NONLINEAR VIBRATIONS OF RECTANGULAR LAMINATED COMPOSITE PLATES WITH DIFFERENT BOUNDARY CONDITIONS

2011 ◽  
Vol 11 (04) ◽  
pp. 673-695 ◽  
Author(s):  
M. AMABILI ◽  
K. KARAZIS ◽  
K. KHORSHIDI
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibrations ◽  
Continuation Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Different Boundary Conditions ◽  
Simply Supported ◽  
First Order ◽  
Nonlinear Plate

Nonlinear vibrations of rectangular laminated composite plates with different boundary conditions are studied by using different nonlinear plate theories. In particular, numerical results for (i) the classical Von Kárman theory, (ii) the first-order shear deformation theory (SDT), and (iii) the third-order SDT are compared. The nonlinear response to harmonic excitation in the frequency neighborhood of the fundamental mode is investigated. Numerical investigation is carried out by using pseudo-arclength continuation method and bifurcation analysis. The boundary conditions of the plates are: simply supported with movable edges, simply supported with immovable edges, and clamped (CL) edges. For thick plates (thickness ratio 0.1), the strongest hardening nonlinear behavior is observed for CL plates, while the simply supported movable plates are the ones with the weakest nonlinearity among the three different boundary conditions studied here. Differences among the three nonlinear plate theories are large for thick laminated plates. For all the other cases, the first-order SDT, with shear correction factor [Formula: see text], and the higher-order SDT give almost coincident results.

scholarly journals A General Ritz Algorithm for Static Analysis of Arbitrary Laminated Composite Plates using First Order Shear Deformation Theory

2013 ◽  
Vol 10 (2) ◽  
pp. 1 ◽  
Author(s):  
RF Rango ◽  
FJ Bellomo ◽  
LG Nallim
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Static Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
General Algorithm ◽  
Laminated Composite Plates ◽  
First Order

 This paper is concerned with the bending of laminated composite plates with arbitrary lay-up and general boundary conditions. The analysis is based on the small deflection, first-order shear deformation theory of composite plates, which utilizes the Reissner-Mindlin plate theory. In solving the aforementioned plate problems, a general algorithm based on the Ritz method and the use of beam orthogonal polynomials as coordinate functions is derived. This general algorithm provides an analytical approximate solution that can be applied to the static analysis of moderately thick laminated composite plates with any lamination scheme and combination of edge conditions. The convergence, accuracy, and flexibility of the obtained general algorithm are shown by computing several numerical examples and comparing some of them with results given in the literature. Some results, including general laminates and nonsymmetrical boundary conditions with free edges, are also presented. 

Nonlinear Vibrations of Circular Cylindrical Shells With Different Boundary Conditions

2009 ◽  
Author(s):  
M. Amabili ◽  
Ye. Kurylov
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibrations ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Continuation Method ◽  
Elastic Strain Energy ◽  
Variable Boundary ◽  
Different Boundary Conditions ◽  
Simply Supported ◽  
Circular Cylindrical Shells

Large-amplitude nonlinear vibrations of circular cylindrical shells with different boundary conditions are investigated. The Sanders-Koiter nonlinear shell theory, which includes shear deformation, is used to calculate the elastic strain energy. Shell’s displacement fields (longitudinal, circumferential and radial) are expanded by means of a double mixed series: harmonic functions for the circumferential variable; Chebyshev polynomials for the longitudinal variable. Boundary conditions for both simply supported and clamped-clamped shells are exactly satisfied. The Lagrangian approach is applied to obtain a system of nonlinear ordinary differential equations. Different expansions involving from 14 to 34 generalized co-ordinates, associated with natural modes of both simply supported and clamped-clamped shells are used to study the convergence of the solution. The nonlinear equations of motion are studied by using arclength continuation method and bifurcation analysis. Numerical responses obtained in the spectral neighborhood of the lowest natural frequency are compared with the results available in literature.

Natural Frequency of Laminated Composite Plates Using a Sinusoidal Theory

2014 ◽  
Vol 709 ◽  
pp. 148-152
Author(s):  
Guo Qing Zhou ◽  
Ji Wang ◽  
Song Xiang
Keyword(s):  
Differential Equations ◽  
Analytical Method ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Sinusoidal Shear Deformation Theory

Sinusoidal shear deformation theory is presented to analyze the natural frequencies of simply supported laminated composite plates. The governing differential equations based on sinusoidal theory are solved by a Navier-type analytical method. The present results are compared with the available published results which verify the accuracy of sinusoidal theory.

A Simple Higher-Order Theory for Laminated Composite Plates

1984 ◽  
Vol 51 (4) ◽  
pp. 745-752 ◽  
Author(s):  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Order Theory ◽  
Higher Order ◽  
Laminated Composite Plates ◽  
First Order ◽  
First Order Theory

A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano [6], but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

A novel first-order shear deformation theory for laminated composite plates

2014 ◽  
Vol 17 (3) ◽  
pp. 321-338 ◽  
Author(s):  
Mohamed Sadoune ◽  
Abdelouahed Tounsi ◽  
Mohammed Sid Ahmed Houari ◽  
El Abbes Adda Bedia
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
First Order
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