybrid detection algorithm for 5G OTFS waveform for 64 and 256 QAM with Rayleigh and Rician channels
- Effect of short heat treatment on mechanical properties and shape memory properties of Cu–Al–Ni shape memory alloy
- Exploring the potential of ammonia and hydrogen as alternative fuels for transportation
- Impact of insulation on energy consumption and CO2 emissions in high-rise commercial buildings at various climate zones
- Advanced autopilot design with extremum-seeking control for aircraft control
- Adaptive multidimensional trust-based recommendation model for peer to peer applications
- Effects of CFRP sheets on the flexural behavior of high-strength concrete beam
- Enhancing urban sustainability through industrial synergy: A multidisciplinary framework for integrating sustainable industrial practices within urban settings – The case of Hamadan industrial city
- Advanced vibrant controller results of an energetic framework structure
- Application of the Taguchi method and RSM for process parameter optimization in AWSJ machining of CFRP composite-based orthopedic implants
- Improved correlation of soil modulus with SPT N values
- Technologies for high-temperature batch annealing of grain-oriented electrical steel: An overview
- Assessing the need for the adoption of digitalization in Indian small and medium enterprises
- A non-ideal hybridization issue for vertical TFET-based dielectric-modulated biosensor
- Optimizing data retrieval for enhanced data integrity verification in cloud environments
- Performance analysis of nonlinear crosstalk of WDM systems using modulation schemes criteria
- Nonlinear finite-element analysis of RC beams with various opening near supports
- Thermal analysis of Fe3O4–Cu/water over a cone: a fractional Maxwell model
- Radial–axial runner blade design using the coordinate slice technique
- Theoretical and experimental comparison between straight and curved continuous box girders
- Effect of the reinforcement ratio on the mechanical behaviour of textile-reinforced concrete composite: Experiment and numerical modeling
- Experimental and numerical investigation on composite beam–column joint connection behavior using different types of connection schemes
- Enhanced performance and robustness in anti-lock brake systems using barrier function-based integral sliding mode control
- Evaluation of the creep strength of samples produced by fused deposition modeling
- A combined feedforward-feedback controller design for nonlinear systems
- Effect of adjacent structures on footing settlement for different multi-building arrangements
- Analyzing the impact of curved tracks on wheel flange thickness reduction in railway systems
- Review Articles
- Mechanical and smart properties of cement nanocomposites containing nanomaterials: A brief review
- Applications of nanotechnology and nanoproduction techniques
- Relationship between indoor environmental quality and guests’ comfort and satisfaction at green hotels: A comprehensive review
- Communication
- Techniques to mitigate the admission of radon inside buildings
- Erratum
- Erratum to “Effect of short heat treatment on mechanical properties and shape memory properties of Cu–Al–Ni shape memory alloy”
- Special Issue: AESMT-3 - Part II
- Integrated fuzzy logic and multicriteria decision model methods for selecting suitable sites for wastewater treatment plant: A case study in the center of Basrah, Iraq
- Physical and mechanical response of porous metals composites with nano-natural additives
- Special Issue: AESMT-4 - Part II
- New recycling method of lubricant oil and the effect on the viscosity and viscous shear as an environmentally friendly
- Identify the effect of Fe2O3 nanoparticles on mechanical and microstructural characteristics of aluminum matrix composite produced by powder metallurgy technique
- Static behavior of piled raft foundation in clay
- Ultra-low-power CMOS ring oscillator with minimum power consumption of 2.9 pW using low-voltage biasing technique
- Using ANN for well type identifying and increasing production from Sa’di formation of Halfaya oil field – Iraq
- Optimizing the performance of concrete tiles using nano-papyrus and carbon fibers
- Special Issue: AESMT-5 - Part II
- Comparative the effect of distribution transformer coil shape on electromagnetic forces and their distribution using the FEM
- The complex of Weyl module in free characteristic in the event of a partition (7,5,3)
- Restrained captive domination number
- Experimental study of improving hot mix asphalt reinforced with carbon fibers
- Asphalt binder modified with recycled tyre rubber
- Thermal performance of radiant floor cooling with phase change material for energy-efficient buildings
- Surveying the prediction of risks in cryptocurrency investments using recurrent neural networks
- A deep reinforcement learning framework to modify LQR for an active vibration control applied to 2D building models
- Evaluation of mechanically stabilized earth retaining walls for different soil–structure interaction methods: A review
- Assessment of heat transfer in a triangular duct with different configurations of ribs using computational fluid dynamics
- Sulfate removal from wastewater by using waste material as an adsorbent
- Experimental investigation on strengthening lap joints subjected to bending in glulam timber beams using CFRP sheets
- A study of the vibrations of a rotor bearing suspended by a hybrid spring system of shape memory alloys
- Stability analysis of Hub dam under rapid drawdown
- Developing ANFIS-FMEA model for assessment and prioritization of potential trouble factors in Iraqi building projects
- Numerical and experimental comparison study of piled raft foundation
- Effect of asphalt modified with waste engine oil on the durability properties of hot asphalt mixtures with reclaimed asphalt pavement
- Hydraulic model for flood inundation in Diyala River Basin using HEC-RAS, PMP, and neural network
- Numerical study on discharge capacity of piano key side weir with various ratios of the crest length to the width
- The optimal allocation of thyristor-controlled series compensators for enhancement HVAC transmission lines Iraqi super grid by using seeker optimization algorithm
- Numerical and experimental study of the impact on aerodynamic characteristics of the NACA0012 airfoil
- Effect of nano-TiO2 on physical and rheological properties of asphalt cement
- Performance evolution of novel palm leaf powder used for enhancing hot mix asphalt
- Performance analysis, evaluation, and improvement of selected unsignalized intersection using SIDRA software – Case study
- Flexural behavior of RC beams externally reinforced with CFRP composites using various strategies
- Influence of fiber types on the properties of the artificial cold-bonded lightweight aggregates
- Experimental investigation of RC beams strengthened with externally bonded BFRP composites
- Generalized RKM methods for solving fifth-order quasi-linear fractional partial differential equation
- An experimental and numerical study investigating sediment transport position in the bed of sewer pipes in Karbala
- Role of individual component failure in the performance of a 1-out-of-3 cold standby system: A Markov model approach
- Implementation for the cases (5, 4) and (5, 4)/(2, 0)
- Center group actions and related concepts
- Experimental investigation of the effect of horizontal construction joints on the behavior of deep beams
- Deletion of a vertex in even sum domination
- Deep learning techniques in concrete powder mix designing
- Effect of loading type in concrete deep beam with strut reinforcement
- Studying the effect of using CFRP warping on strength of husk rice concrete columns
- Parametric analysis of the influence of climatic factors on the formation of traditional buildings in the city of Al Najaf
- Suitability location for landfill using a fuzzy-GIS model: A case study in Hillah, Iraq
- Hybrid approach for cost estimation of sustainable building projects using artificial neural networks
- Assessment of indirect tensile stress and tensile–strength ratio and creep compliance in HMA mixes with micro-silica and PMB
- Density functional theory to study stopping power of proton in water, lung, bladder, and intestine
- A review of single flow, flow boiling, and coating microchannel studies
- Effect of GFRP bar length on the flexural behavior of hybrid concrete beams strengthened with NSM bars
- Exploring the impact of parameters on flow boiling heat transfer in microchannels and coated microtubes: A comprehensive review
- Crumb rubber modification for enhanced rutting resistance in asphalt mixtures
- Special Issue: AESMT-6
- Design of a new sorting colors system based on PLC, TIA portal, and factory I/O programs
- Forecasting empirical formula for suspended sediment load prediction at upstream of Al-Kufa barrage, Kufa City, Iraq
- Optimization and characterization of sustainable geopolymer mortars based on palygorskite clay, water glass, and sodium hydroxide
- Sediment transport modelling upstream of Al Kufa Barrage
- Study of energy loss, range, and stopping time for proton in germanium and copper materials
- Effect of internal and external recycle ratios on the nutrient removal efficiency of anaerobic/anoxic/oxic (VIP) wastewater treatment plant
- Enhancing structural behaviour of polypropylene fibre concrete columns longitudinally reinforced with fibreglass bars
- Sustainable road paving: Enhancing concrete paver blocks with zeolite-enhanced cement
- Evaluation of the operational performance of Karbala waste water treatment plant under variable flow using GPS-X model
- Design and simulation of photonic crystal fiber for highly sensitive chemical sensing applications
- Optimization and design of a new column sequencing for crude oil distillation at Basrah refinery
- Inductive 3D numerical modelling of the tibia bone using MRI to examine von Mises stress and overall deformation
- An image encryption method based on modified elliptic curve Diffie-Hellman key exchange protocol and Hill Cipher
- Experimental investigation of generating superheated steam using a parabolic dish with a cylindrical cavity receiver: A case study
- Effect of surface roughness on the interface behavior of clayey soils
- Investigated of the optical properties for SiO2 by using Lorentz model
- Measurements of induced vibrations due to steel pipe pile driving in Al-Fao soil: Effect of partial end closure
- Experimental and numerical studies of ballistic resistance of hybrid sandwich composite body armor
- Evaluation of clay layer presence on shallow foundation settlement in dry sand under an earthquake
- Optimal design of mechanical performances of asphalt mixtures comprising nano-clay additives
- Advancing seismic performance: Isolators, TMDs, and multi-level strategies in reinforced concrete buildings
- Predicted evaporation in Basrah using artificial neural networks
- Energy management system for a small town to enhance quality of life
- Numerical study on entropy minimization in pipes with helical airfoil and CuO nanoparticle integration
- Equations and methodologies of inlet drainage system discharge coefficients: A review
- Thermal buckling analysis for hybrid and composite laminated plate by using new displacement function
- Investigation into the mechanical and thermal properties of lightweight mortar using commercial beads or recycled expanded polystyrene
- Experimental and theoretical analysis of single-jet column and concrete column using double-jet grouting technique applied at Al-Rashdia site
- The impact of incorporating waste materials on the mechanical and physical characteristics of tile adhesive materials
- Seismic resilience: Innovations in structural engineering for earthquake-prone areas
- Automatic human identification using fingerprint images based on Gabor filter and SIFT features fusion
- Performance of GRKM-method for solving classes of ordinary and partial differential equations of sixth-orders
- Visible light-boosted photodegradation activity of Ag–AgVO3/Zn0.5Mn0.5Fe2O4 supported heterojunctions for effective degradation of organic contaminates
- Production of sustainable concrete with treated cement kiln dust and iron slag waste aggregate
- Key effects on the structural behavior of fiber-reinforced lightweight concrete-ribbed slabs: A review
- A comparative analysis of the energy dissipation efficiency of various piano key weir types
- Special Issue: Transport 2022 - Part II
- Variability in road surface temperature in urban road network – A case study making use of mobile measurements
- Special Issue: BCEE5-2023
- Evaluation of reclaimed asphalt mixtures rejuvenated with waste engine oil to resist rutting deformation
- Assessment of potential resistance to moisture damage and fatigue cracks of asphalt mixture modified with ground granulated blast furnace slag
- Investigating seismic response in adjacent structures: A study on the impact of buildings’ orientation and distance considering soil–structure interaction
- Improvement of porosity of mortar using polyethylene glycol pre-polymer-impregnated mortar
- Three-dimensional analysis of steel beam-column bolted connections
- Assessment of agricultural drought in Iraq employing Landsat and MODIS imagery
- Performance evaluation of grouted porous asphalt concrete
- Optimization of local modified metakaolin-based geopolymer concrete by Taguchi method
- Effect of waste tire products on some characteristics of roller-compacted concrete
- Studying the lateral displacement of retaining wall supporting sandy soil under dynamic loads
- Seismic performance evaluation of concrete buttress dram (Dynamic linear analysis)
- Behavior of soil reinforced with micropiles
- Possibility of production high strength lightweight concrete containing organic waste aggregate and recycled steel fibers
- An investigation of self-sensing and mechanical properties of smart engineered cementitious composites reinforced with functional materials
- Forecasting changes in precipitation and temperatures of a regional watershed in Northern Iraq using LARS-WG model
- Experimental investigation of dynamic soil properties for modeling energy-absorbing layers
- Numerical investigation of the effect of longitudinal steel reinforcement ratio on the ductility of concrete beams
- An experimental study on the tensile properties of reinforced asphalt pavement
- Self-sensing behavior of hot asphalt mixture with steel fiber-based additive
- Behavior of ultra-high-performance concrete deep beams reinforced by basalt fibers
- Optimizing asphalt binder performance with various PET types
- Investigation of the hydraulic characteristics and homogeneity of the microstructure of the air voids in the sustainable rigid pavement
- Enhanced biogas production from municipal solid waste via digestion with cow manure: A case study
- Special Issue: AESMT-7 - Part I
- Preparation and investigation of cobalt nanoparticles by laser ablation: Structure, linear, and nonlinear optical properties
- Seismic analysis of RC building with plan irregularity in Baghdad/Iraq to obtain the optimal behavior
- The effect of urban environment on large-scale path loss model’s main parameters for mmWave 5G mobile network in Iraq
- Formatting a questionnaire for the quality control of river bank roads
- Vibration suppression of smart composite beam using model predictive controller
- Machine learning-based compressive strength estimation in nanomaterial-modified lightweight concrete
- In-depth analysis of critical factors affecting Iraqi construction projects performance
- Behavior of container berth structure under the influence of environmental and operational loads
- Energy absorption and impact response of ballistic resistance laminate
- Effect of water-absorbent polymer balls in internal curing on punching shear behavior of bubble slabs
- Effect of surface roughness on interface shear strength parameters of sandy soils
- Evaluating the interaction for embedded H-steel section in normal concrete under monotonic and repeated loads
- Estimation of the settlement of pile head using ANN and multivariate linear regression based on the results of load transfer method
- Enhancing communication: Deep learning for Arabic sign language translation
- A review of recent studies of both heat pipe and evaporative cooling in passive heat recovery
- Effect of nano-silica on the mechanical properties of LWC
- An experimental study of some mechanical properties and absorption for polymer-modified cement mortar modified with superplasticizer
- Digital beamforming enhancement with LSTM-based deep learning for millimeter wave transmission
- Developing an efficient planning process for heritage buildings maintenance in Iraq
- Design and optimization of two-stage controller for three-phase multi-converter/multi-machine electric vehicle
- Evaluation of microstructure and mechanical properties of Al1050/Al2O3/Gr composite processed by forming operation ECAP
- Calculations of mass stopping power and range of protons in organic compounds (CH3OH, CH2O, and CO2) at energy range of 0.01–1,000 MeV
- Investigation of in vitro behavior of composite coating hydroxyapatite-nano silver on 316L stainless steel substrate by electrophoretic technic for biomedical tools
- A review: Enhancing tribological properties of journal bearings composite materials
- Improvements in the randomness and security of digital currency using the photon sponge hash function through Maiorana–McFarland S-box replacement
- Design a new scheme for image security using a deep learning technique of hierarchical parameters
- Special Issue: ICES 2023
- Comparative geotechnical analysis for ultimate bearing capacity of precast concrete piles using cone resistance measurements
- Visualizing sustainable rainwater harvesting: A case study of Karbala Province
- Geogrid reinforcement for improving bearing capacity and stability of square foundations
- Evaluation of the effluent concentrations of Karbala wastewater treatment plant using reliability analysis
- Adsorbent made with inexpensive, local resources
- Effect of drain pipes on seepage and slope stability through a zoned earth dam
- Sediment accumulation in an 8 inch sewer pipe for a sample of various particles obtained from the streets of Karbala city, Iraq
- Special Issue: IETAS 2024 - Part I
- Analyzing the impact of transfer learning on explanation accuracy in deep learning-based ECG recognition systems
- Effect of scale factor on the dynamic response of frame foundations
- Improving multi-object detection and tracking with deep learning, DeepSORT, and frame cancellation techniques
- The impact of using prestressed CFRP bars on the development of flexural strength
- Assessment of surface hardness and impact strength of denture base resins reinforced with silver–titanium dioxide and silver–zirconium dioxide nanoparticles: In vitro study
- A data augmentation approach to enhance breast cancer detection using generative adversarial and artificial neural networks
- Modification of the 5D Lorenz chaotic map with fuzzy numbers for video encryption in cloud computing
- Special Issue: 51st KKBN - Part I
- Evaluation of static bending caused damage of glass-fiber composite structure using terahertz inspection