Nonlocal fully intrinsic equations for free vibration of Euler–Bernoulli beams with constitutive boundary conditions

Abstract

Fully intrinsic beam theory has presented a relatively new set of equations for modeling of one-dimensional structures. Although this method can be utilized as a useful tool for modeling beam-like structures, it is scale independent and cannot be accurately employed when the size of a structure becomes comparable with its internal characteristic length. In this paper, we develop nonlocal fully intrinsic equations for accommodating the small-scale effect and overcoming this limitation. The original fully intrinsic equations are thus reformulated using the nonlocal differential constitutive relations of Eringen. The so-called constitutive boundary conditions are considered. Here the generalized differential quadrature method is used for numerically solving the nonlocal fully intrinsic equations. Furthermore, applicability of the present formulations for free vibration of both uniform and nonuniform Euler–Bernoulli beams is discussed. Moreover, it is shown that the present formulation is accurate and useful for predicting the mechanical behavior of micro- and nanobeams.