Abstract
Multilayered microresonators commonly use sensitive coating or piezoelectric layers for detection of mass and gas. Most of these microresonators have a variable cross-section that complicates the prediction of their fundamental resonant frequency (generally of the bending mode) through conventional analytical models. In this paper, we present an analytical model to estimate the first resonant frequency and deflection curve of single-clamped multilayered microresonators with variable cross-section. The analytical model is obtained using the Rayleigh and Macaulay methods, as well as the Euler-Bernoulli beam theory. Our model is applied to two multilayered microresonators with piezoelectric excitation reported in the literature. Both microresonators are composed by layers of seven different materials. The results of our analytical model agree very well with those obtained from finite element models (FEMs) and experimental data. Our analytical model can be used to determine the suitable dimensions of the microresonator’s layers in order to obtain a microresonator that operates at a resonant frequency necessary for a particular application.
Highlights
In order to overcome all these drawbacks, we present an analytical model for the first bending resonant frequency of multilayered microresonators with variable cross section and one fixed end
This paper is organized as follows: in Section 2, we describe the analytical model for the bending resonant frequency of a multilayered microresonator with variable cross section
An analytical model to estimate the first bending resonant frequency and deflection curve of multilayered microresonator with variable cross-section was presented. This model is formulated through the Rayleigh and Macaulay methods, as well as the Euler-Bernoulli beam theory
Summary
Multilayered microresonators fabricated using microelectromechanical systems (MEMS) have potential applications such as mixer-filters [1,2] and detection of mass [3,4], prostate-specific antigens [5], proteins [6], virus [7,8], chemical species [9], gas [10,11], and magnetic fields [12,13,14]. Developed lumped and distributed-parameter models for predicting the bending or torsion resonant frequencies of microresonators with variable cross section and serially connected [24,25,26,27,28] They obtained analytically the deflection of this microresonator type; their models do not consider multilayered microresonators. Edqvist et al [37] established a general theoretical model for studying the quasi-static and dynamic electromechanical responses of piezoelectric multilayered microbeams with one fixed end Their model was obtained through Euler-Bernoulli theory and only considers layers with uniform cross section. In order to overcome all these drawbacks, we present an analytical model for the first bending resonant frequency of multilayered microresonators with variable cross section and one fixed end This model includes microresonators composed by an arrangement of different multilayered microbeam types.
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