Research On Wave Propagation In Periodic Timoshenko Beam Based On Multiple Reflection Method

This thesis focuses on the propagation characteristics of waves in periodic Timoshenko beam structures based on the multiple reflection method.The specific steps of multiple reflections,unidirectional propagation and bidirectional propagation between two discontinuous points in the periodic Timoshenko beam structure are given.The mathematical expression for the wave field on any segment in the structure of a periodic Timoshenko beam is obtained.The band gap characteristics and energy propagation of periodic Timoshenko beams are analyzed.Firstly,a structural model of the periodic Timoshenko beam is developed.The periodic Timoshenko beam structure studied in this thesis is composed of two materials with different parameters,material A and material B,arranged alternately in sequence.The mathematical expressions for the incident waves are given based on the specific form of the vibration differential equations and general solutions of the periodic Timoshenko beam structure,where the incident waves include incident propagation waves and incident attenuation waves.Secondly,multiple reflections in periodic Timoshenko beam structures were performed.It is assumed that the incident wave acts on a certain position in the structure of the periodic Timoshenko beam.When an incident wave propagates to a discontinuity,the incident wave produces reflection and transmission at the discontinuity.Multiple reflections of waves occur between two discontinuous points,and the mathematical expression of multiple reflections of incident waves between two discontinuous points is obtained.This process is multiple reflections between discontinuous points.In the next propagation process,as the wave transmission will propagate in two directions separately.So the wave fields in both directions can be established separately to get the mathematical expression of the wave field on a certain section.This process is one-way propagation.Then consider the superposition of waves in the two directions as the correction term to correct the neglected propagation in one-way propagation.The mathematical expressions of the wave fields on each segment are obtained.This process is propagated in both directions.According to the above steps,the functional relationship between the wave amplitude and the incident wave amplitude at any position in the periodic Timoshenko beam structure can be obtained.Finally,the transfer matrix in the periodic Timoshenko beam structure is obtained based on the transfer matrix method.Then the band gap properties of the periodic Timoshenko beam structure are obtained by combining Bloch's theorem.The wave fields on each segment in the periodic Timoshenko beam are obtained based on the multiple reflection method.The energy propagation in the periodic Timoshenko beam is then given in conjunction with the mathematical expression for the energy.Comparing the infinite-length bandgap characteristics and the finite-length energy propagation of the periodic Timoshenko beam structure,it is concluded that the infinite-length bandgap frequency range of the periodic Timoshenko beam structure is in good agreement with the finite-length energy decay frequency range.The validity of using the multiple reflection method to study the periodic Timoshenko beam structure is verified.