Free Vibration Analysis of Symmetrically Laminated Composite Rectangular Plates

Lee, J.M.; Chung, Jung-Hoon; Chung, Tae Young

doi:10.1006/jsvi.1996.0653

Cited by 26 publications

(8 citation statements)

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“…This situation results in various distortions in the shapes of isohips; similarly, nodal lines are changed by the effect of orthotropy. This conclusion was also drawn previously by others (Kocaturk, 1998;Lee et al, 1997).…”

Section: The Analysessupporting

confidence: 86%

“…Biancolini et al (2005) investigated the problem of approximate evaluation of the frequencies of orthotropic plates. Lee et al (1997) conducted detailed free vibration analyses on laminated composite rectangular plates for different fiber orientations of laminas. In their noteworthy study, Wang and Williams (1997) performed both analytical and experimental investigations in order to understand the vibrating behavior of machine stators.…”

Section: Introductionmentioning

confidence: 99%

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The Effects of Orthotropic Materials on the Vibration Characteristics of Structural Systems^#

Altıntaş

Göktepe²

2007

Mechanics Based Design of Structures and Machines

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The rapid growth in anisotropic material (such as composite materials) usage marks a new era in material science. Obviously, in order to understand the physical behavior of structural systems constituted by composite materials, several parameters, such as natural frequencies, mode shapes, and transmissiblities, must be incorporated into anisotropic elastic analyses. Orthotropy, as a special case of anisotropy, is common in almost all fields of civil and mechanical engineering. The objective of this effort is to investigate the effect of orthotropy on the behavior of vibrating plate systems near degenerate modes. A degenerate plate may be lack of geometric stability since the plate may exhibit a qualitatively different behavior under an arbitrarily small change in special parameters. The special parameters considered in this study are orthotropy and the location of additional mass, which have the effect of removing the system symmetry. The method, which depends on a variational procedure in conjunction with a finite difference method, is employed to examine free vibration characteristics as well as to characterize steady state response to a sinusoidally varying force applied to orthotrophic elastic rectangular plate. The problem is reduced to the solution of a system consisting of algebraic equations by using the variational difference method (VDM). In order to sort the effect of orthotropy on the vibration behavior from other factors, locations of external force, and mass are treated as additional parameters 364 Altintas and Goktepe in the analyses. Furthermore, supports are constituted as elastic so as to be able to obtain force transmissibility curves. Finally, plate systems having two different boundary conditions, namely elastically supported and elastically point supported, are utilized to observe the generalization of the outcomes. Results reveal that in case of material orthotropy existence in a plate system, there are several keynote issues that must be taken into account in vibration analyses, which are not important under isotropic conditions. Obviously, these effects are of theoretical importance and should be considered in practical applications.

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Section: The Analysessupporting

confidence: 86%

Section: Introductionmentioning

confidence: 99%

The Effects of Orthotropic Materials on the Vibration Characteristics of Structural Systems^#

Altıntaş

Göktepe²

2007

Mechanics Based Design of Structures and Machines

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“…Rajalingham et al (1996) studied the vibration of rectangular plates using the plate characteristic functions as the deflection shapes in the Rayleigh-Ritz method. Lee et al (1997) analyzed the free vibrations of symmetrically laminated composite rectangular plates using the Rayleigh-Ritz and Kantorovich methods. Chandrashekhara and Kolli (1997) used the finite element method to study the The nonlinear dynamic behavior of plates was studied by Tenneti and Chandrashekhara (1994), Young and Chen (1995), and Harichandran and Naja (1997).…”

Section: Platesmentioning

confidence: 99%

Nonlinear vibrations of doubly-curved cross-ply shallow shells

Alhazza

Nayfeh

2001

19th AIAA Applied Aerodynamics Conference

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The objective of this work is to study the local and global nonlinear vibrations of isotropic single-layered and multi-layered cross-ply doubly curved shallow shells with simply supported boundary conditions. The study is based-on the full nonlinear partial-differential equations of motion for shells. These equations of motion are based-on the von Kármán-type geometric nonlinear theory and the first-order shear-deformation theory, they are developed by using a variational approach. Many approximate shell theories are presented.We used two approaches to study the responses of shells to a primary resonance: a direct approach and a discretization approach. In the discretization approach, the nonlinear partial-differential equations are discretized using the Galerkin procedure to reduce them to an infinite system of nonlinearly coupled second-order ordinary-differential equations. An approximate solution of this set is then obtained by using the method of multiple scales for the case of primary resonance. The resulting equations describing the modulations of the amplitude and phase of the excited mode are used to generate frequency-and force-response curves. The effect of the number of modes retained in the approximation on the predicted responses is discussed and the shortcomings of using low-order discretization models are demonstrated. In the direct approach, the method of multiple scales is applied directly to the nonlinear partial-differential equations of motion and associated boundary conditions for the same cases treated using the discretization approach. The results obtained from these two approaches are compared.For the global analysis, a finite number of equations are integrated numerically to calculate the limit cycles and their stability, and hence their bifurcations, using Floquet theory. The use of this theory requires integrating 2n + (2n) 2 nonlinear first-order ordinary-differential equations simultaneously, where n is the number of modes retained in the discretization. A convergence study is conducted to determine the number of modes needed to obtain robust results.The discretized system of equation are used to study the nonlinear vibrations of shells to subharmonic resonances of order one-half. The effect of the number of modes retained in the approximation is presented. Also, the effect of the number of layers on the shell parameters is shown.Modal interaction between the first and second modes in the case of a two-to-one internal resonance is investigated. We use the method of multiple scales to determine the modulation equations that govern the slow dynamics of the response. A pseudo-arclength scheme is used to determine the fixed points of the modulation equations and the stability of these fixed points is investigated. In some cases, the fixed points undergo Hopf bifurcations, which result in dynamic solutions. A combination of a long-time integration and Floquet theory is used to determine the detailed solution branches and chaotic solutions and their stability. The limit cycles may undergo...

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“…Narita [6] investigated the free vibration of composite laminated thin plates with general edge conditions. In recent years different solution methods have been proposed and successfully applied for the static and dynamic analysis of laminated composite plates [7,8].…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of symmetric laminated composite plates with attached mass

Aydoğdu

Filiz

2015

Mechanics of Advanced Materials and Structures

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In this study, vibration of symmetrically laminated composite plates with attached mass is studied. The Ritz method with algebraic polynomial displacement field is used. The plates with at least two adjacent free edges are considered in the formulations. The effect of various parameters (number of layers, ratio of attached mass to the plate mass, position of attached mass, fiber orientation) upon the frequencies and mode shapes is investigated. It is found that attachment of a mass has important effects on the vibration characteristics of composite laminated plates.

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Free Vibration Analysis of Symmetrically Laminated Composite Rectangular Plates

Cited by 26 publications

References 0 publications

The Effects of Orthotropic Materials on the Vibration Characteristics of Structural Systems^#

The Effects of Orthotropic Materials on the Vibration Characteristics of Structural Systems^#

Nonlinear vibrations of doubly-curved cross-ply shallow shells

Vibration analysis of symmetric laminated composite plates with attached mass

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Free Vibration Analysis of Symmetrically Laminated Composite Rectangular Plates

Cited by 26 publications

References 0 publications

The Effects of Orthotropic Materials on the Vibration Characteristics of Structural Systems#

The Effects of Orthotropic Materials on the Vibration Characteristics of Structural Systems#

Nonlinear vibrations of doubly-curved cross-ply shallow shells

Vibration analysis of symmetric laminated composite plates with attached mass

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Product

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The Effects of Orthotropic Materials on the Vibration Characteristics of Structural Systems^#

The Effects of Orthotropic Materials on the Vibration Characteristics of Structural Systems^#