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This work aims to assess the response of viscoelastic Kelvin–Voigt microscale beams under initial stress. The microbeam is photostimulated by the light emitted by an intense picosecond pulsed laser. The photothermal elasticity model with dual-phase lags, the plasma wave equation and Euler–Bernoulli beam theory are utilized to construct the system equations governing the thermoelastic vibrations of microbeams. Using the Laplace transform technique, the problem is solved analytically and expressions are provided for the distributions of photothermal fields. Taking aluminum as a numerical example, the effect of the pulsed laser duration coefficient, viscoelasticity constants and initial stress on photothermal vibrations has been studied. In addition, a comparison has been made between different models of photo-thermoelasticity to validate the results of the current model. Photo-microdynamic systems might be monolithically integrated on aluminum microbeams using microsurface processing technology as a result of this research.

This investigation uses the absolute nodal coordinate formulation (ANCF) method to solve statics and dynamics of microbeams for the first time. A comprehensive model for the investigation of statics and dynamics of microbeams by using gradient deficient elements of the ANCF and modified couple stress theory (MCST) is developed. The vibration equations of a planar hub-microbeam system with constant angular rotations are derived considering the static equilibrium. Accuracy of the ANCF method for microbeams is demonstrated. Large deformation problems of cantilever microbeams are solved and the influences of material length scale on beam deformation are studied. When the beam thickness becomes smaller, the deflection of the microbeam calculated by the current model is smaller, and the size effect becomes more significant. The size effect only has influence on the bending vibration of the microbeam. The variations of the angular speed as well as the scale parameter can trigger frequency veering phenomena. The present work could be used in dynamic or vibration predictions for microelectromechanical systems (MEMS) with both large displacements and large deformations.

The nonlinear forced vibrations of size-dependent clamped–hinged microbeams to fundamental excitations of respectively the first mode and second mode in the presence of three-to-one internal resonance are investigated both analytically and numerically for the first time. Equation of motion incorporating large deflection, along with the symmetric part of couple stress is derived by virtue of Hamilton’s principle. Utilizing Galerkin discretization with the first two modes, the discretized ordinary differential equations (ODEs) are then handled analytically with multi-dimensional Lindstedt–Poincaré (MDLP) method. The frequency–response relationships in the fundamental resonance for the first mode and the second mode are presented as well as compared with the classical solution. Results reveal that the size-dependent internal resonances are significantly different from the classical situation whenever it is of the first mode or the second mode. Furthermore, the influences of material length scale parameter, excitation force and damping on the performance of nonlinear system are discussed for fundamental excitation of the first order. The frequency–response relationships are illustrated for the first two modes in each case. Moreover, numerical modelings are conducted to compare to the analytical solutions. The numerical results fully support the analytical predictions. Also, simulations indicate the appearance of chaos under relatively large excitation force whether it is the vibration of the first mode or the second mode.