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Panahiha, H. M., Davar, A.. (1394). Assessing different nonlinear analysis methods for free vibrations of initially stressed composite laminated plates. فناوری آموزش, 5(1), 25-35. doi: 10.22061/jcarme.2015.342
H. M. Panahiha; A. Davar. "Assessing different nonlinear analysis methods for free vibrations of initially stressed composite laminated plates". فناوری آموزش, 5, 1, 1394, 25-35. doi: 10.22061/jcarme.2015.342
Panahiha, H. M., Davar, A.. (1394). 'Assessing different nonlinear analysis methods for free vibrations of initially stressed composite laminated plates', فناوری آموزش, 5(1), pp. 25-35. doi: 10.22061/jcarme.2015.342
Panahiha, H. M., Davar, A.. Assessing different nonlinear analysis methods for free vibrations of initially stressed composite laminated plates. فناوری آموزش, 1394; 5(1): 25-35. doi: 10.22061/jcarme.2015.342

Assessing different nonlinear analysis methods for free vibrations of initially stressed composite laminated plates

Journal of Computational & Applied Research in Mechanical Engineering (JCARME)
مقاله 3، دوره 5، شماره 1 - شماره پیاپی 9، مهر 2015، صفحه 25-35    اصل مقاله (1.01 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22061/jcarme.2015.342
نویسندگان
H. M. Panahiha؛ A. Davar*
Malek Ashtar University of Technology, Lavizan, Tehran,15875-1774, Iran
تاریخ دریافت: 22 دی 1393،  تاریخ بازنگری: 02 مرداد 1394،  تاریخ پذیرش: 12 مرداد 1394 
چکیده
In this paper, the nonlinear free vibrations of thin symmetric and non-symmetric cross-ply composite plates subjected to biaxial initial stresses are investigated. Because of their excellent properties such as specific strength and specific stiffness, composite plates have wide applications in aerospace and mechanical structures. Based on Von-Karman's strain-displacement relations and using Galerkin method, the nonlinear differential equation of free vibrations of initially stressed composite plate is obtained. This nonlinear equation is solved using two different analytical perturbation methods, namely method of multiple scales (MTS) and homotopy perturbation method (HPM), to analyze the nonlinear vibrations of initially stressed cross-ply composite plates. Effects of tensile and compressive biaxial initial stresses, initial vibration amplitude, thickness, and aspect ratios of the composite plates on the frequency behavior are investigated. The validity of the results is confirmed by making a comparison with those reported in the literature. According to the results, both analytical solutions show increasing trends for natural frequency parameters by increasing normal initial stresses. Regardless of the value of initial biaxial stresses, for both symmetric and non-symmetric plates, the results of MTS and HPM are in close agreement for the smallest initial amplitude. However, for compressive initial stresses, by increasing initial amplitude ratios, the discrepancies between the results of HPM and MTS increase for symmetric and non-symmetric plates. Although HPM includes less computational effort (smaller length of formulation) than MTS, the linear-to-nonlinear frequency ratios obtained using MTS method become closer to those obtained by HPM as initial vibration amplitude is decreased and initial stress is increased.
کلیدواژه‌ها
Nonlinear vibrations؛ Biaxial initial stress؛ Homotopy perturbation method؛ Multiple scales perturbation method
مراجع
[1] Singh, K. K. Raju, G.V. Rao and N. G. R. Iyengar, “Non-linear Vibration of Simply Supported Rectangular Cross-Ply Plates”, Sound. Vib., Vol. 3, No. 142, pp. 213-226, (1990).

[2] R. Adrian, G. Singh, K. K. Raju, G. V. Rao and N. G. R. Iyengar, “Discussion on: Non-linear Vibration of Simply Supported Rectangular Cross-Ply Plates”, Sound. Vib., Vol. 330, No. 11, pp. 2682-2689, (2011).

[3] Zhen and Wanji Chen, “Free Vibration of Laminated Composite and Sandwich Plates Using Global-Local Higher-Order Theory”, Sound. Vib.,Vol .7, No. 49, pp. 298-333, (2006).

[4] D. Chien, C. S. Chen and Rao  “Nonlinear Vibration of Laminated Plates on a Nonlinear Elastic Foundation”, Compos. Struct.,Vol. 8, No. 70, pp. 90-99, (2005).

[5] Matsunaga, “Vibration and Stability of Cross-ply Laminated Composite Shallow Shells Subjected to In-Plane Stresses”, Compos. Struct.,Vol. 7, No. 78, pp. 377-391, (2007).

[6] Lal, B. N. Singh and R. Kumar, “Nonlinear Free Vibration of Laminated Composite Plates on Elastic Foundation with Random System Properties”, Int. J. Mech. Sci., Vol. 1, No. 50, pp. 1203-1212, (2008).

[7] Shooshtari and S. Razavi, “A Closed Form Solution for Linear and Nonlinear Free Vibrations of Composite and Fiber Metal Laminated Rectangular Plates”, Compos. Struct.,Vol. 2, No. 92, pp. 2663-2675, (2010).

[8] S.   Chen  and   C.  P.   Fung,   “Nonlinear Vibration of An Initially Stressed Hybrid Composite Plates”, Sound. Vib.,Vol. 4, No. 274, pp. 1013-1029, (2004).

[9] Yang and H. S. Shen, “Dynamic Response of Initially Stressed Functionally Graded Rectangular Thin Plates”, Compos. Struct.,Vol. 4, No. 54, pp. 497-508, (2001).

[10] S. Chen, T. J. Chen and R. D. Chien, “Nonlinear Vibration of Initially Stressed Functionally Graded Plates”, Thin-Walled Struct., Vol. 3, No. 44, pp. 844-851, (2006).

[11] H. He and Raju, “Homotopy Perturbation Technique”, Comput. Method. Appl. Mech., Vol. 1, No. 178, pp. 257-262, (1999).

[12] Sun, L. Du and V. Yang “A Homotopy Method for Determining the Eigenvalues of Locally or Non-Locally Reacting Acoustic Liners in Flow Ducts”, Sound. Vib.,Vol. 3, No. 303, pp. 277-286, (2007).

[13] Blendez, T. Blendez, A. Marquez and A. Niepp, “Application of He’s Homotopy Perturbation Method to Conservative Truly Non-Linear Oscillators”, Chaos. Soliton. Fract., Vol. 3, No. 37, pp. 770-780, (2008).

[14] A. Yazdi, “Homotopy Perturbation Method for Nonlinear Vibration Analysis of Functionally Graded Plate”, Vib. Acoust.,Vol. 1, No. 46, pp. 217-222, (2013).

[15] Yongqiang, L. Feng and Z. Dawei, “Geometrically Non-Linear Free Vibrations of the Symmetric Rectangular Honeycomb Sandwich Panels With Simply Supported Boundaries”, Compos. Struct.,Vol. 5, No. 92, pp. 1110-1119, (2010).

[16] Bhimaraddi, “Nonlinear Flexural Vibrations of Rectangular Plates Subjected to In-Plane Forces Using a New Shear Deformation Theory”, Thin-Walled Struct., Vol. 8, No. 5, pp. 309-327, (1987).

[17] Bhimaraddi, “Nonlinear Flexural Vibrations of Rectangular Plates Subjected to In-Plane Forces Using a New Shear Deformation Theory”, Thin-Walled Struct., Vol. 7, No. 5, pp. 309-327, (1987).

[18] N. C. Mazzilli, “Buckling and Post-Buckling of Extensible Rods Revisited: A Multiple Scales Solution”, Non-Lin. Mech., Vol. 1, No. 44, pp. 200-208, (2009).

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