Obtaining Eringens length scale coefficient for vibrating nonlocal beams via continualization method

Author Type

Outside Researcher

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Faculty

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Journal of Sound and Vibration

Publication Status

Version of Record

Abstract

Eringens length scale coefficients e0 are presented herein for initially stressed vibrating nonlocal beams with various boundary conditions. The coefficients are obtained by applying the continualization method to the discrete equations of microstructured beam models. When compared to another continualized approach that is based on the Padé approximant, the proposed continualization method (which is based on assuming continuous exponential displacement functions for the discrete displacement field) is a more straightforward approach for solution. Unlike the Padé approximant approach, this latter method needs no sophisticated mathematical manipulations for obtaining the continuous equation. Moreover, the continualization method allows one to directly solve the discrete governing equations for vibration of microstructured beams in the discrete domain rather than solving an approximated continuous equation obtained via the Padé approximant. By using this method, it is found that e0=1/12 for the buckling case of beams and e0=1/6 for the vibration case for any combination of end conditions. However, the coefficients are not the same in the presence of an initial stress for vibrating beams with different boundary conditions.

First Page

4977

Last Page

4990

DOI

10.1016/j.jsv.2014.05.002

Publication Date

9-29-2014

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