Timoshenko Theory Of Elasticity Pdf Download

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 couple stress theory which implies prediction of size-dependent 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.

More recently theories of continuum of a higher order for prediction of the mentioned size-dependent relations were developed [63]. In the 1960s, some of researchers proposed a couple stress theory of elasticity which can be classified as the non-classical theory [64]. The theory made it possible to interpret the size-dependent effects using two higher-order material constants in state equations. A simplification introduced by Yang et al. [65] to the scale complex relations of the couple stress theory of elasticity resulted in a modified coupled stress theory which is suitable because of effects using only one scale parameter of the material length. Recently, many researchers investigated non-classical theorems of continuum in order to formulate and study the size-dependent mechanical behaviour of beams and plates.

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in general, the thermoelastic PDEs governing the dynamics of microbeams were obtained based on the classical theory of continuum. There are no sufficient results following from the nonlinear model of coupled thermoelasticity of the Timoshenko microbeams based on the MCST.

Our work is aimed at filling the gaps that exist in the research of MEMS/NEMS resonators. In this work, we employ the MCST to study quality factor of microbeam resonators with an account of thermoelastic damping and geometric nonlinearity. The associated mathematical model is constructed which, in contrary to the classical theory, consists of the internal scale length material parameter allowing for a reliable prediction of the size-dependent effect in microbeam resonators. The Hamilton principle yields coupled nonlinear thermoelastic equations of motion of the Timoshenko microbeams in the case of plane stress/deflection state. Based on the obtained equations, both analytical and numerical investigations of the nonlinear thermoelastic vibrations of the microbeams are carried out and then, the values of quality factors of the resonators versus geometric and material microbeam properties are estimated. The results are presented for gold microbeams at different ambient temperatures and beam thicknesses which are compared with the results obtained based on the classical theory of elasticity in both linear and nonlinear cases.

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