Investigation of Thermoelastic Wave Propagation in Euler–Bernoulli Beam via Nonlocal Strain Gradient Elasticity and G-N Theory

Abstract

The size-dependent effect arising in micro/nano-structures has attracted considerable attention in academic and industrial communities. The theories developed to characterize such effect mainly include the nonlocal elasticity theory, the strain gradient theory, the modified coupled stress theory and the more recent nonlocal strain gradient elasticity etc. Meanwhile, the thermal-induced deformation or stress in micro/nano-structures is increasingly becoming a vital issue in their designs and applications. Nevertheless, theoretical investigations to predict the thermoelastic performances of micro/nano-structures are not so common, especially in the case of nonlocal strain gradient elasticity incorporating thermoelastic coupling effect. In present work, investigation of thermoelastic wave propagation in micro-beam is conducted in the context of the nonlocal strain gradient elasticity and the G-N theory, taking the thermoelastic coupling effect into account. The governing equations are formulated based on the Euler–Bernoulli beam model and the G-N theory. By assuming the wave-type solutions, the equations are solved and the dispersion relation between frequency and wave number and the relation between phase velocity and wave number are determined respectively. In calculation, the above two relations are fully investigated and comparisons on them under different theories are provided accordingly. Some new findings are presented and discussed in detail. It is hoped that the present work may provide some guidelines in designing and optimizing micro-structures.