APPLICATION OF HIGHER ORDER HAMILTONIAN APPROACH TO THE NONLINEAR VIBRATION OF MICRO ELECTRO MECHANICAL SYSTEMS
Keywords:HIGHER ORDER HAMILTONIAN, MEMS, FREE VIBRATIONS, EULER-BERNOULLI THEORY, GALERKIN METHOD
AbstractTHIS PAPER IMPLEMENTS THE HIGHER ORDER HAMILTONIAN METHOD TO ANALYZE AN ELECTROSTATICALLY ACTUATED NONLINEAR MICRO BEAM-BASED MICRO ELECTRO MECHANICAL OSCILLATOR. FIRST, SECOND AND THIRD APPROXIMATE SOLUTIONS ARE OBTAINED, AND THE FREQUENCY RESPONSES OF THE SYSTEM ARE VERIFIED BY ENERGY BALANCE METHOD SOLUTION AND VARIATIONAL APPROACH (VA). AFTER DRIVING THE EQUATION OF MOTION BASED ON THE EULER-BERNOULLI BEAM THEORY, GALERKIN METHOD HAS BEEN USED TO SIMPLIFY THE NONLINEAR EQUATION OF MOTION. HIGHER ORDER HAMILTONIAN APPROACH HAS BEEN USED TO SOLVE THE PROBLEM AND INTRODUCE A DESIGN STRATEGY. PHASE PLANE DIAGRAM OF ELECTROSTATICALLY ACTUATED MICRO BEAM HAS PLOTTED TO SHOW THE STABILITY OF PRESENTED NONLINEAR SYSTEM AND NATURAL FREQUENCIES ARE CALCULATED TO USE FOR RESONATOR DESIGN. ACCORDING TO THE NUMERICAL RESULTS, THE SECOND APPROXIMATE IS MORE ACCEPTABLE AND RESULTS SHOW THAT ONE COULD OBTAIN A PREDESIGN STRATEGY BY PREDICTION OF EFFECTS OF MECHANICAL PROPERTIES AND ELECTRICAL COEFFICIENTS ON THE STABILITY AND FREE VIBRATION OF COMMON ELECTROSTATICALLY ACTUATED MICRO BEAM.
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