Vibration analysis of submerged micro rectangular plates with distributed mass loading

Wu, Zhangming and Ma, Xianghong and Brett, Peter N. and Xu, Jinwu (2009) Vibration analysis of submerged micro rectangular plates with distributed mass loading. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 465 (2014). 1323–1336. ISSN 1471-2962 (https://doi.org/10.1098/rspa.2008.0447)

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Abstract

This paper investigates the vibration characteristics of the coupling system of a microscale fluid-loaded rectangular isotropic plate attached to a uniformly distributed mass. Previous literature has, respectively, studied the changes in the plate vibration induced by an acoustic field or by the attached mass loading. This paper investigates the issue of involving these two types of loading simultaneously. Based on Lamb's assumption of the fluid-loaded structure and the Rayleigh–Ritz energy method, this paper presents an analytical solution for the natural frequencies and mode shapes of the coupling system. Numerical results for microplates with different types of boundary conditions have also been obtained and compared with experimental and numerical results from previous literature. The theoretical model and novel analytical solution are of particular interest in the design of microplate-based biosensing devices.

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