Dynamic Response Analysis Of Timoshenko Beams Using The MRRM

The current methods of dynamic response analysis of structures are mainly the Finite Element Method (FEM) and the Direct Integration Method (DIM). There are few researches of the dynamic response analysis of structures using the theory of the wave motion. Thus I dedicated myself to the research on the dynamic response of the beams using the method of wave ray analysis.The current beam theories are the Euler-Bernoulli beam theory and the Rayleigh-Timoshenko beam theory. This paper is mainly about the dynamic response of Timoshenko beams. The Method of Mode Superposition (MMS), the Method of Transfer Matrix (MTM) and the Method of Reverberation-Ray Matrix (MRRM) are introduced here. The three methods are applied to compute the natural frequency, the steady state response and the transient response of the one span beam and two spans continuous beams, respectively. The superiorities and shortcomings of the three methods are summarized. Several methods for signal processing are also introduced and the Hilbert-Huang transform (HHT) is used to analyze the data of the transient response of the beam.Through the contrast, we find that the MMS can only apply to computing the response of one span beam. The MTM has the shortcoming of stability and can not compute the transient response easily. The MRRM adapt to all these problems and can compute the transient response accurately. The HHT can process the transient response data and present the data in a clear and comprehensive way.