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
9 - Nonlinear Stability and Vibration of FGM Rectangular Plates under Static and Dynamic Loads
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. 380 - 401Publisher: Cambridge University PressPrint publication year: 2018
References
Alijani, F., Amabili, M. 2013 International Journal of Non-linear Mechanics 50, 109–126. Nonlinear dynamic instability of functionally graded plates in thermal environments.CrossRefGoogle Scholar
Alijani, F., Bakhtiari-Nejad, F., Amabili, M. 2011 Nonlinear Dynamics 66 251–270. Non-linear vibrations of FGM rectangular plates in thermal environments.CrossRefGoogle Scholar
Amabili, M. 2008 Non-linear Vibrations and Stability of Shells and Plates. Cambridge University Press, New York.CrossRefGoogle Scholar
Bolotin, V. V. 1964 The Dynamic Stability of Elastic Systems. Holden-Day, San Francisco.Google 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
Evan-Iwanowski, R. M. 1965 Applied Mechanics Reviews 18, 699–702. On the parametric response of structures.Google Scholar
Hunag, X. L., Shen, H.S. 2004 International Journal of Solids and Structures 41, 2403–2427. Non-linear vibration and dynamic response of functionally graded plates in thermal environments.CrossRefGoogle Scholar
Lee, Y. Y., Zhao, X., Reddy, J. N. 2010 Computer Methods in Applied Mechanics and Engineering 199, 1645–1653. Post-buckling analysis of functionally graded plates subject to compressive and thermal loads.CrossRefGoogle Scholar
Matsunaga, H. 2008 Composite Structures 82, 499–512. Free vibration and stability of functionally graded plates according to a 2-D higher order shear deformation theory.CrossRefGoogle Scholar
Pellicano, F. 2009 Communications in Nonlinear Science and Numerical Simulation 14, 3449–3462. Dynamic stability and sensitivity to geometric imperfections of strongly compressed circular cylindrical shells under dynamics axial loads.CrossRefGoogle Scholar
Reddy, J. N., Phan, N. D. 1985 Journal of Sound and Vibration 98, 157–170. Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory.CrossRefGoogle Scholar
Sahu, S. K., Datta, D. K. 2007 Applied Mechanics Reviews 60, 65–75. Research advances in the dynamic stability of plates and shells: 1987–2005 Part1: Conservative systems.CrossRefGoogle Scholar
Shen, H. S. 2009 Functionally Graded Materials, Non-linear Analysis of Plates and Shells. CRC Press, Florida.Google Scholar
Shen, H. S., Wang, Z. X. 2012 Composite Structures 94, 2197–2208. Assessment of Voigt and Mori-Tanaka models for the vibration analysis of functionally graded plates.CrossRefGoogle Scholar
Somerset, J. H., Evan-Iwanowski, R. M. 1967 International Journal of Non-linear Mechanics 21, 217–232. Influence of non-linear inertia on the parametric response of rectangular plates.CrossRefGoogle Scholar
Timoshenko, S., Woinowsky-Krieger, S. 1959 Theory of Plates and Shells. McGraw-Hill, New York, USA.Google Scholar
Woo, J., Meguid, S. A., Stranart, J. C., Liew, K. M. 2005 International Journal of Mechanical Sciences 47, 1147–1171. Thermomechanical post-buckling analysis of moderately thick functionally graded plates and shallow shells.CrossRefGoogle Scholar
Yamaki, N., Nagai, K. 1975 Report of the Institute of High Speed Mechanics, Tohoku University 32, 103–127. Dynamic stability of rectangular plates under periodic compressive forces.Google Scholar
Yang, J., Shen, H. S. 2003 International Journal of Non-linear Mechanics 38, 467–482. Non-linear analysis of functionally graded plates under transverse and in-plane loads.CrossRefGoogle Scholar