Nonlocal Vibration Analysis for Micro/Nano Beam on Winkler Foundation via DTM

Abstract

In the present study, vibration of micro/nano beams on Winkler foundation is studied using Eringen's nonlocal elasticity theoy. Hamilton’s principle is employed to derive the governing equations. Differential transform method is used to obtain result. Simply supported and clamped–clamped boundary conditions are used to study natural frequencies. The effect of nonlocal parameter and Winkler elastic foundation modulus on the natural frequencies of the nonlocal Euler-Bernoulli beam is investigated and tabulated. The differential transform method is applicable for micro/nano beams and gives high accuracy results.

Keywords

• Natural frequency,differential transforms method,nonlocal elasticity theory,Winkler elastic foundation

References

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