Vibration analysis for piezoceramic rectangular plates using Ritz's method with equivalent constants

The transverse vibration of piezoceramic rectangular thin plates is investigated theoretically and experimentally using the Ritz's method incorporated with the defined equivalent constants. The equivalent constants are derived by comparing the characteristic equations of transverse resonant frequencies between isotropic and piezoceramic disks. By replacing the Poisson's ratio and flexural rigidity with the equivalent constants, the well-known Ritz's method can be used to investigate the transverse vibration of piezoceramic rectangular plates. Two different types of boundary conditions - clamped-free-free-free (CFFF) and clamped-free-clamped-free (CFCF) - are analyzed in this paper. For the experimental measurement, two optical techniques - amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV) - are used to validate the analytical results. Both the transverse vibration modes and resonant frequencies of piezoceramic rectangular plates are obtained by the AF-ESPI method. Numerical calculations using the finite-element method (FEM) are performed, and the results are compared with the theoretical analysis and experimental measurements. Excellent agreements are obtained for results of both resonant frequencies and mode shapes. According to the theoretical calculations with different equivalent Poisson's ratios, resonant frequency variations versus aspect ratios ranging from 0.1 to 10 also are discussed for the first several modes in the work.