Free Vibration Analysis of Laminated Composite Plates with General Boundary Elastic Supports Under Initial Thermal Load

  • Mohammed B. Hammed Department of Mechanical Engineering/ University of Baghdad
  • Widad I. Majeed Department of Mechanical Engineering/ University of Baghdad


Free vibration behavior was developed under the ratio of critical buckling temperature of laminated composite thin plates with the general elastic boundary condition. The equations of motion were found based on classical laminated plate theory (CLPT) while the solution functions consists of trigonometric function and a continuous function that is added to guarantee the sufficient smoother of the so-named remaining displacement function at the boundaries, in this research, a modified Fourier series were used, a generalized procedure solution was developed using Ritz method combined with the imaginary spring technique. The influences of many design parameters such as angles of layers, aspect ratio, thickness ratio, and ratio of initial in- plane thermal load in addition to different boundary conditions on the natural frequencies of laminated plate is analyzed. In general, the changes of fundamental natural frequency is inversely proportional with the ratio of thermal buckling load, also most parameters aspect ratio effect on the natural frequency about 35 – 40%. The present results were compared with those obtained by other researchers, and show good agreement.


Download data is not yet available.


ACHCHHE LAL and B. N. SINGH, “Stochastic free vibration of laminated composite plates in thermal environments”, Journal of Thermoplastic Composite Materials, Vol. 23, January 2010.

Behrooz Rahmani and Amin Ghorbani Shenas. "Robust vibration control of laminated rectangular composite plates in hygrothermal and thermal environment", Composite Structures, S0263-8223 (16)32874-4(2017).

Chun-Sheng Chen, Chih-Wen Chen, Wei-Ren Chen and Yi-Chen Chang. "Thermally induced vibration and stability of laminated composite plates with temperature-dependent properties", Meccanica, DOI 10.1007/s11012-013-9750-7(2013).

Henry Khov, Wen L. Li and Ronald F. Gibson, “An accurate solution method for the static and dynamic deflections of orthotropic plates with general boundary conditions”, Composite Structures, Vol. 90, P. 474–481, 2009.

Hossein Amoushahi and Farshad Goodarzian. "Dynamic and buckling analysis of composite laminated plates with and without strip delamination under hygrothermal effects using finite strip method", Thin-Walled Structures, 131 (2018) 88–101.

J.N. REDDY, “Mechanics of laminated composite plates and shells: theory and analysis”, 2nd ed.; CRC Press LLC, 2004.

Ibtehal Abbas Sadiq, and Kani Hussein Bawa. “Vibration analysis of cross-ply plates under initial stress using refined theory”. Al-Khwarizmi Engineering Journal, Vol. 14, No.4, December, (2018) P.P. 34- 44.

Wael R. Abdul-Majeed. “Restrained edges effect on the dynamics of thermoelastic plates under different end conditions.” Al-Khwarizmi Engineering Journal, Vol. 8, No. 2, PP 1-11 (2012).

Rath, M., and S. Sahu. "Vibration of woven fiber laminated composite plates in hygrothermal environment", Journal of Vibration and Control, 2012.

Moumita Sit and Chaitali Ray. “A third order nonlinear model to study the dynamic behavior of composite laminated structures under the thermal effect with experimental verification.” Composite Structures, S0263-8223 (18)32606-0 (2019).

Robert G. Brown, “Introductory physics I: elementary mechanics”, Duke University Physics Department, 2007.

Victor Birman, “Solid mechanics and its applications: plate structures”, Springer Science B.V. 2011.

W.L. Li, “Vibration analysis of rectangular plates with general elastic boundary supports”, Journal of Sound and Vibration, Vol. 273, P. 619–635,2004.

W.L. Li, “Free vibrations of beam with general boundary conditions”, Journal of Sound and Vibration, Vol.237, P.709–725, 2000.

Li, Xiangyang, Kaiping Yu, Jingyong Han, Haiyang Song and Rui Zhao. "Buckling and vibro-acoustic response of the clamped composite laminated plate in thermal environment", International Journal of Mechanical Sciences, S0020-7403 (16)30588-4(2016).

Zainab Abdul Kareem Abed. “Buckling and pre stressed dynamics analysis of laminated composite plate with different boundary conditions”. Al-Khwarizmi Engineering Journal, Vol. 15, No. 1, March, (2019) P.P. 46- 55.

W.L. Li.., and M. Daniels. "A Fourier series method for the vibrations of elastically restrained plates arbitrarily loaded with springs and masses." Journal of Sound Vibration Vol. 252 (2002) PP: 768-781.

How to Cite
Hammed, M., & Majeed, W. (2019). Free Vibration Analysis of Laminated Composite Plates with General Boundary Elastic Supports Under Initial Thermal Load. Al-Khwarizmi Engineering Journal, 15(4), 23-32.