Forced Vibration Analysis Of Functionally Graded Piezoelectric Laminate Plates

Functionally graded piezoelectric laminate material is a new intelligent material which played an important role in aerospace,aviation,chemical industry,electric control and machinery fields.The mechanical behavior of functionally graded piezoelectric laminate material have been widely studied in recent years,but there still some challenges need to be solved especially the vibration problems,which have become a research hotspot.Through the background and significance of this research are expounded in this paper,the brief introduction of functionally graded material,piezoelectric material and functionally graded piezoelectric laminate material at home and abroad are also be made.The geometric model of the functionally graded laminate plates is established,the nonlinear dynamic equation of functionally graded laminate plates under mechanical force is derived by using the Hamiltonian Principle.Then the nonlinear primary resonance of the plate was analyzed by Matlab software,mainly discussed the influence of primary resonance on laminate plates under different boundary conditions,then analyzed the effect on the system dynamic caused by damping,power law index and mechanical force,and the analysis showed that the greater of the damping,power law index and mechanical force parameters the more obviously for the system dynamic response,more prone to jump and the system is in an unstable state.Finally,the nonlinear dynamic equations of functional graded piezoelectric laminates under voltage excitation are deduced,based on the stress-strain equation of piezoelectric material and functional graded material,and then use the multi-scale method to derive the amplitudefrequency response equation.The relationships between the primary resonance and the parameters were analyzed by changing the magnitude of the parameters such as harmonic voltage,system damping,the power law index of the functional graded plate and the thickness of the functional graded plate.The influence of voltage and damping on system bifurcation and chaos was analyzed,and the phase diagram of the system was drawn.