On the Linear and Nonlinear Vibration Responses of Elastically End Restrained Beams Using DTM

Abstract

The objective of this paper is to apply the differential transformation method (DTM) to solve linear and nonlinear vibration problems of elastically end-restrained beams. The method demonstrates many advantages such as rapid convergence, high accuracy, and computational stability to determine linear and nonlinear natural frequencies as well as mode shapes of such beams. The mathematical models provided in this paper can be solved easily using symbolic tools in available software packages such as Maple and Matlab. An accuracy of the present solutions is confirmed by comparing with some published results in the open literature. New numerical results of nonlinear frequency ratio of beams supported by various types of elastic boundary conditions are presented and discussed in detail. The significant effects of translational and rotational springs including vibration amplitudes on linear and nonlinear vibration results are also taken into investigation. Based on the numerical exercises, it is revealed that the nonlinear frequency ratios of the beams with elastically end restraints are found to increase as the increment of vibration amplitudes.

Keywords:

• Differential transformation method
• Linear and nonlinear vibration
• Mode shape
• Natural frequency

Notes

^#Communicated by K.-H. Chang.

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