Free flexural vibrations of nanobeams with non-classical boundary conditions using stress-driven nonlocal model. (July 2020)

• Record Type: Journal Article
• Authors: Luciano, Raimondo; Darban, Hossein; Bartolomeo, Chiara; Fabbrocino, Francesco; Scorza, Daniela
• Is Part Of: Mechanics research communications. Volume 107(2020)
• Publication Date: 2020-07
• Subjects: Elastically constrained beam -- Nanostructures -- Natural frequency -- Size effects -- Well-posed nonlocal formulation; Mechanics, Applied -- Periodicals; Mécanique appliquée -- Périodiques; Mechanics, Applied; Periodicals; 530
• DOI: 10.1016/j.mechrescom.2020.103536
• Languages: English
• ISSNs: 0093-6413

Abstract

Highlights: Free vibrations of nanobeams with non-rigid edge supports are studied through SDM. An analytical closed form solution of spatial differential equation is proposed. Effects of non-rigid supports and nonlocal parameter on natural frequencies are studied. Higher vibrations modes are also studied. Comparison between present solutions and results in the literature is excellent. Abstract: Free flexural vibrations of nanobeams with non-rigid edge supports are studied by means of the stress-driven nonlocal elasticity model and Euler-Bernoulli kinematics. The elastic deformations of the supports are modelled by transversal and flexural springs, so that, in the limit conditions when the springs stiffnesses tend to zero or infinity, the classical free, pinned, and clamped boundary conditions may be recovered. An analytical procedure is used to derive the closed form solution of the spatial differential equation. The problem of finding the natural frequencies is then reduced to find the roots of the determinant of a matrix, whose elements are explicitly given. The proposed technique, then, avoids the numerical instabilities usually arising when the numerical techniques are used to obtain the solution. The effects of both non-rigid supports elastic deformations and nonlocal parameter on the natural frequencies are studied also for higher vibrations modes. The comparison between the solutions of the proposed model and those available in the literature shows an excellent agreement, and new insightful results and discussions are presented.