Darabi, Mehdi (2019) Non-linear dynamic instability analysis of uniform and thickness-tapered composite plates. PhD thesis, Concordia University.
Preview |
Text (application/pdf)
5MBDarabi_PhD_F2020.pdf - Accepted Version |
Abstract
Laminated composite plates and shells are being increasingly used in aerospace, automotive, and civil engineering as well as in many other applications of modern engineering structures. Tailoring ability of fiber-reinforced polymer composite (FRPC) materials for the stiffness and strength properties with regard to the reduction of structural weight made them superior compared with metals in such structures. In some specific applications such as aircraft wing skins composite structures need to be stiff at one location and flexible at another location. It is desirable to tailor the material and structural arrangements so as to match the localized strength and stiffness requirements by dropping the plies in laminates. Such laminates are called as tapered laminates.
In the dynamic instability that occurs in the structures subjected to harmonic in-plane loading not only the amplitude of the harmonic in-plane load but also the forcing frequencies make the structures fail at load amplitude that is much less than the static buckling load and over a range of forcing frequencies rather than at a single value. In this case, the bending deformations, the rotations and the strains are not small enough in comparison with unity, so the linear theory just provides an outline about the dynamically-unstable regions and is not capable to determine the amplitude of the steady-state vibration in these instability regions.
The main objective of this dissertation is to develop a geometric non-linear formulation and the corresponding solution method for uniform and internally-thickness-tapered laminated composite plates. This Ph.D. research work is completed by extension of this developed geometric non-linear formulation to the uniform laminated composite cylindrical shells as well. The novel parts of this Ph.D. dissertation are the geometric non-linear formulations and corresponding displacement-based solutions obtained using approximate analytical methods, for dynamic instability analysis of internally-thickness-tapered laminated composite plates and cylindrical panels. To the best of author knowledge, there is no non-linear dynamic instability study on internally-thickness-tapered laminated composite plates and cylindrical panels in literature. There is only one study on the linear dynamic instability of internally-thickness-tapered flat plates using the FEM and Ritz method. Here the developed analytical geometric nonlinear formulation not only is capable of predicting the instability regions but also is capable of determining both stable- and unstable-solutions amplitudes of steady-state vibrations of such internally-thickness-tapered laminated composite plates and cylindrical panels in these dynamically-unstable regions. Furthermore, the effect of the influential parameters on the non-linear dynamic instability of laminated plates and cylindrical shells is extensively studied. These parametric studies were carried out on cross-ply laminated composite uniform plates, flat and cylindrical tapered plates, and uniform cylindrical shells. In this study, the non-linear von Karman strains associated with large deflections are considered. Considering the simply supported boundary condition the Navier’s double Fourier series with the time-dependent coefficient is chosen to describe the out-of-plane displacement function. For the uniform laminated composite rectangular plates and uniform laminated composite cylindrical shells, a combination of displacement and a stress-based solution is considered while for the internally-thickness-tapered laminated composites plates and cylindrical panels a displacement-based solution is considered to solve the equations of motion. Then the general Galerkin method is used for the moment-equilibrium equation of motion to satisfy spatial dependence in the partial differential equation of motion to produce a set of non-linear Mathieu-Hill equations. These equations are ordinary differential equations, with time-dependency. Finally, by applying the Bolotin’s method to these non-linear Mathieu-Hill equations, the dynamically-unstable regions, stable-, and unstable-solutions amplitudes of the steady-state vibrations in these dynamically-unstable regions are obtained for both the uniform and the internally-thickness-tapered laminated composites plates and uniform cylindrical shells.
A comprehensive parametric study on the non-linear dynamic instability of these simply supported cross-ply laminated composite uniform plates, flat and cylindrical internally-thickness-tapered plates and uniform cylindrical shells are carried out to examine and compare: the effects of the orthotropy in the laminated composite uniform plates, number of layers for symmetric and antisymmetric uniform cross-ply laminated composite plates and cylindrical shells, different taper configurations and taper angles in both flat tapered plates and tapered cylindrical panels, magnitudes of both tensile and compressive axial loads in the uniform and tapered plates and uniform cylindrical shells, aspect ratios of the loaded-to-unloaded widths of the uniform plates, flat and cylindrical internally-thickness-tapered panels and length-to-radius ratio of the cylindrical shells, length-to-average-thickness ratio of the flat plates and cylindrical panels and radius-to-thickness ratio of the cylindrical shells, and curvature of the tapered cylindrical panels i.e. radius-to-loaded widths ratio on the instability regions and the parametric resonance particularly the steady-state vibrations amplitudes of cross-ply laminated composite uniform plates, flat and cylindrical internally-thickness-tapered plates and uniform cylindrical shells. The present results show good agreement with those available in the literature.
| Divisions: | Concordia University > Gina Cody School of Engineering and Computer Science > Mechanical, Industrial and Aerospace Engineering |
|---|---|
| Item Type: | Thesis (PhD) |
| Authors: | Darabi, Mehdi |
| Institution: | Concordia University |
| Degree Name: | Ph. D. |
| Program: | Mechanical Engineering |
| Date: | 24 October 2019 |
| Thesis Supervisor(s): | Ganesan, Rajamohan |
| ID Code: | 986965 |
| Deposited By: | MEHDI DARABI |
| Deposited On: | 25 Nov 2020 16:07 |
| Last Modified: | 25 Nov 2020 16:07 |
References:
References[1] Bolotin, V. V.;, The dynamic stability of elastic systems, San Francisco: Holden-Day, 1964.
[2] Darabi, M.; Darvizeh, M.; Darvizeh, A.;, "Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading," Composite Structures, vol. 83, pp. 201-211, 2008.
[3] Argento, A.; Scott, R. A.;, "Dynamic instability of layered anisotropic circular cylindrical shells, part I: Theoretical development,," Sound and Vibration, vol. 162, no. no. 2, pp. 311-322, 1993.
[4] Evan-Iwanowsky, R. M.;, "On the parametric response of structures(Parametric response of structures with periodic loads).," Applied Mechanics Reviews, vol. 18, pp. 699-702, 1965.
[5] Sahu, S. K.; Datta, P. K.;, "Research advances in the dynamic stability behavior of plates and shells: 1987–2005—part I: conservative systems," Sahu, S. K., and P. K. Datta. "Research advances in the dynamic stability behavior of plateApplied mechanics reviews, vol. 60, no. 2, pp. 65-75, 2007.
[6] Srinivasan, R. S.; Chellapandi, P.;, "Dynamic stability of rectangular laminated composite plates," Computers & Structures, vol. 24, no. 2, pp. 233-238, 1986.
[7] Bert, C. W.; Birman, V.;, "Dynamic instability of shear deformable antisymmetric angle-ply plates," Solids and Structures, vol. 23, no. 7, pp. 1053-1061, 1987.
[8] Birman, V.;, "Dynamic stability of unsymmetrically laminated rectangular plates," Mechanics research Communications, vol. 12, no. 2, pp. 81-86, 1985.
[9] Moorthy, J.; Reddy, J. N.; Plaut, R. H.;, "Parametric instability of laminated composite plates with transverse shear deformation," Solids and Structures, vol. 26, no. 7, pp. 801-811, 1990.
[10] Patel, B. P.; Ganapathi, M.; Prasad, K. R.; Balamurugan, V.;, "Dynamic instability of layered anisotropic composite plates on elastic foundation," Engineering Structures, vol. 21, pp. 988-995, 1999.
[11] Ramachandra, L. S.; Panda, S. K.;, "Dynamic instability of composite plates subjected to non-uniform in-plane loads," Sound and Vibration, vol. 331, pp. 53-65, 2012.
[12] Popov, A. A.;, "Parametric resonance in cylindrical shells: a case study in the nonlinear vibration of structural shells," Engineering Structures, vol. 25, pp. 789-799, 2003.
[13] Alijani, Farbod; Amabili, Marco;, "Non-linear vibrations of shells: Aliterature review from 2003 to 2013," Non-linear Mechanics, vol. 58, pp. 233-257, 2014.
[14] Librescu, L.; Thangjitham, S.;, "Parametric instability of laminated composite shear-deformable flat panels sunbjected to in-plane edge loads," Non-linear Mechanics, vol. 25, no. 2-3, pp. 263-273, 1990.
[15] Ganapathi, M.; Patel, B. P.; Boisse, P.; Touratier, M.;, "Non-linear dynamic stability characteristics of elastic plates subjected to periodic in-plane load," Non-linear Mechanics, vol. 35, pp. 467- 480, 2000.
[16] Amabili, Marco;, Nonlinear vibrations and stability of shells and plates, New York, NY, USA: Cambridge University Press, 2008.
[17] Fung, Y. C.;, Foundation of Solid Mechanics, Englewood Cliffs, NJ, USA: Prentice-Hall, 1965.
[18] Cheng-ti, Z.; Lie-dong, W.;, "Nonlinear theory of dynamic stability for laminated composite cylindrical shells," Applied Mathematics and Mechanics, vol. 22, no. 1, pp. 53-62, 2001.
[19] Ostiguy, G. L.; Evan-Iwanowski, R. M.;, "Influence of the aspect ratio on dynamic stability and nonlinear response of rectangular plates," Mechanical Design, vol. 104, pp. 417-425, 1982.
[20] Timoshenko, S. P.; Gere, J. M.;, Theory of elasticity, New York: Mc Graw-Hill, 1961.
[21] Ng, T. Y.; Lam, K. Y.; Reddy, J. N.;, "Dynamic stability of cross-ply laminated composite cylindrical shells," Int. J. Mechanical Science, vol. 40, no. 8, pp. 805-823, 1998.
[22] Najafov, A. M.; Sofiyev, A. H.; Hui, D.; Kadiglu, F.; Dorofeyskaya, N. V.; Huang, H.;, "Non-linear dynamic analysis of symmetric and antisymmetric cross-ply laminated orthotropic thin shells," Mechanica, vol. 49, pp. 413-427, 2014.
[23] Lam, K. Y.; Ng, T. Y.;, "Dynamic stability analysis of laminated composite cylindrical shells subjected to conservative periodic axial loads," Composite Part B, vol. 29B, pp. 769-785, 1998.
[24] He, K.; Hoa, S. V.; Ganesan, R.;, "The study of tapered laminated composite structures: a review," Composite Science and Technology, vol. 60, pp. 2643-2657, 2000.
[25] Ganesan, Rajamohan; Zabihollah, Abolghasem;, "Vibration analysis of tapered composite beams using a higher-order finite element. part I: Formulation," Composite Structures, vol. 77, pp. 306-318, 2005.
[26] Ganesan, Rajamohan; Zabihollah, Abolghasem;, "Vibration analysis of tapered composite beams using a higher-order finite element. Part II: parametric study," Composite Structures, vol. 77, pp. 319-330, 2007.
[27] Steeves, Craig A.; Fleck, Norman A.;, "Compressive strength of composite laminates with terminated internal plies," Composite Part A: Applied Science and manufacturing, vol. 36, pp. 798-805, 2005.
[28] Ganesan, Rajamohan; Liu, Dai Ying;, "Progressive failure and post-buckling response of tapered composite plates under uni-axial compression," Composite Structures, vol. 82, pp. 159-176, 2008.
[29] Ganesan, Rajamohan; Akhlaque-E-Rasul, Shaikh;, "Compressive response of tapered composite shells," Composite Structures, vol. 93, pp. 2153-2162, 2011.
[30] Akhlaque-E-Rasul, Shaikh; Ganesan, Rajamohan, "Non-linear buckling analysis of tapered curved composite plates based on a simplified methodology," Composites: Part B, vol. 43, pp. 797-804, 2012.
[31] Akhlaque-E-Rasul, Shaikh; Ganesan, Rajamohan;, "Compressive response of tapered curved composite plates based on a nin-node composite shell elemnt," Composite Structures, vol. 96, pp. 8-16, 2013.
[32] Darabi, Mehdi; Ganesan, Rajamohan;, "Non-linear dynamic instability analysis of laminated composite cylindrical shells subjected to periodic axial loads," Composite Structures, vol. 147, pp. 168-184, 2016.
[33] Kim, W.; Argento, A.; Scott, R. A.;, "Forced Vibration and dynamic stabilit of a rotating tapered composite Timoshenko shaft: Bending motions in end-millig operation," Sound and Vibration, vol. 246, no. 4, pp. 583-600, 2001.
[34] Liu, Weiguang; Ganesan, Rajamohan, "Dynamic instability analysis of tapered composite plates using Ritz and finite element methods," Concordia University, Montreal, 2005.
[35] Hyer, Michael W.;, Stress analysis of fiber-reinforced composite materials., Lancaster: DEStech Publications, Inc, 2009.
[36] Sahu, S. K.; Datta, P. K.;, "Research advances in the dynamic stability behavior of plates and shells: 1987-2005- Part I: Conservative Systems," Applied Mechanics Reviews, vol. 60, pp. 65-75, 2007.
[37] R. M. Ewan-Iwanowski, "On the Parametric Response of Structures," Applied Mechanics Review, vol. 18, no. 9, pp. 699-702, 1965.
[38] Ng, T. Y.; Lam, K. Y.; Reddy, J. N.;, "Dynamic stability of cylindrical panels with transverse shear e}ects," Solids and Structures, vol. 36, pp. 3483-3496, 1999.
[39] Ganapathi, M.; Varadan, T. K.; Balamurugan, V.;, "Dynamic instability of laminated composite curved panels using finite element method," Computeres & Structures, vol. 53, no. 2, pp. 335-342, 1994.
[40] Sahu, S. K.; Datta, P. K.;, "Dynamic stability of laminated composite curved panels with cutouts," Journal of Engineering Mechanics, vol. 129, no. 11, pp. 1245-1253, 2003.
[41] Liew, K. M.; Lee, Y. Y.; Ng, T. Y.; Zhao, X.;, "Dynamic stability analysis of composite laminated cylindrical panels via the mesh-free kp-Ritz method," International Journal of Mechanical Sciences, vol. 49, pp. 1156-1165, 2007.
[42] Whitney, J. M.;, Structural analysis of laminated anisotropic plates, Lancaster, Pennsylvania: Technomic Publishing Company, 1987.
[43] Darabi, M.; Ganesan, R.;, "Nonlinear dynamic instability analysis of laminated composite thin plates subjected to periodic in-plane loads," Nonlinear Dynamics, pp. DOI 10.1007/s11071-017-3863-9, 2017.
[44] Jones, R. M.;, Mechanics of composite materials, Philadelphia: Taylor & Francis, 1999.
[45] Argento, A.; Scott, R. A.;, "Dynamic instability of layered Anisotropic circular cylindrical shells- Part II: Numerical results," Sound and Vibration, vol. 162, pp. 323-332, 1993.
[46] A. Argento, "Dynamic instability of a composite circular cylindrical shell subjected to combined axial and torsional loading," Composite Materials, vol. 27, pp. 1722-1738, 1993.
[47] Ng, T. Y.; Lam, K. Y.; Reddy, J. N.;, "Dynamic stability of cylindrical panels with transverse shear effects," Solids and Structures, vol. 36, pp. 3483-3496, 1999.
[48] Ng, T. Y.; Lam, K. Y.;, "Parametric resonance of a rotationg cylindrical shell subjevted to periodic axial loads," Sound and Vibration, vol. 214, no. 3, pp. 513-529, 1998.
[49] Ng, T. Y.; Lam, K. Y.;, "Dynamic stability analysis of cross-ply laminated cylindrical shells using different thin shell theories," Acta Mechanica, vol. 134, pp. 147-167, 1999.
[50] Liew, K. M.; Hu, Y. G.; Zhao, X.; Ng., T. Y., "Dynamic stability analysis of composite laminated cylindrical shells via the mesh-free kp-Ritz method," computer methods in applied mechanics and engineering, vol. 196, pp. 147-160, 2006.
[51] Fazilati, J.; Ovesy, H. R.;, "dynamic instability analysis of composite laminated thin-walled structures using two versions of FSM," Composite Structures, vol. 92, no. 9, pp. 2060-2065, 2010.
[52] Ovesy, H. R.; Fazilati, J.;, "Parametric instability analysis of laminated composite curved shells subjected to non-uniform in-plane load," Composite Structures, vol. 108, pp. 449-455, 2014.
[53] Fazilati, J.; Ovesy, H. R.;, "Finite strip dynamic instability analysis of perforated cylindrical shell panels," Composite Structures, vol. 94, no. 3, pp. 1259-1264, 2012.
[54] Fazilati, J.; Ovesy, H. R.;, "Parametric instability of laminated longitudinally stiffened curved panels with cutout using higher order FSM," Composite Structures, vol. 95, pp. 691-696, 2013.
[55] Hui, D.; Du, I.;, "Initial postbuckling behavior of imperfect, antisymmetric cross-ply cylindrical-shelss under torsion," Applied Mechanics, vol. 54, pp. 174-180, 1987.
[56] Xu, C. S.; Xian, Z. Q.; Chia, C. Y.;, "Nonlinear theory and vibration analysis of laminated truncated thick conical shells," Non-Linear Mechanics, vol. 16, pp. 139-154, 1995.
[57] Liu, R. H.; Li, J.;, "Nonlinear vibration of shallow conical sandwich shells," Non-Linear Mechanics, vol. 16, pp. 139-154, 1995.
[58] Lakis, A. A.; Selmane, A.; Toledano, A.;, "Nonlinear free vibration analysis of laminated orthotropic cylindrical shells," Mechanical Science, vol. 40, pp. 27-49, 1998.
[59] Gonçalves, P. B.; Del, P. Z.;, "Nonlinear oscilations and stability of parametrically excited cylindrical shells," Mechanica, vol. 37, pp. 569-597, 2002.
[60] Qatu, M. S.; Sullivan, R. W.; Wang, W.;, "Recent research advances on dynamic analysis of composite shells:2000-2009," Composite Structures, vol. 93, pp. 14-31, 93.
Repository Staff Only: item control page
Download Statistics
Download Statistics