Non-linear parametric vibration responses of composite plates on Pasternak foundations using extended dynamic stiffness method

References

• Aiello, M. A., and L. Ombres. 1999. “Buckling and Vibration of Unsymmetric Laminates Resting on Elastic Foundations under In-Plane and Shear Forces.” Composite Structures 44 (1): 31–41. doi:10.1016/S0263-8223(98)00116-0.
   Web of Science ®Google Scholar
• Asnafi, A., and M. Abedi. 2015. “A Complete Analogical Study on the Dynamic Stability Analysis of Isotropic Functionally Graded Plates Subjected to Lateral Stochastic Loads.” Acta Mechanica 226: 2347–2363. doi:10.1007/s00707-015-1321-7.
   Web of Science ®Google Scholar
• Awrejcewicz, J., L. Kurpa, and O. Mazur. 2016. “Dynamical Instability of Laminated Plates with External Cutout.” International Journal of Non-Linear Mechanics 81: 103–114. doi:10.1016/j.ijnonlinmec.2016.01.002.
   Web of Science ®Google Scholar
• Babu, A. A., and R. Vasudevan. 2016. “Dynamic Instability Analysis of Rotating Delaminated Tapered Composite Plates Subjected to Periodic In-Plane Loading.” Archive of Applied Mechanics 86 (12): 1965–1986. doi:10.1007/s00419-016-1162-4.
   Web of Science ®Google Scholar
• Bolotin, V. V. 1964. The Dynamic Stability of Elastic System. San Francisco: Holden-Day.
   Google Scholar
• Chakrabarti, A., and A. H. Sheikh. 2006. “Dynamic Instability of Laminated Sandwich Plates Using an Efficient Finite Element Model.” Thin-Walled Structures 44 (1): 57–68. doi:10.1016/j.tws.2005.09.003.
   Web of Science ®Google Scholar
• Chen, W.-R., C.-S. Chen, and J.-H. Shyu. 2013. “Stability of Parametric Vibrations of Laminated Composite Plates.” Applied Mathematics and Computation 223: 127–138. doi:10.1016/j.amc.2013.07.095.
   Web of Science ®Google Scholar
• Darabi, M., and R. Ganesan. 2017. “Non-Linear Vibration and Dynamic Instability of Internally-Thickness-Tapered Composite Plates under Parametric Excitation.” Composite Structures 176: 82–104. doi:10.1016/j.compstruct.2017.04.059.
   Web of Science ®Google Scholar
• Hutt, J. M., and A. E. Salam. 1971. “Dynamic Stability of Plates by Finite Elements.” Journal of Engineering Mechanics 97 (3): 879–899.
   Google Scholar
• Huynh, H. Q., H. T. Nguyen, and H. Nguyen. 2016. “Non-Linear Dynamic Instability of Laminated Composite Plates on Winkler Foundation Using Dynamic Stiffness Method.” In The Fourteenth East Asia-Pacific Conference on Structural Engineering and Construction. Vietnam: HoChiMinh City. January 1985–1992.
   Google Scholar
• Huynh, H. Q., H. T. Nguyen, and H. Nguyen. 2017. “Non-Linear Dynamic Instability and Responses Parametric Vibration of Sandwich Composite Plates.” International Journal of Mechanical Engineering and Automation 4 (2): 26–38.
   Google Scholar
• Kumar, R., S. Mondal, S. Guchhait, and R. Jamatia. 2017. “Analytical Approach for Dynamic Instability Analysis of Functionally Graded Skew Plate under Periodic Axial Compression.” International Journal of Mechanical Sciences 130: 41–51. doi:10.1016/j.ijmecsci.2017.05.050.
   Web of Science ®Google Scholar
• Librescu, L., and S. Thangjitham. 1990. “Parametric Instability of Laminated Composite Shear-Deformable Flat Panels Subjected to In-Plane Edge Loads.” International Journal of Non-Linear Mechanics 25 (2): 263–273. doi:10.1016/0020-7462(90)90056-F.
   Web of Science ®Google Scholar
• Lien-Wen, C., and Y. Jenq-Yiing. 1990. “Dynamic Stability of Laminated Composite Plates by the Finite Element Method.” Computers & Structures 36 (5): 845–851. doi:10.1016/0045-7949(90)90155-U.
   Web of Science ®Google Scholar
• Liu, A., H. Lu, J. Fu, Y. L. Pi, Y. Huang, J. Li, and Y. Ma. 2017. “Analytical and Experimental Studies on Out-Of-Plane Dynamic Instability of Shallow Circular Arch Based on Parametric Resonance.” Nonlinear Dynamics 87 (1): 677–694. doi:10.1007/s11071-016-3068-7.
   Web of Science ®Google Scholar
• Moorthy, J., J. N. Reddy, and R. H. Plaut. 1990. “Parametric Instability of Laminated Composite Plates with Transverse Shear Deformable.” International Journal Solids Structures 26 (7): 801–811. doi:10.1016/0020-7683(90)90008-J.
   Web of Science ®Google Scholar
• Nguyen, H., and G. L. Ostiguy. 1989a. “Effect of Boundary Conditions on the Dynamic Instability and Non-Linear Response of Rectangular Plates, Part I: Theory.” Journal of Sound and Vibration 133 (3): 381–400. doi:10.1016/0022-460X(89)90606-8.
   Web of Science ®Google Scholar
• Nguyen, H., G. L. Ostiguy, and L. P. Samson. 1989b. “Effect of Boundary Conditions on the Dynamic Instability and Non-Linear Response of Rectangular Plates, Part II: Experiment.” Journal of Sound and Vibration 133 (3): 401–422. doi:10.1016/0022-460X(89)90607-X.
   Web of Science ®Google Scholar
• Noh, M.-H., and S.-Y. Lee. 2014. “Dynamic Instability of Delaminated Composite Skew Plates Subjected to Combined Static and Dynamic Loads Based on HSDT.” Composites Part B: Engineering 58: 113–121. doi:10.1016/j.compositesb.2013.10.073.
   Web of Science ®Google Scholar
• Panda, H. S., S. K. Sahu, and P. K. Parhi. 2015. “Hygrothermal Response on Parametric Instability of Delaminated Bidirectional Composite Flat Panels.” European Journal of Mechanics- A/Solids 53: 268–281. doi:10.1016/j.euromechsol.2015.05.004.
   Web of Science ®Google Scholar
• Patel, B. P., M. Ganapathi, K. R. Prasad, and V. Balamurugan. 1999. “Dynamic Instability of Layered Anisotropic Composite Plates on Elastic Foundations.” Engineering Structures 21 (11): 988–995. doi:10.1016/S0141-0296(98)00063-7.
   Web of Science ®Google Scholar
• Ramachandra, L. S., and S. K. Panda. 2012. “Dynamic Instability of Composite Plates Subjected to Non-Uniform In-Plane Loads.” Journal of Sound and Vibration 331 (1): 53–65. doi:10.1016/j.jsv.2011.08.010.
   Web of Science ®Google Scholar
• Reddy, J. N. 2004. Mechanics of Laminated Composite Plates and Shells. Boca Raton, London: CRC Press.
   Google Scholar
• Saha, K. N., R. C. Kar, and P. K. Datta. 1997. “Dynamic Stability of a Rectangular Plate on Non-Homogeneous Winkler Foundation.” Computers & Structures 63 (6): 1213–1222. doi:10.1016/S0045-7949(96)00390-2.
   Web of Science ®Google Scholar
• Singh, B. N., A. Lal, and R. Kumar. 2009. “Post Buckling Response of Laminated Composite Plate on Elastic Foundation with Random System Properties.” Communications in Nonlinear Science and Numerical Simulation 14 (1): 284–300. doi:10.1016/j.cnsns.2007.08.005.
   Web of Science ®Google Scholar
• Singh, J. P., and S. S. Dey. 1992. “Parametric Instability of Rectangular Plates by the Energy Based Finite Difference Method.” Computer Methods in Applied Mechanics and Engineering 97 (1): 1–21. doi:10.1016/0045-7825(92)90104-R.
   Web of Science ®Google Scholar
• Srinivasan, R. S., and P. Chellapandi. 1986. “Dynamic Stability of Rectangular Laminated Composite Plates.” Computers & Structure 24 (2): 233–238. doi:10.1016/0045-7949(86)90282-8.
   Web of Science ®Google Scholar
• Srivastava, A. K. L., P. K. Datta, and A. H. Sheikh. 2003. “Dynamic Instability of Stiffened Plates Subjected to Non-Uniform Harmonic In-Plane Edge Loading.” Journal of Sound and Vibration 262 (5): 1171–1189. doi:10.1016/S0022-460X(02)01094-5.
   Web of Science ®Google Scholar
• Srivastava, A. K. L., P. K. Datta, and A. H. Sheikh. 2005. “Dynamic Stability of Stiffened Plates with Cutout Subjected to Harmonic In-Plane Partial Edge Loading.” International Journal of Crashworthiness 10 (4): 403–417. doi:10.1533/ijcr.2005.0358.
   Web of Science ®Google Scholar
• Takahashi, K., and Y. Konishi. 1988. “Dynamic Stability of a Rectangular Plate Subjected to Distributed In-Plane Dynamic Force.” Journal of Sound and Vibration 123 (1): 115–127. doi:10.1016/S0022-460X(88)80082-8.
   Web of Science ®Google Scholar
• Tran, I. T., M. C. Nguyen, and G. N. Dinh. 2014. “Dynamic Stiffnes Formulation for Vibration Analysis of Thick Composite Plates Resting on Non-Homogenous Foundations.” Composite Structures 108: 684–695. doi:10.1016/j.compstruct.2013.10.022.
   Web of Science ®Google Scholar
• Wang, S., and D. J. Dawe. 2002. “Dynamic Instability of Composite Laminated Rectangular Plates and Prismatic Plate Structures.” Computer Methods in Applied Mechanics and Engineering 191 (17): 1791–1826. doi:10.1016/S0045-7825(01)00354-1.
   Web of Science ®Google Scholar
• Wattanasakulpong, N., and A. Chaikittiratana. 2015. “Exact Solutions for Static and Dynamic Analyses of Carbon Nanotube-Reinforced Composite Plates with Pasternak Elastic Foundation.” Applied Mathematical Modelling 39 (18): 5459–5472. doi:10.1016/j.apm.2014.12.058.
   Web of Science ®Google Scholar
• Wu, G.-Y., and Y.-S. Shih. 2005. “Dynamic Instability of Rectangular Plate with an Edge Crack.” Computers & Structures 84 (1): 1–10. doi:10.1016/j.compstruc.2005.09.003.
   Web of Science ®Google Scholar
• Wu, G. Y., and Y. S. Shih. 2006. “Analysis of Dynamic Instability for Arbitrarily Laminated Skew Plates.” Journal of Sound and Vibration 292 (2): 315–340. doi:10.1016/j.jsv.2005.07.042.
   Web of Science ®Google Scholar
• Xiang, Y., S. Kitipornchai, and K. M. Liew. 1996. “Buckling and Vibration of Thick Laminates on Pasternak Foundations.” Journal of Engineering Mechanics 122 (1): 54–63. doi:10.1061/(ASCE)0733-9399(1996)122:1(54).
   Web of Science ®Google Scholar