Book•
Nonlinear Vibrations and Stability of Shells and Plates
01 Aug 2014-
TL;DR: In this article, a comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells is presented. But the authors do not consider the effect of boundary conditions on the large-amplitude vibrations of circular cylinders.
Abstract: Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.
Citations
More filters
TL;DR: In this paper, a nonlinear vibration analysis of metal foam circular cylindrical shells reinforced with graphene platelets is performed, and the results demonstrate that GPL reinforced metal foam (GPLRMF) shells exhibit hardening-spring vibration characteristics.
259 citations
TL;DR: In this article, the authors used the generalized displacement field of the Carrera Unified Formulation (CUF), including the Zig-Zag (ZZ) effect given by the Murakami's function.
Abstract: The theoretical framework of the present manuscript covers the dynamic analysis of doubly-curved shell structures using the generalized displacement field of the Carrera Unified Formulation (CUF), including the Zig-Zag (ZZ) effect given by the Murakami’s function. The partial differential system of equations is solved by using the Generalized Differential Quadrature (GDQ) method. This numerical approach has been proven to be accurate, reliable and stable in several engineering applications. The current paper focuses on Functionally Graded (FG) doubly-curved shells and panels using various higher-order equivalent single layer theories, introduced and applied for the first time by the authors to completely doubly-curved shell structures, and different through-the-thickness volume fraction distributions, such as four-parameter power law, Weibull and exponential distributions. Moreover, the classic theory of mixtures is compared to the Mori–Tanaka scheme for the calculation of the mechanical properties of the materials. In particular, the numerical applications presented in this work are related to particular FG configurations in which it is possible to model a soft-core structure using a continuous variation of the mechanical properties of the materials at hand. The natural frequencies and mode shapes of several structures are presented and compared to numerical solutions taken from the literature.
224 citations
TL;DR: In this article, a study on the vibrations of functionally graded material (FGM) rectangular plates with porosities and moving in thermal environment was conducted, where the porosity distribution of the FGM plates was taken into account by using von Karman nonlinear plate theory.
216 citations
TL;DR: In this paper, a review of geometrically non-linear free and forced vibrations of shells made of traditional and advanced materials is presented, including closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials.
Abstract: The present literature review focuses on geometrically non-linear free and forced vibrations of shells made of traditional and advanced materials. Flat and imperfect plates and membranes are excluded. Closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials are reviewed and great attention is given to non-linear vibrations of shells subjected to normal and in-plane excitations. Theoretical, numerical and experimental studies dealing with particular dynamical problems involving parametric vibrations, stability, dynamic buckling, non-stationary vibrations and chaotic vibrations are also addressed. Moreover, several original aspects of non-linear vibrations of shells and panels, including (i) fluid–structure interactions, (ii) geometric imperfections, (iii) effect of geometry and boundary conditions, (iv) thermal loads, (v) electrical loads and (vi) reduced-order models and their accuracy including perturbation techniques, proper orthogonal decomposition, non-linear normal modes and meshless methods are reviewed in depth.
203 citations
Cites background from "Nonlinear Vibrations and Stability ..."
...In both of these theories, non linearities can be retained in changes in curvature and torsion [7]....
[...]
...The monograph of Amabili [7] has also provided a literature review on non linear vibrations and dynamic stability of shells till 2008 and has shown that many questions in this area still remain unan swered....
[...]
...These theories have been completely discussed in the books of Amabili [7], Reddy [13] and Carrera et al....
[...]
TL;DR: In this paper, a modified power law formulation is employed to depict the material properties of the plates in the thickness direction, and three terms of inertial forces are taken into account due to the translation of plates.
185 citations
References
More filters
Book•
01 Aug 1983TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Abstract: Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.- Hyperbolic Sets, Sympolic Dynamics, and Strange Attractors.- Global Bifurcations.- Local Codimension Two Bifurcations of Flows.- Appendix: Suggestions for Further Reading. Postscript Added at Second Printing. Glossary. References. Index.
12,669 citations
01 Jan 2015
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Abstract: Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.- Hyperbolic Sets, Sympolic Dynamics, and Strange Attractors.- Global Bifurcations.- Local Codimension Two Bifurcations of Flows.- Appendix: Suggestions for Further Reading. Postscript Added at Second Printing. Glossary. References. Index.
12,485 citations
5,359 citations
Book•
19 Nov 1996TL;DR: The use of composite materials in engineering structures continues to increase dramatically, and there have been significant advances in modeling for general and composite materials and structures in particular as discussed by the authors. But the use of composites is not limited to the aerospace domain.
Abstract: The use of composite materials in engineering structures continues to increase dramatically, and there have been equally significant advances in modeling for general and composite materials and structures in particular. To reflect these developments, renowned author, educator, and researcher J.N. Reddy created an enhanced second edit
5,301 citations
Book•
[...]
01 Jan 1996
TL;DR: Mathematica has defined the state of the art in technical computing for over a decade, and has become a standard in many of the world's leading companies and universities as discussed by the authors.
Abstract: From the Publisher:
Mathematica has defined the state of the art in technical computing for over a decade, and has become a standard in many of the world's leading companies and universities From simple calculator operations to large-scale programming and the preparation of interactive documents, Mathematica is the tool of choice
3,566 citations