Dynamic pull-in and oscillations of current-carrying filaments in magnetic micro-electro-mechanical system

Simplified Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Vibration Systems

“…Nonlinear vibration systems arise everywhere in mechanical engineering, as in thinwalled structures [1], rotor vibration [2,3], gyroscope systems [4,5], micro-electromechanical systems [6,7], packaging systems [8], building vibration [9], heavy machinery [10], to name but a few. The most famous nonlinear oscillators include the pendulum systems [11,12], van der Pol oscillator and Duffing oscillator [13].…”

A mathematical control for the pseudo-pull-in stability arising in a micro-electromechanical system

“…Equation ( 8) is the sufficient condition for periodic solution of equation (6). Similarly, we have the following non-periodic criterion, that is…”

“…The last two decades have witnessed a skyrocketing interest in the micro/nanoelectromechanical system, sparked by its wide advanced applications in nanotechnology, micro-devices, micro-sensors, micro-actuators, and micro-power generators, [1][2][3][4][5][6] and it has been caught a renewed attention to the pull-in stability from both industry and academia because the pull-in instability is an unwanted phenomenon, [7][8][9][10][11] which causes unreliability. Much effort was made to avoid the pull-in instability.…”

The periodic solution of a pendulum under magnetic action

“…It has periodic solution when 20,21 f ðθÞ θ > 0 (12) The square of the frequency can be obtained by He's frequency formulation 22…”