Search

The present work is the first part of a study of nonlinear dynamics of parametrically excited transverse oscillations of a clamped-clamped microbeam (the basic sensory element of a promising class of microsensors of various physical quantities) under exposure to laser-induced opto-thermal effects in the form of periodically generated pulses affecting a certain part of the beam-element surface. An analytical solution of the heat-transfer problem for steady harmonic temperature distribution in the resonator volume is found. The static and dynamic components of the temperature-induced axial force and transverse moment are determined. Discretization of the nonlinear coupled partial differential equations describing the longitudinal-transverse vibrations of the resonator is performed using the Galerkin method. Using the asymptotic method of multiple scales, an approximate analytical solution for the nonlinear dynamics problem under the conditions of primary parametric resonance is obtained. [ABSTRACT FROM AUTHOR]

In this work, we study the conditions and scenarios for synchronizing the oscillations of weakly coupled microbeam elements of a differential resonant microelectromechanical systems (MEMS) accelerometer that operates in the dual-loop self-oscillator mode. The model of a system of two Van der Pol self-oscillators with a nonlinear elastic coupling between moving elements, obtained by the Galerkin method, is studied using the multiscale method. The modes of beats and synchronization of oscillations of two resonators are found analytically and numerically, and the boundary between these modes in the space of the system parameters is determined. Along with local bifurcation analysis of the considered steady-state modes, global analysis of the evolution and branching of limit cycles in the space of slow variables is also carried out, which makes it possible to detect zones of coexistence of stable synchronization and beat modes with their basins of attraction. The effect of the factor of the designed or technologically determined nonidentity of the design of two resonators on the location of the parametric zones of synchronization and beats is studied. [ABSTRACT FROM AUTHOR]