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Theoretical studies on the vibration of microcantilever beams in fluids, which are commonly used in micro- and nanoelectromechanical systems (MEMS/NEMS). When microcantilever beams are subjected to photo-thermal excitation, they show that the material properties such as the dynamic response and the one-dimensional temperature field will show significant differences from the macroscopic properties when the size appearance of the microbeam decreases to the scale below a dozen micrometers. In this paper, by correcting the scale constants of the beams, the photothermal vibration model of the microbeam is established using the physical neutral plane theory. The one-dimensional heat transfer equations and scale-corrected temperature field of the microcantilever beam under laser excitation are derived, which are solved by Galerkin’s method, based on the theory of thermoelasticity, the hydrodynamic model of the beams vibrating in incompressible liquids proposed by Sader et al. and the theory of Euler–Bernoulli beams. The equations governing the vibration of micro-cantilever beams corrected for scale effects in different fluids when subjected to photothermal excitation are obtained. The results show that the temperature field, resonant frequency, and quality factor of the microbeam will have a significant upward drift when the size of the microbeam is close to the scale parameter, and the scale effect has a non-negligible influence on the macroscopic performance parameters; the upward drift is gradually weakening when the thickness to scale ratio gradually increases. Finally, the property of the beam is almost the same as that of the theory when the thickness of the beam is 10 times the scale constant. The correction of the theory by the scale effect is insignificant.

Various non-classical continuum mechanics models appearing in previous studies cannot perfectly explain the mechanical properties of micro- and nanomaterials. Establishing a reasonable continuum mechanics model that comprehensively reflects the scale effect on material deformation is of great practical significance for objectively explaining the variation law of mechanical properties of micro- and nanomaterials under the combined action of different scale effects. Based on nonlocal strain gradient theory, a new scale-dependent model is proposed for axially moving nanobeams. In this study, an asymptotic expansion is performed using the multiscale time method to obtain the amplitude-frequency response curve of the equilibrium solutions for the forced vibration problem. Afterwards, the effects of various system parameters, especially the scale parameters, on the resonance curve are examined. Finally, the effects of nonlocal parameters and material characteristic length parameters on the amplitude-frequency response curves are investigated through typical numerical examples. The numerical results show that the nonlocal parameters promote the emergence of the main resonance, whereas the material characteristic length parameters suppress the emergence of the main resonance. Moreover, these parameters also affect the response amplitude and the skewness and jumping point of the amplitude-frequency characteristic curve.

In this paper, we investigate the lateral deflection of a simply supported periodic stepped beam under uniform load by using an analytical method. This study considers each element of the biperiodic stepped beam as a Euler–Bernoulli beam. By using the local coordinates alongside with the boundary and continuity conditions, the different coefficients for each element caused by the jump of the bending rigidity are calculated. The continuous deflection problem of the multi-stepped repetitive beam is formulated as a linear first-order difference equation with second member. With these coefficients, the deflection at mid-span of the biperiodic beam is analytically found in exact form. This deflection is satisfactory compared to the results of a finite element model based on beam discretization techniques using Hermitian cubic shape functions. The normalized deflection at mid span converges non-monotonically towards the homogenization beam model based on equivalent homogenized stiffness.

Coupled thermoelastic analysis in the study of microscale solid mechanics has attracted considerable attention along with the miniaturization and functionalization of devices. Higher-order continuum mechanics theories have considered scale effects; however, the theories to predict thermoelastic performances of structures in micro-scale are still incomplete. The purpose of this paper is to study scale and thermal-induced effects by considering stress nonlocality and strain gradient elasticity in micro-structure resonators. The thermoelastic constitutive relations are established based on the nonlocal strain gradient (NSG) theory. The wave propagation problem of a Timoshenko micro-beam in conjunction with Green and Naghdi’s generalized thermoelastic (G–N) theory is investigated. The governing equations are derived and analytically solved by the eigenvalue method. Finally, the dispersion relation of a frequency spectrum is determined and the influences of scale parameters and coupled thermoelastic effect are discussed; in addition, the analysis results are compared with those under different size-dependent theories accordingly.