Natural frequencies of submerged microplate structures, coupled to stationary fluid, using modified strain gradient theory

Abstract

This paper investigates the free vibration analysis of a microplate, interacting with a stationary fluid. For the fluid part, the potential flow assumptions are considered, and it is supposed to be incompressible, irrotational and inviscid. Different positions for the fluid relative to the structure are studied: a structure in contact with a fluid with a free surface, a submerged microplate and a floating structure. For the structure, the mechanical properties of the microplate such as density, Young modulus and shear modulus are assumed to be a function of structure thickness. Besides, the modified strain gradient theory on the basis of higher-order plate theory is adopted to capture the size effects of the microplate. Using Bernoulli’s relation and fluid velocity potential function, the fluid pressure affecting the microplate is calculated, and then Hamilton’s principle is employed to derive coupled fluid–solid equations of motion. After validation of the presented formulations, a comprehensive parametric study is conducted to exhibit the response of the system under variations of some parameters such as structure mechanical properties, fluid parameters and size-effect parameters.