Strain gradient torsional vibration analysis of micro/nano rods

Document Type : Reasearch Paper


1 Defence Research and Development Laboratory, Kanchanbagh, Hyderabad-500 058, India.

2 Department of Mechanical Engineering, Vardhaman College of Engineering, Shamshabad, Hyderabad-501 218, India.

3 Department of Aerospace Engineering. Indian Institute of Science, Bangalore-560 012, India.



Fabrication, characterization and application of micro-/nano-rods/wires are among the hottest topics in materials science and applied physics. Micro-/nano-rod-based structures and devices are developed for a wide-ranging use in various fields of micro-/nanoscience (e.g. biology, electronics, medicine, optics, optoelectronics, photonics and sensors). It is well known that the structure and properties of micro/nano rods depend greatly on their environment of application. Therefore, in this paper, torsional vibration of microbars is formulated based on the strain gradient theory to study the vibrational behavior at micro/nano scale. The strain gradient theory is a non-classical theory capable of capturing the size-effects. The governing equation and both the classical and the non-classical boundary conditions are derived employing the Hamilton’s principle. In the free-vibration case, the characteristic equation is derived and solved analytically. The torsional free-vibration behavior of a fixed-fixed strain gradient microbar is investigated and the results are compared to those evaluated by the classical and modified couple stress theories noted that the two latter theories are special cases of the strain gradient theory. The effects of the length and the radius of the micro rods on the various modes of torsional natural frequencies are investigated in detail. The results of this study can be useful in the design and analysis of the next generation micro-electro-mechanical-systems and nano-electro-mechanical-systems which uses the torsional vibration properties of the micro-/nano-rods.