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Original Articles

Vibrational Analysis for an Axially Moving Microbeam with Two Temperatures

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Pages 569-590 | Received 25 May 2014, Accepted 06 Aug 2014, Published online: 30 Apr 2015

REFERENCES

  • J. A. Wickert and C. D. Mote Jr ., Current Research on the Vibration and Stability of Axially Moving Materials , Shock Vibration Digest , vol. 20 , pp. 3 – 13 , 1988 .
  • J. A. Wickert and C. D. Mote , Jr., Classical Vibration Analysis of Axially-Moving Continua , Journal of Applied Mechanics ASME , vol. 57 , pp. 738 – 744 , 1990 .
  • L. Q. Chen and J. W. Zu , Transverse Vibration of Axially Moving Strings and its Control , Advanced Mechanics , vol. 31 , pp. 535 – 546 , 2001 .
  • L. Q. Chen , Analysis and Control of Transverse Vibrations of Axially Moving Strings , Applied Mechanics Review ASME , vol. 58 , pp. 91 – 116 , 2005 .
  • G. Chakraborty and A. K. Mallik , Wave Propagation in and Vibration of a Traveling Beam with and Without Non-linear Effects , Journal of Sound and Vibration , vol. 236 , no. 2 , pp. 277 – 290 , 2000 .
  • L. Kong and G. Parker , Approximate Eigensolutions of Axially Moving Beams with Small Flexural Stiffness , Journal of Sound and Vibration , vol. 276 , no. 2 , pp. 459 – 469 , 2004 .
  • X. D. Yang , Determination of the Natural Frequencies of Axially Moving Beams by the Method of Multiple Scales , Journal of Shanghai University , vol. 11 , no. 3 , pp. 251 – 254 , 2007 .
  • J. Avsec and M. Oblak , Thermal Vibrational Analysis for Simply Supported Beam and Clamped Beam , Journal of Sound and Vibration , vol. 308 , no. 3 , pp. 514 – 525 , 2007 .
  • M. Emil and R. Pedro , Coupled, Thermoelastic, Large Amplitude Vibrations of Timoshenko Beams , International Journal of Mechanical Sciences , vol. 46 , pp. 1589 – 1606 , 2004 .
  • W. P. Chang and S. M. Wan , Thermomechanically Coupled Nonlinear Vibration of Plates , International Journal of Non-linear Mechanics , vol. 21 , no. 5 , pp. 375 – 389 , 1986 .
  • M. A. Biot , Thermoelasticity and Irreversible Thermodynamics, Journal of Applied Physics , vol. 27, no. 3, pp. 240–253, 1956.
  • H. W. Lord and Y. Shulman , A Generalized Dynamical Theory of Thermoelasticity , Journal of the Mechanics and Physics of Solids , vol. 15 , pp. 299 – 309 , 1967 .
  • P. J. Chen and M. E. Gurtin , On a Theory of Heat Conduction Involving Two Temperatures , Zeitschrift für angewandte Mathematik und Physik , vol. 19 , pp. 614 – 627 , 1968 .
  • P. J. Chen , M. E. Gurtin , and W. O. Willams , On the Thermodynamics of Non-simple Elastic Material with Two Temperatures , Zeitschrift für angewandte Mathematik und Physik , vol. 20 , pp. 107 – 112 , 1969 .
  • W. E. Warren and P. J. Chen , Wave Propagation in the Two Temperature Theory of Thermoelasticity , Acta Mechanica , vol. 16 , pp. 21 – 23 , 1973 .
  • R. Quintanilla , On Existence, Structural Stability, Convergence and Spatial Behavior in Thermoelastic with Two Temperatures , Acta Mechanica , vol. 168 , pp. 161 – 173 , 2004 .
  • R. Quintanilla , Exponential Stability and Uniqueness in Thermoelasticity with Two Temperatures , Dynamics of Continuous, Discrete and Impulsive Systems A , vol. 11 , pp. 57 – 68 , 2004 .
  • I. A. Abbas and A. N. Abd-alla , Effects of Thermal Relaxations on Thermoelastic Interactions in an Infinite Orthotropic Elastic Medium with a Cylindrical Cavity , Archive of Applied Mechanics , vol. 78 , pp. 283 – 293 , 2008 .
  • I. A. Abbas and H. M. Youssef , Two-Temperature Generalized Thermoelasticity under Ramp-type Heating by Finite Element Method , Meccanica , vol. 48 , no. 2 , pp. 331 – 339 , 2013 .
  • A. M. Zenkour , D. S. Mashat , and A. E. Abouelregal , The Effect of Dual-Phase-Lag Model on Reflection of Thermoelastic Waves in a Solid Half Space with Variable Material Properties , Acta Mechanica Solida Sinica , vol. 26 , pp. 659 – 670 , 2013 .
  • I. A. Abbas and A. M. Zenkour , Dual-Phase-Lag Model on Thermoelastic Interactions in a Semi-Infinite Medium Subjected to a Ramp-Type Heating , Journal of Computational and Theoretical Nanosciences , vol. 11 , pp. 642 – 645 , 2014 .
  • A. M. Zenkour and A. E. Abouelregal , The Effect of Two Temperatures on a Functionally Graded Nanobeam Induced by a Sinusoidal Pulse Heating , Structural Engineering and Mechanics, An International Journal , vol. 51 , no. 2 , pp. 199 – 214 , 2014 .
  • A. M. Zenkour , and A. E. Abouelregal , Effect of Harmonically Varying Heat on FG Nanobeams in the Context of a Nonlocal Two-Temperature Thermoelasticity Theory , European Journal of Computational Mechanics , vol. 23 , no. 1–2 , pp. 1 – 14 , 2014 .
  • I. A. Abbas and A. M. Zenkour , Two-Temperature Generalized Thermoelastic Interaction in an Infinite Fiber-Reinforced Anisotropic Plate Containing a Circular Cavity with Two Relaxation Times , Journal of Computational and Theoretical Nanoscience , vol. 11 , no. 1 , pp. 1 – 7 , 2014 .
  • A. M. Zenkour and A. E. Abouelregal , State-Space Approach for an Infinite Medium with a Spherical Cavity Based upon Two-Temperature Generalized Thermoelasticity Theory and Fractional Heat Conduction , Zeitschriftfuer Angewandte-Mathematik und Physik (ZAMP) , vol. 65 , no. 1 , pp. 149 – 164 , 2014 .
  • D. Y. Tzou , Macro-to-Microscale Heat Transfer: The Lagging Behavior , Taylor & Francis , Washington , DC , 1996 .
  • Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uths.

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