Abstract
A model of laminated cylindrical shells with discontinuous piezoelectric layer is proposed. Based on the first-order shear nonlinear shell theory, the nonlinear vibration control of the piezoelectric laminated cylindrical shell model with point-supported elastic boundary condition is analyzed. In this model, a series of artificial springs are introduced to simulate the arbitrary boundary conditions. And the elastic-electrically coupled differential equations of piezoelectric laminated cylindrical shells are obtained by the Chebyshev polynomials and Lagrange equations and decoupled by using the negative velocity feedback adjustment. Then, the frequency–amplitude responses of the piezoelectric laminated cylindrical shells are obtained by the incremental harmonic balance method. Finally, the influence of the constant gain, size, and position of the piezoelectric layer on the nonlinear amplitude–frequency response is investigated. The results show that the constant gain and the position and size of the piezoelectric layer have a significant influence on the amplitude of the nonlinear amplitude–frequency and time–frequency response.
Highlights
In recent years, with the development of piezoelectric materials, the piezoelectric films (PVDF)have been widely used in the fields of machinery, environmental testing, and medicine because of their functions of vibration detection, vibration control, and energy collection
Kerur et al [3] presented a finite element model using a composite material (AFC) as the piezoelectric actuator and a piezoelectric film (PVDF) as the piezoelectric sensor, and used the negative velocity feedback control algorithm to control the dynamic response of the laminated composite plate
Zhang[16] used various geometrically nonlinear shell theories based on the first-order shear deformation theory (FSDT), including refined von Kármán nonlinear shell theory(RVK5), moderate rotation shell theory(MRT5), fully geometrically nonlinear shell theory with moderate rotations(LRT5) and fully geometrically nonlinear shell theory with large rotations(LRT56), the results showed that the LRT56 can get more accurate results when structures undergo large rotations, and by adopting appropriate feedback actuation voltages, shape and vibration control can be accomplished pretty well in the structures undergoing large deformations and large rotations
Summary
With the development of piezoelectric materials, the piezoelectric films (PVDF). Sheng and Wang[14] proposed a new simplifying model of smart FG laminated cylindrical shells with thin piezoelectric layers in which the inner layer is a sensing layer, the functionally graded layer, and the outer layer is the active layer, and uses the Von Kármán nonlinear theory, the Hamilton’s principle, the FSDT and the multiterm Galerkin method to analyze the active vibration control of smart FG laminated cylindrical shells. Shen and Yang [15] used the higher order shear deformation shell theory with a von Kármán-type of kinematic nonlinearity to study the small and large amplitude flexural vibrations of anisotropic shear deformable laminated cylindrical shells with piezoelectric fiber reinforced composite (PFRC) actuators in thermal environments. Mass density of the based layer, actuator layer and sensor layer x , , xy , y , xz Stresses of the shell
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