On Opto-Thermally Excited Parametric Oscillations of Microbeam Resonators. I

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.