On opto-thermally excited parametric oscillations of microbeam resonators. I

The present article is the first part of work devoted to investigation nonlinear dynamics parametrically excited flexural vibrations a clamped-clamped microbeam - basic sensitive element promising class microsensors various physical quantities under laser thermooptical action in form periodically generated pulses acting on certain surface beam element. An analytical solution heat transfer problem found for steady harmonic distribution temperature volume resonator. static and dynamic components temperature-induced axial force bending moment are determined. Using Galerkin method, discretization coupled partial differential equations describing longitudinal-flexural oscillations resonator performed. asymptotic method multiple time-scales, an approximate obtained conditions primary parametric resonance.