Free Vibration Analysis of a Rotating Non-uniform Nanocantilever Carrying Arbitrary Concentrated Masses Based on the Nonlocal Timoshenko Beam Using DQEM

Pouretemad, Alireza; Torabi, Keivan; Afshari, Hassan

doi:10.1007/s41403-019-00065-x

Cited by 4 publications

(2 citation statements)

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“…Therefore, by rearranging and partitioning Eqs. (30), (31), (33) and (34) into the boundary, adjacent and domain displacement and rotation components, one reaches the following eigenvalue problem:…”

Section: Differential Quadrature Element Methods (Dqem)mentioning

confidence: 99%

“…He used the Euler-Bernoulli beam theory and Eringen's nonlocal model to derive the equations of motion. Pouretemad et al [34], applied Hamilton's principle and the differential quadrature element method to investigate the effects of rotation and presence of multiple concentrated masses on the vibration behavior of nonlocal Timoshenko beams. They studied various geometric, dynamic and nonlocal conditions for this problem.…”

Section: Introductionmentioning

confidence: 99%

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DQEM analysis of free transverse vibration of rotating non-uniform nanobeams in the presence of cracks based on the nonlocal Timoshenko beam theory

2019

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This paper deals with the free transverse vibration characteristics of a rotating non-uniform nanocantilever with multiple open cracks. Employing Eringen's nonlocal elasticity and the Timoshenko beam theory, the non-dimensional governing differential equations for the above-mentioned problem are derived. The cracked beam is divided into intact sub-beams between two subsequent cracks connected by linear and rotational springs. Differential quadrature element method is utilized to solve the established governing equations of motion of each segment, along with the corresponding boundary conditions and compatibility conditions at the cracked sections. The frequency parameters and vibration modes of the rotating cracked beam for different crack positions and severities under various nonlocal, geometric and dynamic conditions are studied, and the relevant graphs are plotted. Since rotating nanocantilevers are found mostly as blades of rotating nanodevices, the results can provide useful guidance for the study and design of the next generations of nanoturbines, nanogears etc.

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