Advances in Vibration Analysis Research by Farzad Ebrahimi

By Farzad Ebrahimi

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H. Register, A note on the vibrations of generally restrained, end-loaded beams, Journal of Sound and Vibration 172 (4) (1994) 561_571. S. C. Lin, Dynamic analysis of generally supported beams using Fourier series, Journal of Sound and Vibration 196 (3) (1996) 285_293. [14] W. T. M. Chang, Applications of dual MRM for determining the natural frequencies and natural modes of an Euler_Bernoulli beam using the singular value decomposition method, Engineering Analysis with Boundary Elements 23 (1999) 339_360.

It is very important that the core, although weaker than the face layers, be strong enough to resist crushing. The current trend in the aerospace industry of using composites and sandwich material, to lighten aircraft in an attempt to make them more fuel efficient, has led to further recent researches on development of reliable methods to predict the vibration behaviour of sandwich structures. In the late 1960s, pioneering works in the field of vibration analysis of viscously damped sandwich beams (Di Taranto, 1965, and Mead and Marcus, 1968) used classical methods to solve the governing differential equations of motion, leading to the natural frequencies and mode shapes of the system.

Figure 5 shows the displacement response, velocity response and acceleration response at the free end of the beam. In order to check the accuracy of the responses from the CEM, a forced vibration analysis for the beam is conducted using the FEM. The beam is discretized into 90 EulerBernoulli beam elements with a total of 182 dofs. The corresponding responses from the FEM and the CEM are compared in Figure 5. This indicates the accuracy of the proposed method for forced vibration of multiple stepped beam.

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