Book contents
- Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials
- Dedication
- Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials
- Copyright page
- Contents
- Preface
- Introduction and Constitutive Equations For Linearly Elastic Materials
- 1 Classical Nonlinear Theories of Elasticity of Plates and Shells
- 2 Classical Nonlinear Theories of Doubly Curved Shells
- 3 Composite, Sandwich and Functionally Graded Materials
- 4 Nonlinear Shell Theory with Thickness Deformation
- 5 Hyperelasticity of Soft Biological and Rubber Materials
- 6 Introduction to Nonlinear Dynamics
- 7 Viscoelasticity and Damping
- 8 Vibrations of Rectangular Plates
- 9 Nonlinear Stability and Vibration of FGM Rectangular Plates under Static and Dynamic Loads
- 10 Nonlinear Static and Dynamic Response of Rectangular Plates in Rubber and Biomaterial
- 11 Vibrations of Isotropic and Laminated Composite Circular Cylindrical Shells
- 12 Effect of Boundary Conditions on Large-Amplitude Vibrations of Circular Cylindrical Shells
- 13 Nonlinear Static and Dynamic Response of a Blood-Filled and Pressurized Human Aorta
- 14 Nonlinear Vibrations and Stability of Doubly Curved Shallow Shells
- 15 Nonlinear Stability of Circular Cylindrical Shells under Static and Dynamic Axial Loads
- Index
- References
8 - Vibrations of Rectangular Plates
Isotropic, Laminated and Sandwich Materials
Published online by Cambridge University Press: 25 October 2018
Book contents
- Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials
- Dedication
- Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials
- Copyright page
- Contents
- Preface
- Introduction and Constitutive Equations For Linearly Elastic Materials
- 1 Classical Nonlinear Theories of Elasticity of Plates and Shells
- 2 Classical Nonlinear Theories of Doubly Curved Shells
- 3 Composite, Sandwich and Functionally Graded Materials
- 4 Nonlinear Shell Theory with Thickness Deformation
- 5 Hyperelasticity of Soft Biological and Rubber Materials
- 6 Introduction to Nonlinear Dynamics
- 7 Viscoelasticity and Damping
- 8 Vibrations of Rectangular Plates
- 9 Nonlinear Stability and Vibration of FGM Rectangular Plates under Static and Dynamic Loads
- 10 Nonlinear Static and Dynamic Response of Rectangular Plates in Rubber and Biomaterial
- 11 Vibrations of Isotropic and Laminated Composite Circular Cylindrical Shells
- 12 Effect of Boundary Conditions on Large-Amplitude Vibrations of Circular Cylindrical Shells
- 13 Nonlinear Static and Dynamic Response of a Blood-Filled and Pressurized Human Aorta
- 14 Nonlinear Vibrations and Stability of Doubly Curved Shallow Shells
- 15 Nonlinear Stability of Circular Cylindrical Shells under Static and Dynamic Axial Loads
- Index
- References
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials , pp. 338 - 379Publisher: Cambridge University PressPrint publication year: 2018
References
Abe, A., Kobayashi, Y., Yamada, G. 1998 International Journal of Non-Linear Mechanics 33, 675–690. Two-mode response of simply supported, rectangular laminated plates.CrossRefGoogle Scholar
Akhvan, H., Ribeiro, P. 2017 Composites Part B 109, 286–296. Geometrically non-linear periodic forced vibrations of imperfect laminates with curved fibres by the shooting method.CrossRefGoogle Scholar
Alijani, F., Amabili, M. 2013 Composite Structures 105, 422–436. Non-linear vibrations of laminated and sandwich rectangular plates with free edges, Part I: theory & numerical simulations.CrossRefGoogle Scholar
Alijani, F., Amabili, M., Ferrari, G., D’Alessandro, V. 2013 Composite Structures 105, 437–445. Non-linear vibrations of laminated and sandwich rectangular plates with free edges, Part II: experiments & comparisons.CrossRefGoogle Scholar
Amabili, M. 2004 Computers and Structures 82, 2587–2605. Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments.CrossRefGoogle Scholar
Amabili, M. 2005 International Journal of Non-Linear Mechanics 40, 683–710. Non-linear vibrations of doubly curved shallow shells.CrossRefGoogle Scholar
Amabili, M. 2006 Journal of Sound and Vibration 291, 539–565. Theory and experiments for large-amplitude vibrations of rectangular plates with geometric imperfections.CrossRefGoogle Scholar
Amabili, M., Farhadi, S. 2009 Journal of Sound and Vibration 320, 649–667. Shear deformable versus classical theories for nonlinear vibrations of rectangular isotropic and laminated composite plates.CrossRefGoogle Scholar
Amabili, M., Garziera, R. 1999 Journal of Sound and Vibration 224, 519–539. A technique for the systematic choice of admissible functions in the Rayleigh-Ritz method.CrossRefGoogle Scholar
Amabili, M., Karazis, K., Khorshidi, K. 2011 International Journal of Structural Stability and Dynamics 11, 673–695. Non-linear vibrations of rectangular laminated composite plates with different boundary conditions.CrossRefGoogle Scholar
Chang, S. I., Bajaj, A. K., Krousgrill, C. M. 1993 Nonlinear Dynamics 4, 433–460. Non-linear vibrations and chaos in harmonically excited rectangular plates with one-to-one internal resonance.CrossRefGoogle Scholar
Chia, C.-Y. 1988 Applied Mechanics Reviews 41, 439–451. Geometrically nonlinear behavior of composite plates: a review.CrossRefGoogle Scholar
Chu, H.-N., Herrmann, G. 1956 Journal of Applied Mechanics 23, 532–540. Influence of large amplitude on free flexural vibrations of rectangular elastic plates.CrossRefGoogle Scholar
Doedel, E. J., Champneys, A. R., Fairgrieve, T. F., Kuznetsov, Y. A., Sandstede, B., Wang, X. 1998 AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont). Concordia University, Montreal, Canada.Google Scholar
El Kadiri, M., Benamar, R. 2003 Journal of Sound and Vibration 264, 1–35. Improvement of the semi-analytical method, based on Hamilton’s principle and spectral analysis, for determination of the geometrically non-linear response of thin straight structures. Part III: steady state periodic forced response of rectangular plates.CrossRefGoogle Scholar
Ganapathi, M., Varadan, T. K., Sarma, B. S. 1991 Computers and Structures 39, 685–688. Nonlinear flexural vibrations of laminated orthotropic plates.CrossRefGoogle Scholar
Gibson, L. J., Ashby, M. F. 1999 Cellular Solids: Structure and Properties. Cambridge University Press, New York, USA.Google Scholar
Gutiérrez Rivera, M. E., Reddy, J. N., Amabili, M. 2016 Composite Structures 151, 183–196. A new twelve-parameter spectral/hp shell finite element for large deformation analysis of composite shells.CrossRefGoogle Scholar
Han, W., Petyt, M. 1997a Computers and Structures 63, 295–308. Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method. I: the fundamental mode of isotropic plates.CrossRefGoogle Scholar
Han, W., Petyt, M. 1997b Computers and Structures 63, 309–318. Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method. II: 1st mode of laminated plates and higher modes of isotropic and laminated plates.CrossRefGoogle Scholar
Harras, B., Benamar, R., White, R.G. 2002 Journal of Sound and Vibration 251, 579–619. Geometically non-linear free vibration of fully clamped symmetrically laminated rectangular composite plates.CrossRefGoogle Scholar
Hui, D. 1984 Journal of Applied Mechanics 51, 216–220. Effects of geometric imperfections on large amplitude vibrations of rectangular plates with hysteresis damping.CrossRefGoogle Scholar
Kurylov, Y. E., Amabili, M. 2010. Journal of Sound and Vibration 329, 1435–1449. Polynomial versus trigonometric expansions for non-linear vibrations of circular cylindrical shells with different boundary conditions.CrossRefGoogle Scholar
Leissa, A. W. 1969 Vibration of Plates. NASA SP-160, U.S. Government Printing Office, Washington, DC, USA (1993 reprinted by the Acoustical Society of America).Google Scholar
Leung, A. Y. T., Mao, S. G. 1995 Journal of Sound and Vibration 183, 475–491. A symplectic Galerkin method for non-linear vibration of beams and plates.CrossRefGoogle Scholar
Messina, A., Soldatos, K .P. 1999 International Journal of Mechanical Sciences 41, 891–918. Vibration of completely free composite plates and cylindrical shell panels by a higher-order theory.CrossRefGoogle Scholar
Noor, A. K., Andersen, C., Peters, J. M. 1993 Computer Methods in Applied Mechanics and Engineering 103, 175–186. Reduced basis technique for nonlinear vibration analysis of composite panels.CrossRefGoogle Scholar
Qatu, M. S. 2004 Vibrations of Laminated Shells and Plates. Elsevier, Amsterdam, The Netherlands.Google Scholar
Rao, S. R., Sheikh, A. H., Mukhopadhyay, M. 1993 Journal of the Acoustical Society of America 93, 3250–3257. Large-amplitude finite element flexural vibration of plates/stiffened plates.CrossRefGoogle Scholar
Ribeiro, P. 2001 Proceedings of the 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Material Conference and Exhibit, Seattle, USA (paper A01–25098). Periodic vibration of plates with large displacements.Google Scholar
Ribeiro, P., Petyt, M. 1999a Journal of Sound and Vibration 226, 955–983. Geometrical non-linear, steady-state, forced, periodic vibration of plate, part I: model and convergence study.CrossRefGoogle Scholar
Ribeiro, P., Petyt, M. 1999b Journal of Sound and Vibration 226, 985–1010. Geometrical non-linear, steady-state, forced, periodic vibration of plate, part II: stability study and analysis of multi-modal response.CrossRefGoogle Scholar
Ribeiro, P., Petyt, M. 2000 International Journal of Non-Linear Mechanics 35, 263–278. Non-linear free vibration of isotropic plates with internal resonance.CrossRefGoogle Scholar
Sathyamoorthy, M. 1987 Applied Mechanics Reviews 40, 1553–1561. Nonlinear vibration analysis of plates: a review and survey of current developments.CrossRefGoogle Scholar
Shi, Y., Mei, C. 1996 Journal of Sound and Vibration 193, 453–464. A finite element time domain modal formulation for large amplitude free vibrations of beams and plates.CrossRefGoogle Scholar
Yuan, J., Dickinson, S. M. 1992 Journal of Sound and Vibration 152, 203–216. On the use of artificial springs in the study of the free vibrations of systems comprised of straight and curved beams.CrossRefGoogle Scholar