Startseite Design of ER damper for recoil length minimization: A case study on gun recoil system
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Design of ER damper for recoil length minimization: A case study on gun recoil system

  • Nguyen Huu Phan , Santosh R. Patil EMAIL logo , Sanjaykumar Gawade , Shailesh S. Shirguppikar , Nguyen Trong Ly , Nguyen Chi Tam und Le Thi Phuong Thanh
Veröffentlicht/Copyright: 30. Mai 2022
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Abstract

Purpose

Recoil length minimization is always been a top concern in various structural, industrial, and defence applications. The traditional passive recoil system is not able to respond quickly to the changes in the impact force. These limitations can be overcome by introducing a semi-active recoil system, which comprises an intelligent fluid damper.

Design, methodology, and approach

The electrorheological (ER) fluid, which responds to the applied electric field and exhibits high yield strength, will be a proper damper for the recoil system. An ER damper can bring back the vibrating system to its equilibrium in a brief period. In this article, the general design procedure of an ER fluid semi-active damper has been developed, which is suitable for a recoil system. The equations of damping forces (viscous, quadratic, and ER) are modified in terms of geometric parameter, namely the piston diameter (D P), which can be selected to obtain the desired dynamic range (greater than two) and optimum damping force. With the MATLAB software, the damper and spring specifications are fixed to meet the required conditions, viz. the dynamic range should be greater than two, and the total damping and spring force should counter-recoil the system.

Findings

Results obtained for a case study of gunfire conclude that the recoil system developed using design specifications exhibits desired performance with maximum recoil of 75.59 mm at 80°, angle of elevation, which is within the allowable range of 150 mm. It is shown that the rate of firing can be increased by decreasing the recoil length.

Originality and value

The novel procedure for the design of ER damper outlined in this work will be helpful for any recoil length minimization problem.

1 Introduction

The selection of appropriate electrorheological (ER) fluid with desired yield strength and post-yield viscosity is a prerequisite of the design process of an ER damper. As the response time of ER fluids (in milliseconds) is greater than magnetorheological (MR) fluids, ER fluids have been selected for the application of gun recoil system. The barium titanyl oxalate (BTO)-based ER fluid is selected to exhibit a yield strength of 20 kPa at 3 kV/mm. The design of ER fluid damper within certain constraints of dynamic range and damping force is carried out. Also, calculations of recoil parameters, damper specifications, and the development of modified damper force formulae in terms of piston diameter for the general design process of ER damper have been carried out. The recoil mechanism considered here is of hydro-spring type in which a damper is incorporated with ER fluid with a recuperator as a spring. In the design of ER damper, the maximum impact force for the respective charge (firing a projectile) is taken as an input. The recoil force and recoil velocity are calculated and are used in the design process. Though the spring stiffness is calculated by using impact force equations, the stiffness of this system is adjusted to avoid vibration chattering. The damper rod size is fixed by using buckling theory, and by using empirical relation, damper diameter is fixed to meet criteria like dynamic range and total damping force. For this purpose, simple MATLAB codes are generated and run to fix these criteria’ piston diameter. Other parameters of the damper are determined using empirical relations. In many applications where recoil length minimization is paramount, this general design procedure of the recoil system will be helpful. In the present study, the recoil system designed has been applied as a case study to recoil minimization of battlefield gun.

Tian [1] derived a powerful yield strength equation, which can be used for selecting the ER fluid for industrial applications. Xianxiang et al. [2] proposed mechanisms of the ER effect. Laszlo et al. [3] investigated different properties of two ER fluids to check their suitability in gun recoil application. Tao [4], a pioneer in introducing the ER fluid with a yield stress of more than 100 kPa, studied the behaviour of physical phenomena of ER mechanism. Li et al. [5] synthesized giant electrorheological (GER) effect fluids. The fluid exhibits anti-sedimentation property with a yield strength of 194 kPa. Singh and Wereley [6] developed a control mechanism for the minimum transfer of gun recoil load to the structure and optimized the gunfire rate by introducing an MR damper in the semi-active control system. Wen et al. [7] carried out synthesis and characterization of GER fluid with the yield strength of 130 kPa at 5 kV/mm. Li and Wang [8] developed a recoil system with an MR absorber and have shown an improvement in the capacity of the absorber. Carlos and Lopez [9] have proved that semi-active suspension systems with ER damper can dissipate more energy. Xiangcong et al. [10] designed and analysed an intelligent gun recoil system with a damper. Mehdi et al. [11] studied the application of MR damper for controlling recoil dynamics. Zekeriya et al. [12] carried out a performance analysis of the flow mode MR damper having the annular gap in the piston. Kathe et al. [13] determined venting time, impulse reduction estimate, and bore heating reduction for 120 mm bore diameter gun. Dixon [14] developed a mathematical model for a damping system considering the quadratic damping coefficient. Shams et al. [15] have carried out the coupled computational: fluid dynamics (CFD) and finite element analysis (FEA) analysis of hydraulic shock absorber valve behaviour.

Because of the scope and depth of this research, there is no study in the literature on improving the performance by minimizing recoil length using an intelligent recoil mechanism. The major contribution of the present work is a novel design process of ER damper. The proposed design process can be helpful in recoil system applications. From the literature, it has been observed that there is no such systematic design process readily available. The main challenge is to design a recoil system within the constraints of maintaining a dynamic range of more than two and producing the required damping force. The better controllability over the structure, such as battlefield gun, has been achieved; it is necessary to develop an ER damping force more significantly than the force created by a viscous damper. The dynamic range is defined considering these forces, which is essential for better controllability. The MATLAB codes are generated and run to fix the piston diameter. The remarkable achievement of the proposed ER damper-based recoil system is that it showed percentage reduction in recoil mass displacement as 92% with respect to technical report by US ARDE and 43% compared to recoil system incorporated with MR damper at 63° of firing angle.

2 Design of an ER damper subjected to transient excitation

The general procedure of the design of ER damper subjected to external transient force excitation is presented in this section. The suitable ER damper has been designed by the iterative method, considering various parameters, which typically affect the performance of ER fluid damper. The dynamic range is the most crucial parameter concerned with the damper, which controls such a fluid damper. The dynamic range strongly depends on damper parameters like piston diameter, gap thickness, and length of recoil. During the designing of the damper, emphasis has been given to these parameters to maintain the required controllability and force. The design process is carried out by considering the maximum transient input to the recoil system. Design details are given in the following sub-sections.

2.1 Non-linear damping force equations to design ER damper

The equation of motion of a recoil system using a semi-active ER damper is given as:

(1) m x ̈ + F D + k x = F F ( t ) ,

where F D is the non-linear damping force provided by the ER damper and is given as:

(2) F D = C D V d + C Q V d 2 + F ER .

The first term on the right-hand side of equation (2) represents viscous damping force, the second term represents quadratic damping force, and the third term is the ER damping force [14]. Here, C D is the coefficient of viscous damping and C Q is the coefficient of quadratic damping.

With this value of F D, Eq. (1) becomes:

(3) m x ̈ + C D V d + C Q V d 2 + F ER + k x = F F ( t ) .

Eq. (3) is used when the firing angle, θ is zero. When θ is not equal to zero, the equation of motion (3) is modified to take into account the effect of the component of gravitational force in the direction of the motion. The modified Eq. (4) is as follows:

(4) m x ̈ + ( C D 1 x + C D 2 x 2 + F ER ) sign x ̇ + k x = F F ( t ) + m g Sin θ .

2.1.1 Problem of the requirement of a priori knowledge of ER damper piston diameter

In the development of the recoil system, the design of an ER damper is the most important one, as shown in Figure 1. From a review of the literature on the design and development of an ER damper, it is seen that the main problem encountered is the requirement of a priori knowledge of the damper piston diameter. To overcome this problem, in this article, the formulae for viscous damping, quadratic damping, and ER damping are expressed in terms of piston diameter.

Figure 1 
                     Cut section model of ER damper. E – applied voltage to the electrodes, L
                        FA – length of the fluid annulus, R
                        FA – radius of fluid annulus, D
                        FA – diameter of the fluid annulus, t
                        FA – thickness of fluid annulus, t
                        OC – thickness of outer cylinder, t
                        IC – thickness of inner cylinder, L
                        R – length of the piston rod, and the damping force expressions for F
                        DV
                        , F
                        DQ, and F
                        ER are modified in terms of piston diameter (D
                        P).
Figure 1

Cut section model of ER damper. E – applied voltage to the electrodes, L FA – length of the fluid annulus, R FA – radius of fluid annulus, D FA – diameter of the fluid annulus, t FA – thickness of fluid annulus, t OC – thickness of outer cylinder, t IC – thickness of inner cylinder, L R – length of the piston rod, and the damping force expressions for F DV , F DQ, and F ER are modified in terms of piston diameter (D P).

2.1.2 Modification of equations for F DV, F DQ, and F ER

The annular flow design approach is employed while designing ER damper, as shown in Figure 1, and the controlling force is achieved by varying the electric field, as the orifices are not provided in the main piston. The ER phenomenon is achieved by maintaining an air gap less than 1 mm between two-cylinder electrodes. High DC voltage is applied across these electrodes.

The viscous damping force is given as follows:

(5) F DV = C D V d = 6 μ L FA  A PA 2 π R FA t FA 3 V d ,

where µ is the viscosity of ER fluid and A PA is the cross-sectional area of piston annulus.

(6) A PA = π 4 ( D P 2 D R 2 ) .

The cross-sectional area of the fluid annulus is obtained as:

(7) A FA = 2 π R FA t FA .

Assuming geometric relations, diameter of rod, D R = 0.6 D P and the radius of fluid annulus, R FA = 0.6 D P.

Eq. (5) is modified by using Eqs. (6) and (7) with the aforementioned geometric relations as:

(8) F DV = 6 × 0.409 π 16 × 0.6 μ L FA  V d t FA 3 D P 3 .

Thus, Eq. (8) is deduced in terms of piston diameter. All other terms like the length of the fluid annulus, the viscosity of fluid, and gap maintained between two electrodes are fixed and assuming the maximum piston velocity as 2 m/s; the piston diameter can be adjusted to achieve the required damping force. Similarly, equation of quadratic damping force can be deduced in terms of piston diameter as:

(9) F DQ = C D V d 2 = 1 2 ρ α f A 2 A PA V d 2 ,

where ρ is the density of the fluid and α is the kinetic energy correction factor. f A the area factor is given as:

(10) f A = A PA A FA = π / 4 ( 0.64 × D P 2 ) 2 π R FA t FA = 0.1333 × D p t FA .

Using Eqs. (9) and (10), equation of quadratic damping coefficient is simplified in terms of piston diameter as:

(11) F DQ = 0.0044 ρ α V d 2 t FA 2 D P 4 .

Eq. (11) represents the quadratic damping force in terms of piston diameter.

The ER damping force equation is also deduced in terms of piston diameter. The ER force is subjected to the resulting ER effect, ultimately which depends upon the applied electric field between the gap of the electrodes. The ER effect produces yield shear stress (τ ER) in ER fluid, which acts over the ER fluid trapped between the two electrodes. The ER shear force acting over the cross-sectional area of the fluid annulus is due to the pressure drop at the fluid annulus. Thus, resisting pressure acting over the cross-sectional area of piston annulus is given as:

(12) F ER = 2 L FA τ ER t FA A PA .

Upon simplification F ER is given as:

(13) F ER = 1.005 L FA τ ER t FA D P 2 .

Eq. (13) represents the ER damping force in terms of piston diameter.

2.1.3 Development of a MATLAB problem to determine the piston diameter D P

A MATLAB program is developed to calculate the total damping force (F D), which comprises viscous, quadratic, and ER damping forces in terms of piston diameter (D P). The diameter of the piston will be determined from a specific range of values with a fixed step size. The value of one such piston diameter from the range of value will be selected such that the total force obtained is approximately equal to the input firing force.

2.2 Testing suitability of damper diameter

While obtaining a piston diameter of ER damper, it is necessary to check the dynamic range ratio and total damping force for maximum impact force. The dynamic range ratio is the ratio of damping force obtained during the off-state condition to applied electric field condition. It can be given as [16]:

(14) D R = 1 + F ER F VD + F DQ .

In order to get a significant effect of ER force, it is required to maintain a dynamic range more than or equal to 2. At the same time, the ratio of viscous damping force to ER damping force should be less than 1. Thus, the piston diameter can be fixed to fulfil both the conditions of dynamic range and maximum recoil force.

The radius of the fluid annulus is given as:

R FA = 0.6 × D P .

Furthermore, the thicknesses of the inner and outer cylinders are determined by using pressure vessel theory. For the inner cylinder, inner diameter (D i) is taken as the diameter of the piston. The dimensions of the piston rod are obtained by using the theory of buckling.

3 A case study on gun recoil system

The general design process of a recoil system discussed in Section 2 is implemented to design the recoil system of a battlefield gun. The ER damper and mechanical spring specifications are obtained based on the dynamics of the gun recoil system and the general design approach.

3.1 Gun recoil system and its dynamics

A schematic model of the typical gun recoil system is shown in Figure 2. When the gun fires a projectile, it leaves a barrel due to high pressure created behind it by the propellant. As per Newton’s third law, the same pressure forces back the gun barrel. For heavy-duty guns, it is necessary to design recoil system with spring force “k” and damper with high damping coefficient “c.”

Figure 2 
                  Schematic model of gun recoil system. 1 – Britch, 2 – barrel, 3 – caliber (projectile), 4 – muzzle brake, 5 – gun chasis, 6 – wheel, 7 – trail, 8 – ER damper, 9 – mechanical spring, 10 – gun carriage, and 11 – recoil system.
Figure 2

Schematic model of gun recoil system. 1 – Britch, 2 – barrel, 3 – caliber (projectile), 4 – muzzle brake, 5 – gun chasis, 6 – wheel, 7 – trail, 8 – ER damper, 9 – mechanical spring, 10 – gun carriage, and 11 – recoil system.

3.2 Parametric analysis of gun recoil system

The peak force generated by a projectile of gun is of the order of 460 kN [17]. Considering this as maximum input force to the recoil system, the design process is carried out. Calculations have been performed on separate excel sheets using empirical equations. The results obtained are as follows: spring stiffness k = 1,850 kN/m, critical damping coefficient c c = 153.280 kN/s, and the damping coefficient, c = 91.96 kN/s. Assuming maximum damper piston velocity as 2 m/s, the total damping force, F d is obtained as 184 kN.

Total recoil force = Damping force + spring force = 184 + 277.5 = 461.5 kN .

The total recoil force is nearly equal to the maximum firing force (460 kN).

3.3 Design calculations of ER damper

As described in Section 2.1.3, the diameter of the piston is determined from the range of values: 50–225 mm with a step size of 1 mm. The value of one such piston diameter is selected such that the total damping force obtained is approximately equal to input firing force and dynamic range is equal to 2. The dynamic range for the calculated diameter of the piston (140 mm) is 2, as shown in Figure 3. The total damping force for different values of piston diameter is shown in Figure 4.

Figure 3 
                  Dynamic range and range ratio vs different values of piston diameter (m).
Figure 3

Dynamic range and range ratio vs different values of piston diameter (m).

Figure 4 
                  Total damping forces (F
                     t) vs different values of piston diameter (m).
Figure 4

Total damping forces (F t) vs different values of piston diameter (m).

Simultaneously,

  1. Piston rod diameter is determined by using buckling theory.

  2. For calculated piston diameter, the dynamic range and damping force are checked.

  3. The buckling length for stroke length of 150 mm is determined as, Lengthbuckling = 450 mm.

Using this calculated buckling length and considering the factor of safety as 2, for the stroke of 150 mm the piston rod diameter is calculated as 82.25 mm. It will sustain maximum load of 460 kN without buckling.

By using geometric relation, D R = 0.6 × D P ; D P is calculated as 137.08 mm.

Thus, the diameter of the piston is rounded off to the value of 140 mm. The dynamic range for 140 mm diameter of piston is nearly equal to 2 as shown in Figure 3 and the total damping force is 310 kN as shown in Figure 4.

The radius of fluid annulus is given as R FA = 0.6 × D P = 0.6 × 140 = 84 mm.

The inner diameter of inner cylinder is exactly equal to piston diameter, D ii = 140 mm. The material selected for inner cylinder is mild steel.

The thickness of the cylinder can be determined as:

t = 29.88 × 140 2 × 140.16 = 14.92 15  mm .

The outer diameter of inner cylinder, D oi = D ii + 2t = 170 mm.

Gap between two cylinders is already decided as 0.7 mm. The dimensions of outer cylinder are:

Inner diameter of outer cylinder (D io) = 170 + 1.4 = 171.4 mm.

Outer diameter of outer cylinder (D oo) = 171.4 + 2t = 201.4 mm.

All the specifications of the designed ER damper are summarized in Table 1.

Table 1

Specifications of designed ER damper

Sr. no. Design parameter Notations Dimension (mm)
1 Piston rod diameter D R 82.25
2 Piston diameter D P 140
3 Inner diameter of inner cylinder D ii 140
4 Outer diameter of inner cylinder D oi 170
5 Gap between cylinders/electrode gap t FA 0.7
6 Inner diameter of outer cylinder D io 171.4
7 Outer diameter of outer cylinder D oo 201.4

The simulation based on designed ER damper is carried out for an application concerning gunfire.

4 The effect of angle of elevation on the gun recoil system performance: a simulation study

The 3D model of ER damper with designed specifications is developed. With this 3D model, performance evaluation of recoil system in MATLAB/Simulink environment has been carried out. The recoil displacement in terms of the desired value of stopping distance and total process time is recorded for different values of angles at which the gun is oriented.

For this purpose, Eq. (4) of recoil mass is rearranged as:

(15) x ̈ ( t ) = 1 m { F F ( t ) k x + m g Sin θ ( C D 1 x + C D 2 x 2 + F ER ) sign ( x ̇ ) } .

The Simulation Model is developed based on Eq. (15) using Simulink blocks. A Simulink code is developed using various inputs such as impact force, ER fluid characteristics, spring and damper specifications, and recoil mass. The resulting output is presented in graphical form, the velocity vs. displacement, displacement vs time, damping force vs time, and spring force vs time. The performance of the recoil system changes with firing elevation angle θ. The calculations of the projectile range and its height for different firing elevation angles θ (0–80°) have been carried out. The range for the projectile is maximum (32.315 km) at an elevation angle of 45°. Hence, the results are obtained for a firing elevation angle of 45°. The results of the analysis are given in Figures 5 and 6. Figure 5 presents the recoil mass that comes back to its’ equilibrium position or at battery position. Figure 6 displays the maximum displacement covered by recoil mass during its motion and is 69.32 mm, which is less than the limiting recoil-stopping distance of 150 mm.

Figure 5 
               Velocity vs displacement at 45° firing angle.
Figure 5

Velocity vs displacement at 45° firing angle.

Figure 6 
               Displacement vs time at 45° firing angle.
Figure 6

Displacement vs time at 45° firing angle.

For the sake of completeness of the analysis, the values of maximum displacement at different firing elevation angles of 0°, 10°, 20°, 30°, 40°, 45°, 50°, 70°, and 80° have been obtained and are given in Table 2. Table 2 also gives yield strength of ER fluid required at respective firing angle to generate sufficient damping force so that the mass will recoil within the restricted distance of 150 mm and will come back to its equilibrium position.

Table 2

Displacement and yield strength at different firing angles

Firing angle in degrees Yield strength of ER fluid (Pa) Max. displacement by Simulink model (mm)
0 5,100 54.55
10 4,650 58.02
20 4,225 61.50
30 3,850 64.85
40 3,525 67.93
45 3,400 69.32
50 3,250 70.69
70 2,900 74.59
80 2,825 75.59

It can be observed from Table 2 that the maximum displacement of recoil mass is achieved at 80°. The recoil mass displacement increases with the increase of angle of elevation. The maximum displacement even at an angle of 80° is less than the allowable displacement of 150 mm. Therefore, the specifications obtained for the developed ER damper are satisfactory to achieve the desired performance.

5 Comparative study

Based on this comparative study presented in Table 3, it is found that there is a large reduction in recoil displacement, hence the cycle duration will reduce and the number of fires per minute will increase significantly.

Table 3

Comparison of recoil mass displacement

Firing inclination in degrees Recoil mass displacement in (m)
Technical report MR damper recoil system Proposed ER damper recoil system
0 1.219 0.1225 0.05455
63 0.9525 0.1296 0.07342

The proposed ER damper-based recoil system exhibited percentage reduction in recoil mass displacement as 95% with respect to technical report and 55% compared to recoil system incorporated with MR damper at 0° of firing angle and it is 92 and 43%, respectively, at 63° of firing angle.

6 Conclusion

In this research, we aimed to design the ER fluid damper for a recoil system. The equations of damping forces (viscous, quadratic, and ER) are modified in terms of geometric parameter, namely the piston diameter (D P). The value of one such piston diameter is used such that the desired results like dynamic range greater than 2 and better controllability can be achieved. The design is also checked for piston rod buckling, and it is found safe. The great success of this study is to increase the firing rate by decreasing the recoil length, i.e. by restricting piston displacement of the innovative damper to 75 mm. The designed damper is developed for the semi-active gun recoil system to reduce the recoil length, cycle time, and firing rate. The experimental performance of the proposed recoil system reveals that the recoil displacement is varying from 40 to 60 mm with the recoil time of 0.25–0.35 s from 10° to 80° of firing inclination. Also, it showed significant reduction in recoil displacement as 92% compared to technical report of US ARDE and 43% to recoil system with MR damper at 63° firing angle. It is shown that the firing rate can be increased by decreasing the recoil length for this designed recoil system, and hence this is a viable alternative to counter the vibrations in the gun structure to improve the efficiency of the weapon.

The modified model is helpful to design ER damper for any application where recoil minimization is the prime objective.

Acknowledgment

The authors would like to express their deep gratitude to Prof. S.G. Joshi Walchand, College of Engineering, Sangli, for his contributions and valuable critiques of this study.

  1. Funding information: Authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: Authors state no conflict of interest.

Nomenclature

BTO

barium titanyl oxalate

D R

piston rod diameter

D P

piston diameter

D ii

inner diameter of inner cylinder

D oi

outer diameter of inner cylinder

D io

inner diameter of outer cylinder

D oo

outer diameter of outer cylinder

E

applied voltage to the electrodes

ER

electrorheological

F DV

viscous damping force

F DQ

quadratic damping force

F D

total damping force

F ER

ER force

GER

giant electrorheological

L FA

length of the fluid annulus

L R

length of the piston rod

R FA

radius of fluid annulus

t OC

thickness of outer cylinder

t IC

thickness of inner cylinder

t FA

gap between cylinders/electrode gap

τ ER

yield shear stress

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Received: 2021-09-22
Revised: 2022-02-20
Accepted: 2022-04-07
Published Online: 2022-05-30

© 2022 Nguyen Huu Phan et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  38. The effect of using polyolefin fiber on some properties of slurry-infiltrated fibrous concrete
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  61. The behavior of piled rafts in soft clay: Numerical investigation
  62. The impact of evaluation and qualification criteria on Iraqi electromechanical power plants in construction contracts
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  67. Concrete strength development by using magnetized water in normal and self-compacted concrete
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  69. Comparison of time extension provisions between the Joint Contracts Tribunal and Iraqi Standard Bidding Document
  70. Numerical modeling of single closed and open-ended pipe pile embedded in dry soil layers under coupled static and dynamic loadings
  71. Mechanical properties of sustainable reactive powder concrete made with low cement content and high amount of fly ash and silica fume
  72. Deformation of unsaturated collapsible soils under suction control
  73. Mitigation of collapse characteristics of gypseous soils by activated carbon, sodium metasilicate, and cement dust: An experimental study
  74. Behavior of group piles under combined loadings after improvement of liquefiable soil with nanomaterials
  75. Using papyrus fiber ash as a sustainable filler modifier in preparing low moisture sensitivity HMA mixtures
  76. Study of some properties of colored geopolymer concrete consisting of slag
  77. GIS implementation and statistical analysis for significant characteristics of Kirkuk soil
  78. Improving the flexural behavior of RC beams strengthening by near-surface mounting
  79. The effect of materials and curing system on the behavior of self-compacting geopolymer concrete
  80. The temporal rhythm of scenes and the safety in educational space
  81. Numerical simulation to the effect of applying rationing system on the stability of the Earth canal: Birmana canal in Iraq as a case study
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Heruntergeladen am 5.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jmbm-2022-0017/html
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