An Analytical Solution For Free Vibrations Of A Cantilever Nanobeam With A Spring Mass System

Abstract

An analytical solution for the title problem is presented using the nonlocal elasticity theory based on Euler-Bernoulli beam theory. Fourier sine series is used to represent lateral displacement of the nanobeam. Stokes’ transformation is applied to derive the coefficient matrix of the corresponding systems of linear equations. This matrix also contains the relationship between spring and mass parameters. A convergence study is provided to show how the first three frequency parameter of the nanobeam would converge by an increase of series terms in the literature. The results are given in a series of figures and tables for various combinations of boundary conditions

Keywords

• Nonlocal elasticity theory, nanobeam, Fourier sine series, Stokes’ transformation

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