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The dependence of the quality factor of nonlinear microbeam resonators under thermoelastic damping for Timoshenko beams with regard to geometric nonlinearity has been studied. The constructed mathematical model is based on the modified cou-Russian Federation 634050 ple stress theory which implies prediction of sizedependent effects in microbeam resonators. The Hamilton principle has yielded coupled nonlinear thermoelastic PDEs governing dynamics of the Timoshenko microbeams for both plane stresses and plane deformations. Nonlinear thermoelastic vibrations are studied analytically and numerically and quality factors of the resonators versus geometric and material microbeam properties are estimated. Results are presented for gold microbeams for different ambient temperatures and different beam thicknesses, and they are compared with results yielded by the classical theory of elasticity in linear/nonlinear cases.

Regular and chaotic dynamics of the flexible Timoshenko-type beams is studied using both the standard Fourier (FFT) and the continuous wavelet transform methods. The governing equations of motion for geometrically nonlinear Timoshenko-type beams are reduced to a system of ODEs using both finite element method (FEM) and finite difference method (FDM) to ensure the reliability of numerical results. Scenarios of transition from regular to chaotic vibrations and beam dynamical stability loss are analyzed. Advantages and disadvantages of various wavelet functions are discussed. Application of continuous wavelet transform to the investigation of transitional and chaotic phenomena in nonlinear dynamics is illustrated and discussed.

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