Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Thermally Induced Vibration of Beams with Consideration of Rotary Inertia

Authors
Mohammad Reza Yaghoubi 1
Yaser Kiani 2
1 Mechanical Engineering Group, College of Engineering, Shahrekord University
2 Sharekord University
Abstract
Present research deals with the thermally induced vibrations of beams. The structure is made of an isotropic homogeneous material and is subjected to rapid surface heating on the upper surface while the lower one in thermally insulated. Based on the assumptions of uncoupled thermo-elasticity, the one-dimensional transient heat conduction equation is solved analytically. The transverse vibration equation of the beam is obtained with the aid of the Euler-Bernoulli assumption with consideration of the rotary inertia. This equation is also solved analytically for simply supported beams using the Fourier series expansion. The solution of this equation is divided into two parts, namely the quasi-static response and the complementary response. All of the results are presented in a dimensionless form and the obtained formula are compared with those provided by neglecting the inertia effects. Finally, graphical presentation of mid-span vibrations of the beam are given which accept the existence of thermally induced vibrations.
Keywords
Euler-Bernoulli Beam
Thermally Induced Vibration
Uncoupled Thermoelasticity
Rotary Inertia

Subjects

 
[1] Boley, B. A., "Thermally Induced Vibrations of Beams", Journal of Aeronautical Sciences, Vol. 23, pp. 170-181, (1956).
 
[2] Boley, B. A., and Barber, A. D., "Dynamic Response of Beams and Plates to Rapid Heating", Journal of Applied Mechanics, Vol. 24, pp. 413-425, (1957).
 
[3] Hetnarski, R., and Eslami, M.R., "Thermal Stresses Advanced Theory and Applications", 1st Editions, Springer, Amsterdam, (2009).
 
[4] Reddy, J.N., "Mechanics of Laminated Composite Plates and Shells", 1st Editions, CRC Press, Boca Raton, (2003).
 
[5] Boley, B. A., and Weiner, J.H.,"Theory of Thermal Stresses", 1st Editions, Wiley, New York, (1960).
Iranian Journal of Mechanical Engineering Transactions of ISME
Volume 19, Issue 3 - Serial Number 48
System Dynamics and Solid Mechanics
Autumn 2016
Pages 108-126

  • Receive Date 28 July 2017
  • Revise Date 17 August 2017
  • Accept Date 21 August 2017