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Longitudinal vibration analysis of nonlocal nanorods with elastic end restraints by an improved Fourier series method

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In this paper, an exact solution for the free longitudinal vibration of nanorod with arbitrary boundary conditions has been developed by an improved Fourier series method. Based on the nonlocal elasticity theory, the nanorod model with general boundary restraints has been formulated by introducing artificial springs and then all the classical boundary conditions can be simply realized by setting the spring stiffness to zero or infinity accordingly. With the aim to guarantee the differential continuities at both elastically restrained ends, the nonlocal axial displacement is invariantly expanded as the superposition of standard Fourier series and the auxiliary polynomials to ensure that the field function is sufficiently smooth in the whole region [0, L]. The problem is then tackled by solving the nonlocal governing equation and boundary conditions simultaneously in an exact manner. Numerical results are presented and compared with those in the literature to illustrate the reliability and effectiveness of the proposed model. The combined influences of small-scale parameter, boundary conditions and nanorod length on the longitudinal modal behavior are discussed and analyzed. This work can provide an efficient way for the longitudinal vibration characteristics study of nanorod, especially with complicated boundary conditions.
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Keywords: 41.1; 74.8

Document Type: Research Article

Affiliations: Harbin Engineering Univesity

Publication date: November 1, 2016

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