Abstract
In this paper, transverse vibration analysis of rotating micro-beam is investigated based on the modified couple stress theory. The simply-supported micro-beam is modeled utilizing Euler-Bernoulli and Timoshenko beam theories. The system is rotating around a fixed axis perpendicular to the axial direction of the beam. For the first time, displacement filed is introduced as a coupled field to the translational field. In other words, the mentioned rotational displacement field is expressed as a proportional function of translational displacement field using first (axial), second (lateral), and third (angular or rotational) velocity factors. Utilizing Hamilton’s approach as a variational method, dynamic-vibration equations of motion of the proposed model are derived. Galerkin’s method is adopted to solve the equation corresponding to the Euler–Bernoulli and Timoshenko beams. For the case considering shear deformation effects, Navier method is chosen. For evaluation of current results and models, they are compared with those available at the benchmark. In this paper; effects of slenderness ratio, axial, lateral, and angular velocity factors, and rotations of the beam on the frequency are reported. Based on the results presented, mentioned factors should be counted in the analysis and design of such rotating micro-systems.
Highlights
Accepted: 13 April 2021Through the past decade, micro-electro-mechanical-system (MEMS) technology has been attractive to a significant number of researchers from Mechanical, Electrical, Chemical, and Biomedical engineering
Ω = ωL2 ρA/EIin In Table 1, current results based on the modified couple stress theory are compared with results of Rahmani and Pedram (2014) and Eltaher et al (2013), based on the nonlocal theory (NLET)
10.3849 In Table 1, we have provided the results for small values of slenderness ratio
Summary
Micro-electro-mechanical-system (MEMS) technology has been attractive to a significant number of researchers from Mechanical, Electrical, Chemical, and Biomedical engineering. Based on the mentioned non-classical theory, several researchers have studied static and dynamic analysis of micro and nano-scaled systems. Bending and vibration analysis of a micro-beam considering position of the neutral axis is carried out by Al-Basyouni et al [19] They suggested a variable material length scale parameter. Changing material length scale parameter effects upon the dynamic-vibration analysis of Timoshenko beam is studied by Babaei and Rahmani [27]. Babaei et al [29] carried out the vibrational analysis of a micro-Euler–Bernoulli beam, in which thermo-mechanical properties vary through thickness direction They proposed the model based on the modified couple stress theory. According to the presented literature review, there is not any published research work about vibration analysis of rotating micro-beams based on the coupled displacement filed and accounting the shearing effects in the course of Timoshenko beam model. ), u is displacement vector, l is nonclassical material length scale parameter, G is shear modulus of rigidity, λ shows Lame’s constant, Id shows identity tensor, and θ is rotation vector
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