NONLINEAR DYNAMICS AND STABILITY OF MICROSYSTEMS ENGINEER-ING ELEMENTS

Subject of Research. Static and dynamic problems of coupled electroelasticity are considered for electrostatic (capacitive) transducers used in sensors and actuators based on nano- and microsystem technology of various applications. Method. Above-mentioned problems are analyzed by mathematical apparatus of nonlinear mechanics and bifurcation theory as well as modern numerical methods, including numerical continuation techniques for nonlinear boundary-value problems of mathematical physics. Main Results. Comparative analysis of analytical and numerical methods was performed for nonlinear static and dynamic boundary-value problems of electroelasticity for microsystems and nanosystems engineering. Basic discrete (nonlinear nano/micro-electromechanical oscillators) and distributed (membranes, plates) electromechanical models were considered. Equilibrium forms, their stability and bifurcations were studied for afore-named elastic systems under the influence of electric fields of various configurations. Bifurcation diagrams were derived depending on key physical parameters. Nonlinear dynamic problems for elastic systems at time-varying electric fields were also considered. Practical Relevance. The present research is of considerable practical significance because it reveals and analyzes qualitatively the elastic elements properties and characteristics that are important for nano/micro-system design, such as equilibria structure and stability, amplitude and force response of the system, etc. Used methods and mathematical formulations can be applied in the design process of micromechanical accelerometers and gyroscopes, pressure sensors, micro-pumps, capacitive micro-machined ultrasound transducers, radio-frequency and optical switches, electromagnetic energy harvesting systems and biomedical devices.

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