Abstract
An efficient isogeometric analysis method (IGA) based on a simple first-order shear deformation theory is presented to study free vibration, static bending response, dynamic response, and active control of functionally graded plates (FGPs) integrated with piezoelectric layers. Based on the neutral surface, isogeometric finite element motion equations of piezoelectric functionally graded plates (PFGPs) are derived using the linear piezoelectric constitutive equation and Hamilton’s principle. The convergence and accuracy of the method for PFGPs with various mechanical and electrical boundary conditions have been investigated via free vibration analysis. In the dynamic analysis, both time-varying mechanical and electrical loads are involved. A closed-loop control method, including displacement feedback control and velocity feedback control, is applied to the static bending control and the dynamic vibration control analysis. The numerical results obtained are accurate and reliable through comparisons with various numerical and analytical examples.
Highlights
Graded materials (FGMs) [1] have been used extensively in the aerospace, nuclear power industries, biomedical field, and other applications [2,3,4] for their superior thermo-mechanical properties, such as low thermal conductivity and high thermal resistance
To avoid the decrease in the calculation accuracy [20,21] caused by element distortion in the finite element method (FEM), various scholars attempted to use the mesh-free method to analyze the behaviors of piezoelectric functionally graded plates (PFGPs)
We investigated the bending response of PFGPs which are subjected to the voltage range
Summary
Graded materials (FGMs) [1] have been used extensively in the aerospace, nuclear power industries, biomedical field, and other applications [2,3,4] for their superior thermo-mechanical properties, such as low thermal conductivity and high thermal resistance. To avoid the decrease in the calculation accuracy [20,21] caused by element distortion in the FEM, various scholars attempted to use the mesh-free method to analyze the behaviors of PFGPs. Using the element-free Galerkin method, Dai et al [22] investigated the static, active control analysis of FGPs with surface-bonded piezoelectric materials in thermal environments. IGA method has only four unknowns, response of the structures under time-varying voltage loads can provide a more comprehensive and it is applied to the open-source frameworks; smart (iii) the investigation of dynamic response understanding of the mechanical behaviorIGA of piezoelectric structures. Isogeometric finite element equations of PFGPs are derived through the linear piezoelectric constitutive mechanical loads and voltage loads are studied by using the Newmark-β direct integration method. The static and dynamic closed-loop control are used for controlling the shapes and vibration of the plates
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