Volume 1, Issue 3-4

In the present study, harmonic and chaotic behaviors of a thin circular functionally graded (FG) plate are studied. Using nonlinear governing equations of FG plate subjected to one-term excitation force and utilizing special shape function, Duffing equation of the system is derived. Employing Melnikov analysis, the conditions of existence of harmonic and chaotic motions for derived Duffing equation are expressed. By use of the Poincare maps, the identified dynamical behaviors are illustrated based on the numerical solutions of the governing equations. The bifurcation diagrams are presented in the case that the excitation amplitude increases, while other parameters are fixed. It is indicated that, with the increase of the excitation amplitude, the motion changes from period-1 to period-2, and then to period-4, and finally is chaotic. It is confirmed that the graded plate with more ceramic constituent has higher resistance to chaotic phenomenon in comparison with the graded plate with more metal constituent. Finally, a simple control method is employed to control the chaotic vibration of the plate.

The vibration of a structure coupled with liquid is an important problem that has many significant engineering applications such as the bionics of flapping fin, harvest of tide energy, and the conventional areas of marine and offshore structures. It is critical to experimentally validate the dynamic parameters of structures coupled with fluid so as to accurately and efficiently model, design and develop related engineering systems. This paper presents an experimental study to quantify the shifts of multiple modes of cantilever flexible plate under water due to hydrodynamics effects. This goal is accomplished by using free-decay response measurement of a cantilever flexible plate exposed in air and submerged in water. Free-decay responses are used to identify the plate dynamic properties. The FFT, power spectrum, spectrogram, empirical modal decomposition are used to quantify plate spectrum signatures. The hydrodynamic effects of liquid on the natural frequencies and the damping of plates are characterized. A comparison between the power spectra of response and empirical mode shows a good correlation. The nonlinear hydrodynamic effects on the plate response are also discussed based on experimental results.

This research focuses on diagnosing the nonlinear dynamic responses of a fluttering plate excited by high-velocity air flow. An approach based on the Periodicity Ratio method is developed such that the characteristics of a nonlinear system subjected to nonperiodic excitations can be diagnosed. The governing equations of the nonlinear dynamic responses of a fluttering plate are derived and solved numerically. Eight modes of motion are used for obtaining accurate results. With the implementation of the present approach, a regular-irregular region diagram is generated for quantitatively analysing and directly visualizing the behavior of the fluttering plate with varying system parameters. Bifurcation of the plate’s motion is analyzed with utilization of the regular-irregular region diagrams. The routes from regular motion to irregular motion are investigated and illustrated. Comparison is made with the diagnosing results available in the literature. The present approach demonstrates the efficiency and accuracy in the characteristic diagnosis for the fluttering plate.

This research work is focused on solving the practical problems that arise in trajectory tracking control of Hilare robots when the conventional Linear Time-Variant Controller (LTVC) is employed. The trajectory tracking of a Hilare robot on a flat 2D ground is considered. The left and the right wheel speeds of the robot are considered as the control inputs. It is assumed that the control inputs have a maximum affordable limit. The practical problems arise when the LTVC calculates control inputs that are beyond the affordable limit, and hence are truncated when applied to the real robot. The application of truncated control inputs causes system instability (and control failure) in practical situations. The failure of the LTVC when the control inputs are saturated is demonstrated by experimentation on a real robot. The Nonlinear Model Predictive Controller (NMPC) is proposed for eliminating the system instability due to an input saturation. The maximum affordable wheel speeds of the robot are implemented as constraints for the control input calculation by the NMPC. So, the calculated control inputs never exceed the affordable limit. The experimentation on a robot with the NMPC exhibits that the system instability due to the input saturation is eliminated.

Wear of wheel profiles is one of the most critical issues affecting cost and performance of railway transportation systems. By altering the profile from the shape originally chosen by the designer, wear has a very large effect on vehicle dynamics, so that excessive modifications of the original have to be recovered by griding and re-profiling the wheel to its original profile. Clearly, with high-speed train development, wheel profile design has been driven by keeping high level of passenger comfort and running safety and low track aggressiveness performances. A reliable wheel profile wear prediction model is developed and applied to a vehicle operating high-speed rail lines in China. The methodology is based on wheel wear simulations which are performed based on actual track data, and pertinent operating conditions. The vehicle model is built in the Simpack MBS software utilising validated suspension models. The contact between wheel and rail is modelled with an equivalent ellipse method and Kalker’s simplified theory (FASTSIM). The wear modelling is based on Archard’s wear model. Finally, validation against wheel profile measurements is performed by simulating approximately 240,000 km of running. Comparisons between simulated and measured wheel profiles, including four wheel wear indexes are presented. The agreement is generally very good.

Flat ride is the condition in which the uncomfortable pitch oscillation of the vehicle body turns into more tolerable bounce oscillation, when a car hits a bump in forward motion. Based on experimental results, Maurice Olley discovered and introduced two conditions for flat ride: 1: The radius of gyration in pitch should be equal to the product of the distance from the mass centers a 1 ; a 2 of the front and rear wheels of the car (r 2 = a 1 a 2 ). 2: The rear suspension should have around 20% higher rate then the front. The equation r 2 = a 1 a 2 makes the car to be considered as two separated uncoupled mass-spring systems of front and rear suspensions. In this study, we will analytically review the flat ride conditions and provide design charts to satisfy the required conditions. The nonlinear practical model of shock absorbers modifies the conditions which were based on linear models.

In this paper, the dynamic response of the elastic support beam under the moving load is studied. The second order modal of the beam is considered. Because the second order modal contain the rigid body rotation of the beam, which influence to the response is studied. Using modal superposition method, it is studied that the stiffness of elastic support influence to the pre-two order frequency. And then the dynamic response of the elastic support beam under the action of moving load or moving vehicle is studied. The finite element method and assumed modal method are used to study the influence of bearing support stiffness to the frequencies of the system. Using the numerical method, the coupling vibration of vehicles-bridge system is studied. Some conclusion shows the second order modal can not be ignored when the stiffness of bearing support is not hard enough.