Large Vibration Amplitudes of Circular Functionally Graded Thin Plates Resting on Winkler Elastic Foundations
This paper describes a study of geometrically
nonlinear free vibration of thin circular functionally graded (CFGP)
plates resting on Winkler elastic foundations. The material properties
of the functionally graded composites examined here are assumed to
be graded smoothly and continuously through the direction of the
plate thickness according to a power law and are estimated using the
rule of mixture. The theoretical model is based on the classical Plate
theory and the Von-Kármán geometrical nonlinearity assumptions.
An homogenization procedure (HP) is developed to reduce the
problem considered here to that of isotropic homogeneous circular
plates resting on Winkler foundation. Hamilton-s principle is applied
and a multimode approach is derived to calculate the fundamental
nonlinear frequency parameters which are found to be in a good
agreement with the published results. On the other hand, the
influence of the foundation parameters on the nonlinear fundamental
frequency has also been analysed.
[1] M. Koizumi The concept of FGM. Ceram Trans Func Grad Mater 1993;
34:3-10.W.-K. Chen, Linear Networks and Systems (Book
style).Belmont, CA: Wadsworth, 1993, pp. 123-135.
[2] M. Koizumi FGM activities in Japan. Composite B 1997;28:1-4.
[3] S .Suresh, Mortensen A. Fundamentals of Functionally Graded
Materials: Processing and Thermomechanical Behavior of Graded
Metals and Metal-Ceramic Composites.London, UK: IOM
Communications Ltd, 1998.
[4] Y .Miyamoto, Kaysser W A, Rabin B H, et al. Functionally Graded
Materials: Design, Processing and Applications.Boston, UK: Kluwer
Academic Publishers, 1999.
[5] A. Allahverdizadeh, M.H. Naei, M. Nikkhah Bahrami, Nonlinear free
and forced vibration analysis of thin circular functionally graded plates,
Journal of Sound and Vibration 310 (2008) 966-984.
[6] A.Zerkane,K.El Bikri,R.Benamar," A homogenization procedure for
nonlinear free vibration analysis of functionally graded beams resting on
nonlinear elastic foundations"
[7] H.Shen Shen,Functionally graded materials : nonlinear analysis of plates
and shells. Taylor & Francis Group, LLC. 2009
[8] R. Benamar, M.M.K. Bennouna, R.G. White, The effects of large
vibration amplitudes on the mode shapes and natural frequencies of thin
elastic structures, part II: fully clamped rectangular isotropic plates,
Journal of Sound and Vibration 164 (1991) 399-424.
[9] M. El Kadiri, R. Benamar, R.G. White, The non-linear free vibration of
fully clamped rectangular plates: second non-linear mode for various
plate aspect ratios, Journal of Sound and Vibration 228 (2) (1999) 333-
358.
[1] M. Koizumi The concept of FGM. Ceram Trans Func Grad Mater 1993;
34:3-10.W.-K. Chen, Linear Networks and Systems (Book
style).Belmont, CA: Wadsworth, 1993, pp. 123-135.
[2] M. Koizumi FGM activities in Japan. Composite B 1997;28:1-4.
[3] S .Suresh, Mortensen A. Fundamentals of Functionally Graded
Materials: Processing and Thermomechanical Behavior of Graded
Metals and Metal-Ceramic Composites.London, UK: IOM
Communications Ltd, 1998.
[4] Y .Miyamoto, Kaysser W A, Rabin B H, et al. Functionally Graded
Materials: Design, Processing and Applications.Boston, UK: Kluwer
Academic Publishers, 1999.
[5] A. Allahverdizadeh, M.H. Naei, M. Nikkhah Bahrami, Nonlinear free
and forced vibration analysis of thin circular functionally graded plates,
Journal of Sound and Vibration 310 (2008) 966-984.
[6] A.Zerkane,K.El Bikri,R.Benamar," A homogenization procedure for
nonlinear free vibration analysis of functionally graded beams resting on
nonlinear elastic foundations"
[7] H.Shen Shen,Functionally graded materials : nonlinear analysis of plates
and shells. Taylor & Francis Group, LLC. 2009
[8] R. Benamar, M.M.K. Bennouna, R.G. White, The effects of large
vibration amplitudes on the mode shapes and natural frequencies of thin
elastic structures, part II: fully clamped rectangular isotropic plates,
Journal of Sound and Vibration 164 (1991) 399-424.
[9] M. El Kadiri, R. Benamar, R.G. White, The non-linear free vibration of
fully clamped rectangular plates: second non-linear mode for various
plate aspect ratios, Journal of Sound and Vibration 228 (2) (1999) 333-
358.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:51365", author = "El Kaak and Rachid and El Bikri and Khalid and Benamar and Rhali", title = "Large Vibration Amplitudes of Circular Functionally Graded Thin Plates Resting on Winkler Elastic Foundations", abstract = "This paper describes a study of geometrically
nonlinear free vibration of thin circular functionally graded (CFGP)
plates resting on Winkler elastic foundations. The material properties
of the functionally graded composites examined here are assumed to
be graded smoothly and continuously through the direction of the
plate thickness according to a power law and are estimated using the
rule of mixture. The theoretical model is based on the classical Plate
theory and the Von-Kármán geometrical nonlinearity assumptions.
An homogenization procedure (HP) is developed to reduce the
problem considered here to that of isotropic homogeneous circular
plates resting on Winkler foundation. Hamilton-s principle is applied
and a multimode approach is derived to calculate the fundamental
nonlinear frequency parameters which are found to be in a good
agreement with the published results. On the other hand, the
influence of the foundation parameters on the nonlinear fundamental
frequency has also been analysed.", keywords = "Functionally graded materials, nonlinear vibrations,
Winkler foundation.", volume = "7", number = "2", pages = "190-4", }