Active Control And Analysis Of Static And Dynamic For Functionally Graded Piezoelectric Material Plate

Functionally graded piezoelectric material(FGPM)is a new heterogeneous composite material whose mechanical properties change smoothly and continuously from one surface to another.Compared with traditional layered piezoelectric composites,FGPM is able to reduce the thermal stress and withstand severe high-temperature gradient,and piezoelectric materials as the composition of FGPMs are used to control the static and dynamic response of structures.Therefore,FGPMs are widely used in many fields such as ships,spacecraft and space structures.The present paper concentrates on the control and analysis of the static and dynamic for FGPM plates with thermo-electro-mechanical loads.Firstly,using the first order shear deformation theory(FSDT)and Hamilton principle,the equation of motion of the FGPM plate with thermo-electro-mechanical loads is established,where the gradient of temperature and electric field in the thickness direction is considered.The assumed mode method is used to discretize the equation of motion of the system,and the modal function of the four simply supported boundary condition is given.Before proceeding with the detailed study,the validity of the formula and the MATLAB calculation program is verified.For the static bending of the FGPM plate,the effects of volume fraction index,temperature and load parameter on the central point deflection and axial stress of the FGPM plate are studied.The static bending of the FGPM plate is controlled by mechanical load feedback control method.And the effects of bending control gain and load parameter on active control of the structure are studied.For the dynamic response of the FGPM plate,the influence of temperature,input voltage and volume fraction index on the natural frequency of the FGPM plate is analyzed.The vibration active controller of the structure is designed by velocity feedback and LQR control algorithm.The effect of the two controllers on active vibration control of the FGPM plate is compared.Based on the research on active vibration control of the FGPM plate,an improved equation of functional gradient distribution is proposed,and the optimization design of active vibration control of the structure is studied.The active damping of the FGPM plate is obtained by the velocity feedback control method.The influence of the distribution types of piezoelectric materials on the active vibration control of the FGPM plate is analyzed,and an optimal gradient distribution function of piezoelectric material is selected.Then,the influence of the control voltage application position on the active vibration control of the FGPM plate is also studied.