LONGITUDINAL VIBRATION ANALYSIS OF STRAIN GRADIENT ELASTIC BAR WITH VARIOUS BOUNDARY CONDITIONS

Vlasios Dimosthenis

doi:10.5937/jaes0-51432

Vlasios Dimosthenis Aristotle University of Thessaloniki, Faculty of Engineering, School of Civil Engineering, Hellas https://orcid.org/0000-0003-3521-2284

DOI: https://doi.org/10.5937/jaes0-51432

Keywords: longitudinal free vibration, bar, strain gradient elasticity, GradEla, boundary conditions

Abstract

In this paper, strain gradient elasticity (GradEla) is employed to investigate bar's longitudinal free vibration (LFV) behavior with several boundary conditions (BCs). The governing differential equation of motion for the bar is derived using Hamilton's principle. Various combinations of clamped, free, attached mass and/or spring BCs are used to solve it analytically. Notably, many of these solutions are the first in the literature for the gradient elastic bars. The effect of the internal length parameter, the modes, the attachments, the BCs, and the length of the bar is identified and assessed. It is concluded that the GradEla bar shows size-dependent and stiffer mechanical behavior compared with the classical one. Also, the presence of mass mainly decreases the longitudinal frequencies (LF) of bars, while the presence of the spring increases them. In addition, GradEla is applied to model a literature experiment demonstrating its applicability in real problems. Presenting these novel solutions and showcasing their effectiveness through experimental validation contributes to the advancement of understanding the use of GradEla theory in a wide range of longitudinal vibration (LV) problems of structural mechanics.

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