Micromechanical Systems: Modal Analysis

This chapter studies the resonant/modal response of micromechanical systems by separating their components in either mass elements, which only contribute to the system’s inertia, or spring elements, which only affect the overall elastic properties. The lumped-parameter method can thus conveniently be applied to model the free vibratory response of micromechanical systems. While some of them behave as single degree-of-freedom (DOF) systems, others undergo complex vibratory motion, which is defined by more than one DOF. For the latter category, it is possible at times to analyze each DOF individually, and such a motion is known as uncoupled. In other cases, two or more DOF combine in terms of stiffness and/or inertia, which make the respective motions to be coupled. Lagrange’s equations are used to model the free response of multiple DOF micromechanical systems. Several example problems of massspring microsystems undergoing linear or/and rotary resonant vibrations are amply discussed and fully solved.