Dynamic Characteristic Of Piezoelectric Composite Beck's Column

Dynamic stability of elastic system has been investigated since 50's last century. Generally, when the force is nonconservative, even for the equilibrium stability of elastic system, it must be investigated by the kinetic method. the inertial characters must be considered. Beck's column is one of this typical structure model. Research on piezoelectric artificial intelligence beam has draw serious attention recently. How to improve stability of beam structure subjected to nonconservative force by piezoelectric material, it has not attracted much attention from the scientific community. Dynamic stability and other character of piezoelectric composite Beck's column and varying cross-section piezoelectric composite Beck 's column is investigated in this article. A new method of improving dynamic stability of Beck's column by piezoelectric material is induced, feasibility of improving dynamic stability of Beck's column by piezoelectric material is analyzed theoretically. The main work is as follows:Firstly, basic information of piezoelectric material are introduced, construction equation, character of material, important parameter of performance, and problem must attention in use , etc. With reference of construction equation and other basic knowledge, related information of model foundation in the third chapter and the fifth chapter is introduced particularly.Secondly, stability and other dynamic characters of piezoelectric composite Beck's column is investigated. The differential equations of motion of homogeneous Beck's column with piezoelectric layer are derived in the third chapter, eigenvalue of matrix is founded analytically. Relations between frequency and other parameters are obtained. Axial compressive force , tip mass, and length, position, voltage of piezo-layer , it's contribution to the stability and frequency of beam is analyzed. Axial compressive force can influence the lowest three frequency, the flutter instability critical value in a certain extent; length, position and voltage of piezoelectric layer can all improve stability of Beck's column in a certain extent; How long the piezoelectric layer is most efficiency; When the column is placed horizontally, the presence of tip mass can decrease stability of column.Thirdly, stability and other dynamic characters of varying cross-section piezoelectric Beck's column is investigated. The differential equations of motion of varying cross-section Beck's column with piezoelectric layer are derived in fifth chapter. Eigenvalue of matrix is founded analytically. Relations between frequency and other parameters are obtained. Thickness ratio, mass ratio, nondimensional axial compressive force, voltage of piezoelectric layer and it's effectiveness to the critical value of flutter instability and divergence instability is analyzed. Diversification of thickness ratio can influence the lowest three frequency, the critical value of nondimensional follower force, the critical value of nondimensional axial compressive force in a certain extent; Mass ratio can influence the lowest three frequency, the critical value of nondimensional follower force; length, position and voltage of piezoelectric layer, can all improve stability of varying cross-section Beck's column in a certain extent. By contrast different length and position, the extent of transform is most distinctness.