Dynamic Analysis Of Beam-plate Structure With Elastic Boundary Conditions

Beam and plate structures are widely used in various engineering fields. It is of greatimportance both in practice and theory to investigate the structural vibration characteristics ofbeam and plate structures. Boundary conditions have great effect on the vibrationcharacteristics of structure. So it is of first importance to deal with the boundary conditions.Based on Improved Fourier Series Method (IFSM), this research investigates the vibrationcharacteristics of beam and plate structure with elastic boundary conditions. Also the effect ofboundary conditions on the vibration characteristics is studied.Firstly, the vibration analysis model of beam with elastic supports is constructed basedon1-D improved Fourier series. The displacement field is expressed as the superposition of asingle Fourier cosine series and four single Fourier sine series. The vibration analysis undergeneral boundary supports is carried out with Rayleigh-Ritz method. Based on vibrationanalysis, the influence factors of vibration characteristics are studied, such as boundaryconditions and concentrated mass.Then, the vibration analysis model of rectangular plate with elastic supports isestablished. The displacement function is invariantly sought as2-D improved Fourier series.In each direction of plate, four single Fourier sin series are introduced to overcome thediscontinuity or jump in the solution domain. The expansion coefficients are considered as thegeneralized coordinates, and determined by solving a standard matrix eigenvalue problembased on Rayleigh-Ritz technique. Since the displacement is constructed with sufficientsmoothness, other variables of interest such as shear forces and power flow can be calculateddirectly by applying appropriate mathematical operation to the displacement function. Theinfluence of boundary spring stiffness and structure size on vibration response is investigatedwith point mobility theory.Finally, the vibration prediction model of T shaped plate with general coupling positionis established. Along the structure conjunction, four types of uniform coupling springs areintroduced to completely model the coupling effect of flexural vibration and in-planevibration. Two sets of2-D improved Fourier series are used to describe the flexural andin-plane vibration displacement fields. The vibration analyses of T shaped plate with various boundary conditions and coupling settings are performed. Also the effect of boundary springand coupling spring stiffness on the vibration performance are investigated. The accuracy andreliability of the current method are validated by both FEA and reference results under variousboundary conditions.This paper presents a new analytical method for the vibration analysis of beam and platestructure. It can be further extended to the analysis of curved beam, curved shell andtrapezoidal plate and so on. Also this method can be readily modified to model thenon-uniform boundary conditions.