Thermal vibration of nonhomogeneous Euler nanobeam resting on Winkler foundation. (July 2022) - Karmakar, Somnath; Chakraverty, S.
Abstract: In this paper, thermal vibration of nonhomogeneous Euler nanobeam resting on Winkler foundation is investigated. For this purpose, at first, Euler–Bernoulli beam theory is used and the governing differential equations are obtained by using Hamilton's principle. The nonlocal strain gradient theory is implemented to capture the small scale effects. Adomian decomposition Method (ADM) and Homotopy Perturbation Method (HPM) are used to obtain the frequencies of vibration. Also, the nonhomogeneous beam model has been considered, where Young's modulus and density of the beam vary linearly and quadratically with respect to longitudinal direction of the beam for three different boundary conditions: simply supported, clamped, and clamped simply supported.