Influence of bending-extension coupling on the modal frequencies of nonsymmetrically laminated MEMS microcantilevers

Many microelectromechanical systems (MEMS) devices are based on some aspect of the modal vibration response of microcantilever beams, and these microcantilevers often have nonsymmetrically laminated construction. Such construction can lead to complex mechanical coupling effects which are not included in elementary beam theory, yet this theory is often used to estimate the modal frequencies of microcantilevers. In this paper, the bending-extension coupling effects on the modal frequencies of a typical two-layer microcantilever beam element in a MEMS chemical sensor are analyzed. Classical Lamination Theory is combined with a Rayleigh-Ritz analysis to develop a model for the modal frequencies of this microcantilever. Results are compared with those from the elementary beam theory and a finite element model. Bending-extension coupling effects are found to depend on the beam length-to-thickness ratio, on the coating thickness-to-beam thickness ratio, and on the mode number. [1369].