Solid-liquid coupling of in-phase and out-of-phase vibrations for two piezoelectric disks

Theoretical analysis is used to solve the solid–liquid coupled vibration characteristics for two piezoelectric disks in a limited space and verified with experimental measurements. Based on the Navier–Stoke equation and equilibrium of motion, the Rayleigh-Ritz and energy methods were developed to analyze the solid–liquid coupled system. Following an entire systematic procedure, two piezoelectric disks immersed in hydrostatic compressible fluids were analyzed using the piezoelectric constitutive equation to perform the in-phase and out-of-phase vibration. The full-field, non-contact, optical technique, called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), was applied to experimentally measure the vibration properties in a solid–liquid coupling system, including the mode shapes and resonant frequencies. The experimental results are presented in good agreement with the theoretical solutions and finite element calculations. Under the solid–liquid coupled system, the distributions of pressure fields and velocity vectors of fluids were also determined in the correspondent vibrating modes. Finally, it is interesting to show the tendency to close the same resonant frequency both on the in-phase and out-of-phase vibrations when the fluid depth increases. The research outcomes can provide a guide in the design of hydrostatic components.