Strong Nonlinear Natural Vibration Of Rotating Motion Functionally Graded Circular Plate

Circular plates and circular plates have always been a very widely used type of component in engineering.In practical applications,components often need to meet a specific working environment and have new requirements on the material properties of components.Functionally graded material(FGM)is a new type of non-uniform composite material.Due to its advantages of high mechanical strength and thermal shock resistance,the application field of functionally graded materials is very wide.Functionally graded materials are mostly in a complex environment under multi-field coupling and exhibit complex dynamic behavior.Therefore,the nonlinear dynamic behavior of functionally graded structures under thermal load has become an important research direction in recent years.This paper mainly adopts the method of theoretical derivation and numerical calculation to study the natural vibration of rotating motion functional gradient circular plate and circular plate in thermal environment.Based on Kirchhoff's basic assumption,considering the geometric nonlinearity,the kinetic energy and deformation potential energy of the rotating functional gradient gradient plate are given.The expressions of thermal stress and thermal bending moment are obtained according to the one-dimensional heat conduction equation.The functional gradient is derived using the Hamiltonian variational principle Differential equation of thermoelastic coupling vibration of circular plate.The problem of linear natural vibration of a functionally graded circular plate with rotating motion in a thermal environment is studied.Under the condition of considering temperature field and rotating motion,considering the influence of in-plane displacement on lateral vibration,the linear natural frequency expression of lateral vibration of circular plate is obtained by applying Galerkin method.Through calculation examples,the transverse vibration response diagram and phase diagram of the circular plate are drawn,and the characteristic curves of the natural frequency with the volume fraction index,surface temperature,speed,etc.are given.The influence of point behavior and the law of static deflection vary with different parameters.The problem of strong nonlinear natural vibration of rotating functional gradient circular plates in thermal environment is studied.The perturbation method is used to find the static deflection caused by rotation and the differential equations about the perturbation deflection.The improved multi-scale method is used to solve the strong nonlinear vibration differential equations.Through an example,the characteristic curve and power spectrum of the nonlinear natural frequency of the circular plate under different influences are given,and the calculation results are compared and analyzed.The problem of nonlinear natural vibration of functionally rotating circular gradient plates in thermal environment is studied.Aiming at the constraints of internal and external clamps,through the Galerkin discrete and perturbed solutions,the thermoelastic perturbation differential equation of the rotating circular plate is derived.Through analytical solutions and numerical calculations of strong nonlinear equations,free vibration multi-frequency response solutions and nonlinear natural vibration frequency expressions are obtained,and the effects of volume fraction index,rotation speed and temperature on the vibration characteristics of the system and the law of static deflection varies with different parameters.