248 / 2021-04-14 21:19:48

The study on underwater vibration and acoustic radiation of functionally graded piezoelectric plates with general boundary conditions

Functionally graded piezoelectric plates; Vibro-acoustic radiation; Chebyshev polynomials; Rayleigh-Ritz

This paper investigates the underwater vibration and acoustic radiation of functionally graded piezoelectric plates (FGPPs) with general boundary conditions based on the first-order shear deformation theory (FSDT) and the second type constitutive equation of piezoelectric materials. The mechanical and electrical properties of FGPPs are assumed to vary continuously in the thickness direction by utilizing the Voigt model and power-low function. Regardless of boundary conditions, the fields of mechanical displacement, electric potential and sound pressure are unified expanded as the Chebyshev polynomials to remove the matching difficulties. The penalty method is applied and six groups of penalty factors are used for the boundary conditions of the FGPPs. In this way, the energy stored in the boundary conditions can be considered as a part of the total energy function, releasing the limitation of geometrical boundary restraints on the selection of admissible functions. The energy description is derived considering of the interaction of fluid and plate and uniting Rayleigh integral formula, and the characteristic of underwater vibro-acoustic radiation is obtained based on Rayleigh-Ritz procedure. In the numerical examples, the convergence and accuracy of the proposed method are validated. Finally, the influences of boundary conditions, geometrical parameters, amplitude of external excitation and material distribution on the underwater vibro-acoustic radiation are examined.