Abstract
This work presents the nonlinear dynamical analysis of a multilayer d31 piezoelectric macrofiber composite (MFC) laminated shell. The effects of transverse excitations and piezoelectric properties on the dynamic stability of the structure are studied. Firstly, the nonlinear dynamic models of the MFC laminated shell are established. Based on known selected geometrical and material properties of its constituents, the electric field of MFC is presented. The vibration mode-shape functions are obtained according to the boundary conditions, and then the Galerkin method is employed to transform partial differential equations into two nonlinear ordinary differential equations. Next, the effects of the transverse excitations on the nonlinear vibration of MFC laminated shells are analyzed in numerical simulation and moderating effects of piezoelectric coefficients on the stability of the system are also presented here. Bifurcation diagram, two-dimensional and three-dimensional phase portraits, waveforms phases, and Poincare diagrams are shown to find different kinds of periodic and chaotic motions of MFC shells. The results indicate that piezoelectric parameters have strong effects on the vibration control of the MFC laminated shell.
Highlights
macrofiber composite (MFC) is a piezoelectric fiber material, consisting of monotonic piezoelectric material, epoxy matrix, and electrodes with a specific arrangement, which can be considered as homogenized orthotropic materials with arbitrary piezoelectric fiber angles like composite structures
Suresh Kumar and Ray [23] analyze the geometrically nonlinear vibrations of doubly curved smart sandwich shells integrated with a patch of 1–3 piezoelectric composites active constrained layer damping (ACLD) treatment
The vibration mode-shape functions are obtained according to the boundary conditions, and Galerkin method is employed to transform the partial differential equations into two nonlinear ordinary differential equations
Summary
MFC is a piezoelectric fiber material, consisting of monotonic piezoelectric material, epoxy matrix, and electrodes with a specific arrangement, which can be considered as homogenized orthotropic materials with arbitrary piezoelectric fiber angles like composite structures. Kim et al [19] study the vibration suppression of an end-capped cylindrical shell structure with surface bonded macrofiber composite actuators and analyze the dynamic characteristics of the cylindrical shell structure. Li et al [22] present the active control of random vibration for piezoelectric fiber reinforced composites laminated plates and discuss the effect of piezoelectric fiber orientation in the PFRC layers. Suresh Kumar and Ray [23] analyze the geometrically nonlinear vibrations of doubly curved smart sandwich shells integrated with a patch of 1–3 piezoelectric composites active constrained layer damping (ACLD) treatment. Based on the developed Kirchhoff plate theory, in some articles [30, 31], the actuation responses of d33 and d31 MFCs integrated smart structures are studied subjected to transverse excitations. Kashiwao et al [32] propose an optimization method of a vibration energy harvesting system which is made of MFC piezoelectric elements
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