Dynamic Stability of Nano FGM Beam Using Timoshenko Theory

Document Type : Persian

Authors

1 MSc Student, Department of Mechanical Engineering, Islamic Azad University, Khomeinishar Branch, Esfahan, Iran

2 Assistant Prof., Department of Mechanical Engineering, Islamic Azad University, Khomeinishar Branch, Esfahan, Iran

Abstract

Based on the nonlocal Timoshenko beam theory, the dynamic stability of functionally gradded (FG) nanoeams under axial load is studied in thermal environment, with considering surface effect. It is used power law distribution for FGM and the surface stress effects are considered based on Gurtin-Murdoch continuum theory. Using Von Karman geometric nonlinearity, governing equations are derived based on Hamilton’s principle. The developed nonlocal models have the capability to interpret small scale effects. Winkler and Pasternak types elastic foundation are employed to represent the interaction of the nano FG beam and the surrounding elastic medium. A parametric study is conducted to investigate the influences of the static load factor, temperature change, nonlocal elastic parameter, slenderness ratio, surface effect and springs constant of the elastic medium on the dynamic stability characteristics of the FG beam, with simply-supported boundary conditions. It is found that the difference between instability regions predicted by local and nonlocal beam theories is significant for nanobeams with lower aspect ratios. Moreover, it is observed that in contrast to high temperature environments, at low temperatures, increasing the temperature change moves the origins of the instability regions to higher excitation frequencies and leads to further stability of the system at lower excitation frequencies, considering surface stress effect shifts the FG beam to higher frequency zone

Keywords

References

[1] Peddieson, J., G.R. Buchanan, and R.P.   McNitt, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, vol. 41, No. 3–5, 2003, pp. 305-312.
[2] قربانپورآرانی ع.، شریف زارعی م.، محمدی مهر م.،  تأثیرحرارت بر کمانش پیچشی نانو لوله کربنی دو جداره تحت بستر الاستیک نوع پاسترناک، فصل نامه علمی پژوهشی مکانیک جامدات، سال 4، شماره 1، 2011،  صفحات 11 تا 16.
[3] الهامی م.،  زینلی م.، تحلیل پایداری دینامیکی یک تیر دو سر آزاد تحت نیروی تعقیب­کننده ناپایستار، مجله مکانیک هوا فضا، سال 7، شماره 1، 2011، صفحات 15 تا 26.
[4] Ansari R., Gholami R., Sahmani S., On the dynamic stability of embedded single-walled carbon nanotubes including thermal environment effects, Scientia Iranica, vol. 19, No. 3, 2012, pp. 919-925.
[5] Hosseini-Hashemi S. Nazemnezhad R., An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects, Composites Part B: Engineering, vol. 52, 2013, pp. 199-206.
[6] Eltaher M.A., et al., Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position, Applied Mathematics and Computation, vol. 235, 2014, pp. 512-529.
[7] Malekzadeh P. Shojaee M., Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams, Composites Part B: Engineering, vol. 52, 2013, pp. 84-92.
[8] Ansari, R., et al., Nonlinear vibration analysis of Timoshenko nanobeams based on surface stress elasticity theory, European Journal of Mechanics - A/Solids, vol. 45, 2014. pp. 143-152.
[9] Ghorbanpour Arani A., Kolahchi R., Hashemian M., Nonlocal surface piezoelasticity theory for dynamic stability of double-welled boron nitride nanotube conveying viscose fluid based on different theories, Mechanical Engineering Science, 2014, pp. 23.
[10] Goldberg J.E., The dynamic stability of elastic systems: by V. V. Bolotin. Russian trans. by V. I. Weingaxten et al. 451 pages, diagrams, 7 × 10 in. San Francisco, Calif., Holden-Day, Inc., 1964. Price, $12.95, Journal of the Franklin Institute, vol. 279, No. 6, 1965, pp. 478-479.
 
 
 
 
 
 
Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering
Volume 8, Issue 4 - Serial Number 4
Winter 2015
Pages 239-250

Files

Share

How to cite

Statistics