This study presents the frequency analysis of a size-dependent laminated polymer composite microtube using a nonlocal strain-stress gradient (NSG) model. By applying energy methods (known as Hamilton’s principle), the motion equations of the laminated micro tube composites are developed. The thermodynamic equations of the laminated microtube are based on first-order shear deformation theory (FSDT), and a generalized differential quadrature method (GDQM) is employed to find the model for the natural frequencies. The results show that by considering C-F boundary conditions (BCs) and every even layers’ number in lower value of length scale parameter, the frequency of the structure drops by soaring this parameter. However, this matter is inverse in its higher value. Eventually, the ply angle’s influences, nonlocality as well as length scale element on the vibration of the laminated composite microstructure are investigated.
To investigate the surface effects on thermomechanical vibration and buckling of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension, and surface density for modeling the nanoscale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported nanobeam at both ends. Solving these equations enables us to estimate the natural frequency and critical buckling load for circular curved nanobeam including Winkler and Pasternak elastic foundations and under the effect of a uniform temperature change. The results determined are verified by comparing the results with available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations, temperature, and opening angle of circular curved nanobeam on the natural frequency and critical buckling load are successfully studied. The results reveal that the natural frequency and critical buckling load of circular curved nanobeam are significantly influenced by these effects.
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