Vibration characteristics of nanobeam with exponentially varying flexural rigidity resting on linearly varying elastic foundation using differential quadrature method

Abstract

The target of the present research is to analyze the free vibration of non-uniform nanobeam resting on variable Winkler elastic foundation using the differential quadrature method. Non-uniformity in nanobeam is taken along the flexural rigidity, and the nanobeam is modeled with linearly varying Winkler elastic foundation. Eringen’s nonlocal theory is employed in Euler–Bernoulli beam theory for different scaling parameters concerning the boundary conditions are explored. In order to illustrate the efficiency and accuracy of the method, the convergence study is carried out, and the obtained results are validated with known results in particular cases showing excellent agreement. Further, the sensitivity analysis of frequency parameters is carried out to examine the response of various scaling parameters.