Free Vibration Analysis of Functionally Graded Pretwisted Plate in Thermal Environment Using Finite Element Method
The free vibration behavior of thick pretwisted cantilevered functionally graded material (FGM) plate subjected to the thermal environment is investigated numerically in the present paper. A mathematical model is developed in the framework of higher order shear deformation theory (HOST) with C0 finite element formulation i.e. independent displacement and rotations. The material properties are assumed to be temperature dependent and vary continuously through the thickness based on the volume fraction exponent in simple power rule. The finite element model has been discretized into eight node quadratic serendipity elements with node wise seven degrees of freedom. The effect of plate geometry, temperature field, material composition, and the modal analysis on the vibrational characteristics is examined. Finally, the results are verified by comparing with those available in literature.
[1] S. M. Nabi and N. Ganesan, “Vibration and damping analysis of pre-twisted composite blades,” Comput. Struct., vol. 47, no. 2, pp. 275–280, 1993.
[2] Y. J. Kee and J. H. Kim, “Vibration characteristics of initially twisted rotating shell type composite blades,” Compos. Struct., vol. 64, no. 2, pp. 151–159, 2004.
[3] A. W. Leissa and A. S. Kadi, “Curvature effects on shallow shell vibrations,” J. Sound Vib., vol. 16, pp. 173–187, 1971.
[4] A. W. Leissa, J. K. Lee, and A. J. Wang, “Vibrations of cantilevered doubly-curved shallow shells,” J. Sound Vib., vol.3, pp. 311-328, 1983.
[5] H. Jari, H.R. Atri, S. Shojaee, "Nonlinear thermal analysis of functionally graded material plates using a NURBS based isogeometric approach,'' Composite structures vol. 119, pp. 333-345, 2015
[6] X. LI, J. Zhang, Y. Zheng, ''Static and free vibration analysis of laminated composite plates using isogeometric approach based on the third order shear deformation theory,'' Advances in mechanical engineering 2014, pp. 1-16, 2014.
[7] Q. Li, V.P. Iu, K.P. Kou, ''Three dimensional vibration analysis of functionally graded material plates in thermal environment,'' J. Sound Vib., vol. 324, pp. 733-750, 2009.
[8] A. Leissa, J. Macbain, R. Kielb, ''Vibration of twisted cantilevered plates-Summary of previous and current studies,'' J. Sound Vib., vol. 96, pp. 159-173, 1984.
[9] S. K. Sinha and K. E. Turner, “Natural frequencies of a pretwisted blade in a centrifugal force field,” J. Sound Vib., vol. 330, no. 11, pp. 2655–2681, 2011.
[10] H. Nguyen-Xuan, L. V. Tran, C. H. Thai, and T. Nguyen-Thoi, “Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing,” Thin-Walled Struct., vol. 54, pp. 1–18, May 2012.
[11] J. N. Reddy, “Analysis of functionally graded plates,” Int. J. Numer. Methods Eng., vol. 684, no. June 1999, pp. 663–684, 2000.
[12] J. N. Reddy, N. D. Phan, “Stability and vibration of isotropic , orthotropic and laminated plates according to a higher-order shear deformation theory,” J. Sound Vib.,, vol. 98, pp. 157–170, 1985.
[13] A. Bazoune, “Relationship between softening and stiffening effects in terms of Southwell coefficients,” J. Sound Vib., vol. 287, no. 4–5, pp. 1027–1030, 2005.
[14] K. Chandrashekhara, “Free vibrations of anisotropic laminated doubly curved shells,” Comput. Struct., vol. 33, no. 2, pp. 435–440, 1989.
[15] T. L. Zhu, “The vibrations of pre-twisted rotating Timoshenko beams by the Rayleigh-Ritz method,” Comput. Mech., vol. 47, no. 4, pp. 395–408, 2011
[16] S. C. Choi, J. S. Park, and J. H. Kim, “Vibration control of pre-twisted rotating composite thin-walled beams with piezoelectric fiber composites,” J. Sound Vib., vol. 300, no. 1–2, pp. 176–196, 2007.
[17] S. H. Hashemi, S. Farhadi, and S. Carra, “Free vibration analysis of rotating thick plates,” J. Sound Vib., vol. 323, no. 1–2, pp. 366–384, 2009.
[18] X. X. Hu, T. Tsuiji,“Free vibration analysis of curved and twisted cylindrical thin panels,” J. Sound Vib., vol. 219, pp. 63–88, 1999.
[19] S. Sreenivasamurthy and V. Ramamurti, “Coriolis effect on the vibration of flat rotating low aspect ratio cantilever plates,” J. Strain Anal. Eng. Des., vol. 16, no. 2, pp. 97–106, 2007.
[20] J. Yang and H.-S. Shen, “Vibration Characteristics and Transient Response of Shear-Deformable Functionally Graded Plates in Thermal Environments,” J. Sound Vib., vol. 255, no. 3, pp. 579–602, Aug. 2002.
[21] Y.-W. Kim, “Temperature dependent vibration analysis of functionally graded rectangular plates,” J. Sound Vib., vol. 284, no. 3–5, pp. 531–549, Jun. 2005.
[22] M. A. Dokainish, S. Rawtani, “Vibration analysis of rotating cantilever plates”, Int. J. Numer. Methods Eng. vol. 3,pp. 233-248, 1971.
[23] X.L Huang, H.S Shen, ‘ Nonlinear vibration and dynamic response of functionally graded plates in thermal environments,” Int. J. solids and Struct., vol. 41, pp. 2403-2427, 2004.
[24] R.E.D. Bishop, “The Mechanics of Vibration”, Cambridge University Press, New York, 1979.
[25] Touloukin YS. Thermophysical properties of high temperature solid materials, Macmillan, New York,1967
[26] Petyt M. Introduction to finite element vibration analysis, 2nd ed., Cambridge university press, 2010.
[1] S. M. Nabi and N. Ganesan, “Vibration and damping analysis of pre-twisted composite blades,” Comput. Struct., vol. 47, no. 2, pp. 275–280, 1993.
[2] Y. J. Kee and J. H. Kim, “Vibration characteristics of initially twisted rotating shell type composite blades,” Compos. Struct., vol. 64, no. 2, pp. 151–159, 2004.
[3] A. W. Leissa and A. S. Kadi, “Curvature effects on shallow shell vibrations,” J. Sound Vib., vol. 16, pp. 173–187, 1971.
[4] A. W. Leissa, J. K. Lee, and A. J. Wang, “Vibrations of cantilevered doubly-curved shallow shells,” J. Sound Vib., vol.3, pp. 311-328, 1983.
[5] H. Jari, H.R. Atri, S. Shojaee, "Nonlinear thermal analysis of functionally graded material plates using a NURBS based isogeometric approach,'' Composite structures vol. 119, pp. 333-345, 2015
[6] X. LI, J. Zhang, Y. Zheng, ''Static and free vibration analysis of laminated composite plates using isogeometric approach based on the third order shear deformation theory,'' Advances in mechanical engineering 2014, pp. 1-16, 2014.
[7] Q. Li, V.P. Iu, K.P. Kou, ''Three dimensional vibration analysis of functionally graded material plates in thermal environment,'' J. Sound Vib., vol. 324, pp. 733-750, 2009.
[8] A. Leissa, J. Macbain, R. Kielb, ''Vibration of twisted cantilevered plates-Summary of previous and current studies,'' J. Sound Vib., vol. 96, pp. 159-173, 1984.
[9] S. K. Sinha and K. E. Turner, “Natural frequencies of a pretwisted blade in a centrifugal force field,” J. Sound Vib., vol. 330, no. 11, pp. 2655–2681, 2011.
[10] H. Nguyen-Xuan, L. V. Tran, C. H. Thai, and T. Nguyen-Thoi, “Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing,” Thin-Walled Struct., vol. 54, pp. 1–18, May 2012.
[11] J. N. Reddy, “Analysis of functionally graded plates,” Int. J. Numer. Methods Eng., vol. 684, no. June 1999, pp. 663–684, 2000.
[12] J. N. Reddy, N. D. Phan, “Stability and vibration of isotropic , orthotropic and laminated plates according to a higher-order shear deformation theory,” J. Sound Vib.,, vol. 98, pp. 157–170, 1985.
[13] A. Bazoune, “Relationship between softening and stiffening effects in terms of Southwell coefficients,” J. Sound Vib., vol. 287, no. 4–5, pp. 1027–1030, 2005.
[14] K. Chandrashekhara, “Free vibrations of anisotropic laminated doubly curved shells,” Comput. Struct., vol. 33, no. 2, pp. 435–440, 1989.
[15] T. L. Zhu, “The vibrations of pre-twisted rotating Timoshenko beams by the Rayleigh-Ritz method,” Comput. Mech., vol. 47, no. 4, pp. 395–408, 2011
[16] S. C. Choi, J. S. Park, and J. H. Kim, “Vibration control of pre-twisted rotating composite thin-walled beams with piezoelectric fiber composites,” J. Sound Vib., vol. 300, no. 1–2, pp. 176–196, 2007.
[17] S. H. Hashemi, S. Farhadi, and S. Carra, “Free vibration analysis of rotating thick plates,” J. Sound Vib., vol. 323, no. 1–2, pp. 366–384, 2009.
[18] X. X. Hu, T. Tsuiji,“Free vibration analysis of curved and twisted cylindrical thin panels,” J. Sound Vib., vol. 219, pp. 63–88, 1999.
[19] S. Sreenivasamurthy and V. Ramamurti, “Coriolis effect on the vibration of flat rotating low aspect ratio cantilever plates,” J. Strain Anal. Eng. Des., vol. 16, no. 2, pp. 97–106, 2007.
[20] J. Yang and H.-S. Shen, “Vibration Characteristics and Transient Response of Shear-Deformable Functionally Graded Plates in Thermal Environments,” J. Sound Vib., vol. 255, no. 3, pp. 579–602, Aug. 2002.
[21] Y.-W. Kim, “Temperature dependent vibration analysis of functionally graded rectangular plates,” J. Sound Vib., vol. 284, no. 3–5, pp. 531–549, Jun. 2005.
[22] M. A. Dokainish, S. Rawtani, “Vibration analysis of rotating cantilever plates”, Int. J. Numer. Methods Eng. vol. 3,pp. 233-248, 1971.
[23] X.L Huang, H.S Shen, ‘ Nonlinear vibration and dynamic response of functionally graded plates in thermal environments,” Int. J. solids and Struct., vol. 41, pp. 2403-2427, 2004.
[24] R.E.D. Bishop, “The Mechanics of Vibration”, Cambridge University Press, New York, 1979.
[25] Touloukin YS. Thermophysical properties of high temperature solid materials, Macmillan, New York,1967
[26] Petyt M. Introduction to finite element vibration analysis, 2nd ed., Cambridge university press, 2010.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:77173", author = "S. Parida and S. C. Mohanty", title = "Free Vibration Analysis of Functionally Graded Pretwisted Plate in Thermal Environment Using Finite Element Method", abstract = "The free vibration behavior of thick pretwisted cantilevered functionally graded material (FGM) plate subjected to the thermal environment is investigated numerically in the present paper. A mathematical model is developed in the framework of higher order shear deformation theory (HOST) with C0 finite element formulation i.e. independent displacement and rotations. The material properties are assumed to be temperature dependent and vary continuously through the thickness based on the volume fraction exponent in simple power rule. The finite element model has been discretized into eight node quadratic serendipity elements with node wise seven degrees of freedom. The effect of plate geometry, temperature field, material composition, and the modal analysis on the vibrational characteristics is examined. Finally, the results are verified by comparing with those available in literature.
", keywords = "FGM, pretwisted plate, thermal environment, HOST, simple power law. ", volume = "11", number = "8", pages = "1523-11", }
