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Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads

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Abstract

The exact thermoelastic analysis of a functionally graded piezoelectrical (FGP) rotating cylinder is investigated analytically. The cylinder is subjected to a combination of electrical, thermal, and mechanical loads simultaneously. The structure is a simplified model of a rotational sensor or actuator. The basic governing differential equation of the system is obtained by using the energy method. A novel term, named as the additional energy, is introduced to exact the evaluation of the energy functional. The solution to the governing differential equation is presented for two types of boundary conditions including free rotating and rotating cylinders exposed to the inner pressure. The effect of the angular velocity is investigated on the radial distribution of various components. The mentioned structure can be considered as a sensor for measuring the angular velocity of the cylinder subjected to the pressure and temperature. The obtained results indicate that the electrical potential is proportional to the angular velocity.

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Abbreviations

C :

elastic stiffness

D :

electrical displacement

e :

piezoelectric coefficient

k :

heat conductivity coefficient

p :

pyroelectric coefficient

P i :

inner pressure

r :

radius

E r :

electrical field

T :

temperature

u :

displacement

W b :

body force energy

Q T :

additional energy

J :

Jacobin

α :

heat expansion coefficient

φ :

electrical potential

η :

dielectric coefficient

σ :

stress

ɛ :

strain

References

  1. Liu, X., Wang, Q., and Quek, S. T. Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates. International Journal of Solids and Structures, 39, 2129–2151 (2002)

    Article  MATH  Google Scholar 

  2. Hou, P. F. and Leung, A. Y. T. The transient responses of magneto-electro-elastic hollow cylinders. Smart Materials and Structures, 13(4), 762–776 (2004)

    Article  Google Scholar 

  3. Kollias, A. T. and Avaritsiotis, J. N. A study on the performance of bending mode piezoelectric accelerometers. Sensors and Actuators A: Physical, 121, 434–442 (2005)

    Article  Google Scholar 

  4. Dai, H. L. and Wang, X. Stress wave propagation in piezoelectric fiber reinforced laminated composites subjected to thermal shock. Composite Structures, 74, 51–62 (2006)

    Article  Google Scholar 

  5. Pietrzakowski, M. Piezoelectric control of composite plate vibration: effect of electric potential distribution. Computers and Structures, 86, 948–954 (2008)

    Article  Google Scholar 

  6. Babaei, M. H. and Chen, Z. T. Exact solutions for radially polarized and magnetized magneto-electroelastic rotating cylinders. Smart Materials and Structures, 17(2), 025035 (2008)

    Article  Google Scholar 

  7. Khoshgoftar, M. J., Ghorbanpour, A. A., and Arefi, M. Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material. Smart Materials and Structures, 18(11), 115007 (2009)

    Article  Google Scholar 

  8. Jabbari, M., Sohrabpour, S., and Eslami, M. R. Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads. International Journal of Pressure Vessels and Piping, 79, 493–497 (2002)

    Article  Google Scholar 

  9. Frank, P. I. Introduction to Heat Transfer, John Wiley and Sons, New Jersey, 79–86 (1996)

    Google Scholar 

  10. Kang, J. H. Field equations, equations of motion, and energy functionals for thick shells of revolution with arbitrary curvature and variable thickness from a three-dimensional theory. Acta Mechanica, 188, 21–37 (2007)

    Article  MATH  Google Scholar 

  11. Lai, M., Rubin, D., and Krempl, E. Introduction to Continuum Mechanics, 3rd ed., Buttenvorth-Heinemann Press, Oxford, 95–108 (1999)

    Google Scholar 

  12. Boresi, A. P., Schmidt, R. J., and Sidebottom, O. M. Advanced Mechanics of Materials, 5th ed., John Wiley and Sons, New Jersey, 55–67 (1993)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Tarbiat Modares University, Tehran, 14115-143, Iran

    G. H. Rahimi, M. Arefi & M. J. Khoshgoftar

Authors
  1. G. H. Rahimi
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  2. M. Arefi
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  3. M. J. Khoshgoftar
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Correspondence to G. H. Rahimi.

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Rahimi, G.H., Arefi, M. & Khoshgoftar, M.J. Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads. Appl. Math. Mech.-Engl. Ed. 32, 997–1008 (2011). https://doi.org/10.1007/s10483-011-1475-6

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  • DOI: https://doi.org/10.1007/s10483-011-1475-6

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2010 Mathematics Subject Classification

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