Size-dependent hydroelastic vibration of FG microplates partially in contact with a fluid

This work focuses on the hydroelastic vibration of vertical functionally graded (FG) microplates partially in contact with a fluid. The nonlocal Lam strain gradient theory is here proposed to include small-scale effects, with the introduction of three higher-order material constants within the formulation. This non-classical model would revert to the modified couple stress theory (MCST) or the classical continuum model (CCM) for a vanishing value of two or three length scale parameters, respectively. A fifth-order shear deformation theory is employed to capture the transverse shear stresses and rotary inertia effects. An ideal fluid is also assumed to simplify the dynamic problem, where the continuity equation is enforced to determine the fluid velocity potential associated with bulging and sloshing modes. Once the kinetic and potential energy are calculated for the both of structure and interacting fluid, the Rayleigh-Ritz method is employed to determine the wet frequencies of the system. After a preliminary validation of the proposed model, a systematic investigation is performed to check effects of different mechanical and/or geometrical parameters on the vibrational characteristics of the microplate, namely, the small-scale parameters, the aspect ratio, the thickness ratio and the fluid dimensions contacting with the microstructure.