Strongly Nonlinear Primary Resonance Of Functionally Graded Circular Plate In Rotational Motion

Functionally graded material as a new material,has good mechanical properties,is a material widely used in recent years.Various shapes of components made of functionally graded materials,such as circular plates,ring plates,and rectangular plates,are a type of component commonly used in industrial production,and are often in complex and specific working environments.Therefore,in order to meet the needs of production practice,it is necessary to study the mechanical properties of functionally graded material components in complex environments.In recent years,the study of nonlinear vibration of functionally graded materials considering thermal effects has become an important research direction.In this paper,theoretical analysis and numerical calculation are used to study the main resonance of functionally graded circular plates and annular plates in rotational motion when thermal effects are considered.Based on the large deflection theory of the thin plate,the material composition is assumed to change according to the power exponential along the thickness of the plate without considering the thermal effect and the thermal effect,and the influence of geometric nonlinearity and in-plane displacement on the lateral vibration is considered.Derive the expressions of the kinetic energy and potential energy of the functionally graded disc.The Hamiltonian principle is used to derive the vibration differential equations of functionally graded circular plates and annular plates in rotational motion.The main resonance of a functionally graded circular plate in rotational motion is studied.For the metal-ceramic functionally graded plate,based on the boundary constraint conditions as the surrounding clamp,select the polynomial mode function,and use the Galerkin method to obtain the axisymmetric nonlinear vibration differential equation of the rotating circular plate,and obtain the rotation and density Static deflection caused by the difference.Multi-scale method is used to solve the equation,and the frequency response equation and analytical solution of the system are obtained.Through the analysis of calculation examples,the amplitude-excitation force curve,amplitude-speed curve,amplitude-plate thickness curve and amplitude-radius curve under different parameters are obtained,and the influence law of different parameters on the system amplitude is obtained.In addition,the analytical solution and the numerical solution are compared,and the results of the two are more consistent.The main resonance of a functionally graded circular plate in rotational motion in a thermal environment is studied.Establish the nonlinear vibration differential equation of the rotating circular plate under the influence of temperature.Taking into account the strong nonlinearity of the vibration equation,an improved multi-scale method is used to solve the equation,and the stability criterion of the steady-state motion solution of the system is obtained through the Lyapunov stability theorem.Through the analysis of calculation examples,the frequency and amplitude response curves of different parameters are obtained,the influence of different parameters on the resonance response of the system is analyzed,and the time-history diagram and phase diagram of the system vibration are given.The problem of strong nonlinear primary resonance of functionally graded toroidal plate in rotational motion in thermal environment is studied.Aiming at the constraints of the internal and external clamps,the Galerkin discretization and improved multi-scale method are used to solve the problem,and the strong nonlinear vibration differential equation is obtained.Through analytical solution and numerical analysis,the frequency-amplitude curves under different parameters are obtained,and the influence law of excitation force,excitation frequency,inner and outer diameters on the system amplitude is explained,and the results are compared and analyzed.