Dynamics Analysys And Application Of Axial Functionally Graded Cantilever Beam

Functionally gradient material is a new type of composite material composed of two or more materials with continuous gradient changes in composition and structure.It is a new type of functional material developed to meet the needs of modern aerospace industry and other high-tech fields,and to meet the requirements of repeated normal work in the extreme environment.With the development of science and technology,FGM structure has been widely used in aerospace and other harsh engineering environment.For the FGM Structure,its components can change gradiently along the thickness and axis direction.At present,there are many researches on the dynamic characteristics of FGM beam with transverse gradient change.However,for the FGM Structure with axial gradient change,the dynamic equation is variable coefficient differential equation,which is difficult to be solved analytically.At present,most of them are analyzed by numerical method or finite element method The main purpose of this paper is to solve the natural frequency of FGM and to get more accurate natural frequency and mode shape.In this paper,the theory and finite element simulation of the axial FGM are studied.Firstly,in order to solve the natural frequency and array of axial FGM more accurately,a special function Meijer-G is proposed and studied to solve the linear natural frequency and array;secondly,the vibration characteristics of axial FGM are studied based on the domain decomposition method;finally,an axial FGM is studied by using the domain decomposition method Cantilever piezoelectric energy capture device.The research content of this paper is mainly composed of the following aspects:(1)Based on Meijer-G function,the vibration characteristics of an axial functionally gradient cantilever beam are studied.The control equation of the system is established by using Euler Bernoulli beam theory,the fourth order differential equation is obtained by dimensionless method,and the natural frequency and array expression of the functionally graded cantilever beam are obtained by using the general expression and differential property of Meijer-G function.The influence of different functional gradient parameters on the natural frequency is obtained by numerical analysis,and the natural frequency is verified by finite element simulation Correctness.(2)Nonlinear vibration of a functionally gradient cantilever beam.The matrix expression with Meijer-G function is used for Galerkin discretization,and the amplitude frequency response equation is obtained by multi-scale method.The influence of different small parameters,functional gradient parameters,excitation force and damping coefficient on the amplitude frequency response curve is obtained by numerical analysis.(3)Based on the Adomian decomposition method,the vibration characteristics of axial FGM cantilever beams are studied.This paper mainly studies the functional gradient cantilever beam.The parameters of the functional gradient change exponentially along the axis direction.The free vibration characteristics of the system are studied by using the Adomian decomposition method.The expressions of the natural frequency and the formation are derived.The approximate accurate natural frequency and the formation are obtained by the numerical analysis method,and the correctness is verified by the finite element software simulation.Finally,the multi-scale method is used to study the nonlinear vibration,and the influence of different parameters on it is analyzed according to the amplitude frequency response equation.(4)Study on vibration and energy capture characteristics of piezoelectric energy capture device with axial functionally gradient cantilever beam.Consider that the shape of the beam is rectangle,trapezoid and triangle.Firstly,the free vibration of the system is studied by using the Adomian decomposition method,and the approximate analytical expression of the natural frequency is derived.Then,a finite segment model is proposed,and the accuracy of the results is verified by the finite element simulation.The effects of gradient and geometric parameters on the fundamental frequency are studied.Finally,the finite element simulation is used to study the energy capture characteristics of the system,and the influence of gradient parameters and geometric parameters on the voltage frequency response curve is analyzed.