Optimal locations of discontinuous piezoelectric laminated cylindrical shell with point supported elastic boundary conditions for vibration control

In this paper, the vibration control of discontinuous piezoelectric laminated shell with point supported elastic boundary conditions are investigated, and the location of piezoelectric layer are optimized. The point supported boundary condition are simulated by using artificial springs. The position with the piezoelectric layer are considered to be a laminated shell, and the position without the piezoelectric layer are regarded as a thin-walled cylindrical shell. The strain and curvature expressions of the cylindrical shell are obtained by the first-order shear shell theory, and the Chebyshev polynomial is used as the admissible displacement functions. Then, the differential equation of coupling motion of piezoelectric laminated cylindrical shells is established by using Lagrange equation, and the negative velocity feedback control is used as the control strategy. The Newmark method is used to obtain the response curves. The accuracy of the model are verified by comparing with the ANSYS results. For better vibration control, the optimal locations of the piezoelectric layer are obtained by using the Multi-Objective Particle Swarm Optimization algorithm based on the crowding distance. Finally, the optimization results and the vibration control of the piezoelectric layer are verified by analyzing the radial displacement response of the cylindrical shell.