Vibration analysis of a rotating cantilever double-tapered AFGM nanobeam
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TECHNICAL PAPER
Vibration analysis of a rotating cantilever double-tapered AFGM nanobeam Mohammadali Ghafarian1
•
Bijan Shirinzadeh1 • Weichen Wei1
Received: 15 February 2020 / Accepted: 30 March 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Nano-structures such as carbon nanotube, nanobeams, nanorods, nanoplates, nanowires, and nanorings are tremendously used in various small-scale devices and investigating their dynamical behavior has been a hot research topic and can be beneficial in manufacturing and designing new devices. Therefore, free vibration analysis of a rotating cantilever doubletapered axially functionally graded material nanobeam is presented in this work. Due to the nano-scale dimension, classical beam theories are incompetent at describing the behavior of nanobeams. Thus, the nonlocal Eringen elasticity theory is adopted which considers the nonlocal scale effect for the small dimension effect of the structure of a nano-scale mechanism. The proposed nanobeam structure is assumed to taper linearly in two different axes, and its material is changing nonlinearly along its length. The equation of motion of the proposed system is found utilizing the nonlocal Eringen theory, and it is solved using a semi-analytical technique, differential transform method. Mode shapes and natural frequencies are extracted as the solution of the equation of motion of the system. Furthermore, the effects of several parameters such as nonlocal scale effect, rotational speed, hub radius, and taper ratios on the natural frequencies are investigated. Finally, a comparison between the presented work and other reported results show an excellent agreement.
1 Introduction Beams are crucial components in any mechanical structure such as automotive and aircraft components, machine frames, and other mechanical or structural systems that contain beam structures and are designed to carry structural loads. Flexure beams with small thickness have been used widely in micro/nano manipulation mechanisms and grippers. Many studies (Ghafarian et al. 2018, 2019; Zhang et al. 2017; Pinskier and Shirinzadeh 2019; Gu et al. 2018) have been conducted on the design, analysis, and optimization of flexure beams for Micro/Nano electromechanical systems’ (MEMS/NEMS) applications. Dynamic analysis of micro/nano beams is essential as the strength and desired performances of the structure directly related to the dynamic characteristics. Therefore, during the past decade, there have been important insights into the modeling of the vibrational behavior of such micro/nano & Mohammadali Ghafarian [email protected] 1
Robotics and Mechatronics Research Laboratory (RMRL), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
structures. Nanobeams are an essential component which have been used in biomedical sensors (e-nose), atomic force microscopy (AFM), nanoscale memory devices, photonic crystal nanobeam cavities, res
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