Studies on dynamic behavior of functionally graded cylindrical shells with PZT layers under moving loads

Based on the first-order shear deformation theory (FSDT), the Hamiltonʹs principle and the Maxwell equation, this paper presents the coupling equations to govern the electric potential and the displacements of the functionally graded cylindrical shell with surface-bonded PZT piezoelectric layer, and subjected to moving loads. The frequencies equations are obtained by using displacement functions and one electric potential function. The modal analysis technique and Newmarkʹs integration method are used to calculate the displacements and sensory electric potential of the shell subjected to moving loads. The effects of the moving velocities of the loads, volume fraction exponents Φ of functionally graded materials (FGMs) and temperature environment on the dynamic responses of shells are investigated. An analytical approximate equation is obtained to describe the relationship between critical velocities of moving loads and natural frequencies of shells. The present approach is validated by comparing the natural frequencies with the result presented by Ng et al. In addition, numerical results show the relationship between the displacements and sensory electric potential of the shell. The present work shows that some meaningful and interesting results presented in this paper are helpful for the application and the design of smart sensory structures.