Dynamics Modeling And Nonlinear Analysis Of Piezoelectric Composite Cantilever Rectangular Plates

In recent years,with the development of science and technology,unmanned aerial vehicle(UAV)has been rapidly studied,developed and applied in military and civil fields.However,due to the limited battery power,the endurance of UAV is generally low,which could not meet the needs of various fields.Through the vibration of UAV engine,aerodynamic load and the positive piezoelectric effect of piezoelectric material,the vibrational energy can be transformed into electric energy,which can supply power for UAV.This is a feasible method to increase the endurance ability of UAV.In this paper,the wing of UAV is simplified as a composite laminated cantilever plate,and piezoelectric material is laid on the surface of the composite cantilever plate.The nonlinear dynamic response and power generation performance of the piezoelectric composite cantilever plates are studied by theoretical and numerical methods,which subjected different excitations and different lay-up parameters.The research provides scientific basis for the vibration-based piezoelectric energy harvester,and has important value in engineering application.The main contents of this dissertation are as follows.(1)The UAV wing is simplified as a composite laminated piezoelectric cantilever rectangular plate,which is subjected to transverse harmonic and in-plane excitations.Using classical plate theory and Hamilton principle,the nonlinear partial differential equations of the system are established.Employing the Galerkin approach discretize the partial differential equations into the ordinary differential equations with two-degree-of-freedom.The asymptotic perturbation method is utilized to analyze the nonlinear vibration properties of an antisymmetric cross-ply piezoelectric cantilever rectangular plate.The case of 1:2 internal resonance and primary parametric resonance are taken into account.Based on the four-dimensional average equation,the nonlinear effects of transverse and in-plane excitations on the system are analyzed numerically.Considering the resonant case of 1:3 internal resonance and primary parametric resonance,we use the multi-scale method to analyze the nonlinear behaviors of an antisymmetric angle-ply piezoelectric cantilever rectangular plate.The results show that the nonlinear behaviors of the piezoelectric cantilever plate with antisymmetric angle-ply are more complex and changeable than that of the piezoelectric cantilever plate with antisymmetric cross-ply.(2)The mechanical-electrical coupling equation of piezoelectric composite cantilever rectangular plate energy haverster is established.The amplitude-frequency response equation of the system is derived by using multi-scale method.By drawing a series of amplitude-frequency response curves,the effects of transverse excitation and damping coefficient on the nonlinear amplitude-frequency characteristics are studied.Based on the mechanical-electrical coupling equation,the influence of transverse excitation on the nonlinear response and electricity generation performance of the system with different damping coefficients are analyzed by using Matlab software.From these above figures,it can be seen that the system exsits nonlinear phenomena such as period-doubling bifurcation,crisis and chaos.(3)Employing the Galerkin approach discretize the partial differential equations into the ordinary differential equations with four-degree-of-freedom at the first time.Substituting the geometric and physical parameters of the laminated composite piezoelectric cantilever rectangular plate into governing equation of motion,we use numerical method to investigate the effects of transverse excitation,damping coefficient and piezoelectric coefficient on the nonlinear dynamic responses of this system.We find that the complex nonlinear phenomena appear synchronously for the first four modes of this system.So it is necessary and important to study the first four modes of the system.(4)Based on the Reddy’s third-order plate theory and the Hamilton’s principle,the nonlinear partial differential equations of motion for the arbitrary angle-ply composite piezoelectric cantilever rectangular plate are established.The cantilever plate is subjected to the first-order transverse aerodynamic force and in-plane excitation.Utilizing Galerkin method,the three-degree-of-freedom dimensionless nonlinear ordinary differential equations are obtained.We use numerical method to investigate the effects of lay-up parameters on the first-order dimensionless natural frequency.These lay-up parameters include width-thickness ratio,the percentage of 0~?lay-up and some ply angles.Frequency-response curves are plotted with different lay-up parameters.The three-degree-of-freedom nonlinear ordinary differential equation of the arbitrary angle-ply piezoelectric cantilever rectangular plate is carried out by using the multi-scale method.Selecting several different amplitudes of in-plane excitation,the bifurcation diagrams of the first mode transverse displacement versus airflow velocity are drawn respectively.It can be seen that the critical instability speed of the system increase with the decrease of the amplitude of in-plane excitation.The bifurcation diagram of the first mode transverse displacement versus the airflow velocity is plotted with different the partial ply angle of the piezoelectric laminated cantilever plate.The effects of two lay-up parameters on the nonlinear vibration characteristics of the system are compared.