Modeling the thermal dynamic behavior of a perforated Timoshenko nanobeam with deformable ends based on nonlocal elasticity

In this study, the thermo-mechanical dynamic behavior of a perforated nanobeam is performed under non-rigid boundary conditions. The Timoshenko beam theory is utilized in conjunction with nonlocal elasticity theory to capture size-dependent effects. Thermal loads are incorporated to investigate the vibration behavior under varying temperature conditions. The displacement field is defined in three different forms: the two ends of the nanobeam are represented by constant coefficients, while the region between them is expressed using the Fourier sine series. Since the governing equation is reduced to a form that depends only on the lateral displacement function, it is sufficient to use the Fourier sine series. Then, Stokes' transforms are applied to introduce boundary flexibility analytically. Based on the force boundary conditions, a general eigenvalue problem is formulated. Solving the characteristic equation derived from this eigenvalue problem yields the natural frequencies of the perforated Timoshenko nanobeam considering the combined effects of hole, nonlocality, thermal loading and boundary flexibility. The summarized results indicate that increasing the number of holes, the nonlocal parameter and the thermal load causes a decrease in the natural frequencies of the nanobeam. Conversely, an increment in the filling ratio and the spring coefficients at the boundaries leads to an increase in the vibration frequencies. In addition, detailed analyses are provided. The study results are expected to be useful for nano devices with perforated structures and vibration behavior.