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A new approach is proposed to solve for the eigen-values and eigen-functions of circular plates with circular holes by using the Rayleigh Ritz Method. In this method, the spatial solution is expanded into separable functions in terms of polar coordinates. While trigonometric functions are used along the circumferential direction, the Boundary Characteristic Orthogonal Polynomials build the radial shape functions. Written in terms of the assumed functions, the potential and kinetic energies are modified in order to account for the holes. Although the proposed approach is applicable for plates with different boundary conditions and different hole shapes, the free vibration of a clamped circular plate with circular holes is considered in the present study. The edges of the holes are free. Four different case studies are carried out. The results of the Rayleigh Ritz Method are compared with those available in the literature.

In this paper, the driver ride comfort in a heavy vehicle (city bus) is studied under the sky-hook semi-active damping force policy. A new hybrid dynamic model composed of a continuous system and a discrete system are integrated in the current work. The chassis of the vehicle is assumed as the continuous beam supported on the discrete suspension springs and dampers. The driver and the seat are also considered as a discrete vibrating system. The dynamic equations are solved by using the assumed mode method, where the mode shapes of a free-free beam have been employed. The results of the semi-active system are compared with those of the passive one through simulations. The results indicate that the new hybrid dynamic model represents more degrees-of-freedom of the system for driver ride analysis compared to the discrete model. In addition, the results show that the semi-active system has a superior performance in terms of the ride comfort.

In this study the dynamic analysis of the vehicle system modeled as a hybrid discrete and continuous system has been investigated. The discrete system modeling has formed the traditional ride dynamic analysis model for vehicle systems. In such a model the chassis is assumed as a discrete block attached to different degrees of freedom that can account for the unsprung masses, engine and driver among many others. However, this model cannot accommodate all the aspects of a chassis which is strictly a continuous system. In the present study the chassis is assumed as a flexible beam on which a pair of single degree of freedom systems is added to account for the engine and driver. Moreover, the beam is mounted on a couple of spring-damper elements that simulate the suspension of the vehicle which results in a combination of continuous and discrete systems. In order to solve this problem, the assumed mode method has been employed using the mode shapes of a free-free beam.