Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force
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Using Reddy’s high-order shear theory for laminated plates and Hamilton’s principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom (DOF) nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics, including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.
KeywordsDeploying piezoelectric laminated composite plate Time-varying nonlinear dynamics Third-order shear deformation plate theory Time-dependent modal function Aerodynamic force
The project was supported by the National Natural Science Foundation of China (Grants 11402126, 11502122, and 11290152) and the Scientific Research Foundation of the Inner Mongolia University of Technology (Grant ZD201410).
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