On free vibration response and mode shapes of arbitrarily laminated rectangular plates

Kabir, Humayun

doi:10.1016/j.compstruct.2003.10.001

Cited by 14 publications

(8 citation statements)

References 8 publications

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“…In analyses, the stacking sequence and lamination materials were constant. Kabir 2 evaluated the natural vibration characteristic of arbitrarily rectangular laminated plates made of composite materials and investigated the mode shapes of plates. Motaghian et al 3 presented an analytical approach for free vibration behavior of rectangular plates on partial elastic foundation based on various mode sequences and they used different boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Experimental and statistical free vibration analyses of laminated composite beams with functionally graded fiber orientation angles

Evran

2020

Polymers and Polymer Composites

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In this experimental and statistical study, free vibration behavior of laminated composite beams with functionally graded fiber orientation angles was investigated under clamped-free boundary conditions. The beams were manufactured using E-glass/epoxy. Fiber orientation angles of the beams were analyzed based on Taguchi’s L9 (33) orthogonal array. The effect of fiber orientation angles and beams with optimum levels were assessed using analysis of signal-to-noise ratio. Significant laminates of the beams and their percent contributions on the free vibration responses were obtained using analysis of variance. According to this study, the increase of fiber orientation angle from 0° to 80° causes a decrease in the fundamental frequency behavior of laminated composite beams. The most effective control factors were found to be the first and the second laminates symbolized as L1 with 85.86% contribution, the third and the fourth laminates symbolized as L2 with 12.29% contribution, the fifth and the sixth laminates symbolized as L3 with 1.84% contribution, respectively. This study can be used as a reference for free vibration analysis of cantilever laminated composite beams made of functionally graded fiber orientation angles as experimentally and statistically.

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Section: Introductionmentioning

confidence: 99%

Experimental and statistical free vibration analyses of laminated composite beams with functionally graded fiber orientation angles

Evran

2020

Polymers and Polymer Composites

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“…This procedure is simply referred to as the Fourier series direct‐expansion method. This method has been applied by Chaudhuri and Kabir to various subclasses, such as 2 r = 2, 4 of the general system. The Fourier series direct‐expansion method was also developed by Chaudhuri for the general system, represented by a system of completely coupled linear 2 r th order differential equations with constant coefficients and subjected to general boundary conditions.…”

Section: Application To the Fourier Series Methods For Linear Elasto‐mentioning

confidence: 99%

“…Because of the inherent complexity of higher order differentiation of Fourier series of the functions, only Fourier series of (partial) derivatives up to fourth order have been derived for the one-dimensional or two-dimensional functions with general boundary conditions. As to arbitrary order (partial) derivatives of the functions with general boundary conditions, the general formulas for the Fourier series are heretofore unavailable, which holds up further development of some new types of Fourier series methods for linear elastodynamical systems such as the Fourier series direct-expansion method [1][2][3][4][5][6] and the Fourier series method with supplementary terms [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Take the Fourier series direct-expansion method for example, Chaudhuri [1] investigated a general system that is represented by a set of completely coupled linear 2rth (r is a positive integer) order partial differential equations with constant coefficients.…”

Section: Introductionmentioning

confidence: 99%

On Fourier series for higher order (partial) derivatives of functions

Sun

Zhang

2016

Math Methods in App Sciences

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This paper is focused on higher order differentiation of Fourier series of functions. By means of Stokes's transformation, the recursion relations between the Fourier coefficients in Fourier series of different order (partial) derivatives of the functions as well as the general formulas for Fourier series of higher order (partial) derivatives of the functions are acquired. And then, the sufficient conditions for term‐by‐term differentiation of Fourier series of the functions are presented. These findings are subsequently used to reinvestigate the Fourier series methods for linear elasto‐dynamical systems. The results given in this paper on the constituent elements, together with their combinatorial modes and numbering, of the sets of coefficients concerning 2rth order linear differential equation with constant coefficients are found to be different from the results deduced by Chaudhuri back in 2002. And it is also shown that the displacement solution proposed by Li in 2009 is valid only when the second order mixed partial derivative of the displacement vanishes at all of the four corners of the rectangular plate. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Hause and Librescu (2006) performed a study considering the effects of anisotropy of core layer's face sheets and other mechanical/geometrical parameters of flat sandwich plates on their eigen frequencies. Kabir (2004) implemented numerical results, eigenvalues, and mode shapes by comparing the analytical solutions with commercially available finite element packages. Biancolini et al (2005) investigated the problem of approximate evaluation of the frequencies of orthotropic plates.…”

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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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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On free vibration response and mode shapes of arbitrarily laminated rectangular plates

Cited by 14 publications

References 8 publications

Experimental and statistical free vibration analyses of laminated composite beams with functionally graded fiber orientation angles

Experimental and statistical free vibration analyses of laminated composite beams with functionally graded fiber orientation angles

On Fourier series for higher order (partial) derivatives of functions

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

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On free vibration response and mode shapes of arbitrarily laminated rectangular plates

Cited by 14 publications

References 8 publications

Experimental and statistical free vibration analyses of laminated composite beams with functionally graded fiber orientation angles

Experimental and statistical free vibration analyses of laminated composite beams with functionally graded fiber orientation angles

On Fourier series for higher order (partial) derivatives of functions

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

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Resources

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