Simulation of classical edge conditions by finite elastic restraints in the vibration analysis of plates

Bapat, A.V.; Venkatramani, N.; Suryanarayan, S.

doi:10.1016/0022-460x(88)90338-0

Cited by 27 publications

(10 citation statements)

References 14 publications

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“…Joga Rao and Lakshmi Kantham [18] studied the variation of the three first vibration modal frequencies of as quare plate having uniform butvariable slope restraints along all edges. Bapat et al studied the simulation of classical edge conditions [19] (clamped or simply-supported)b yd efining adequate values of flexibility in simulations that could be representative of either infinite or zero flexibility (intheir work, flexibility wasp refered to stiffness). These previously published results were used to propose atheoretical basis for experimentally achieving these specificboundary conditions [20], butnoexperimental validation wasgiven.…”

Section: Simulations Fora Pproaching Actual Boundary Conditions Of Asmentioning

confidence: 99%

“…On their side, Warburton and Edney [21] numerically studied the variation of the fundamental frequencyo fp lates with different aspect ratios and boundary conditions (including asimply-supported plate)using dimensionless rotational and translational restraints. The reader interested in further readings concerning such simulation works can refer to the bibliographyg iven in [19,21], and also to pages 117-123 in Leissa'sbook [2] concerning plates having continuous simply supported edge conditions.…”

Section: Simulations Fora Pproaching Actual Boundary Conditions Of Asmentioning

confidence: 99%

“…As the plate'sfundamental mode frequency( mode (1, 1))w as shown to be the most sensitive to changes in boundary conditions [19,7,21], the following results mainly focus on this eigenfrequency (from Equation (2),that is f 11 = ω 11 /2π = 77.03 Hz). these figures, the values of the ratio k b r /k p r nearly vary as the percentage deviation on the frequencyofmode (1, 1).…”

Section: Simulations Fora Pproaching Actual Boundary Conditions Of Asmentioning

confidence: 99%

See 2 more Smart Citations

A Plane and Thin Panel with Representative Simply Supported Boundary Conditions for Laboratory Vibroacoustic Tests

Robin¹,

Chazot²,

Boulandet³

et al. 2016

Acta Acustica united with Acustica

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At echnique to setup as imply supported rectangular plane panel for laboratory vibroacoustic tests is described and validated. Forag iven panel fixed to thin vertical supports, ad imensionless parameter is proposed to size these supports following adesired frequencyprecision compared to theoretical eigenfrequencies of apanel with such boundary conditions. An umerical study confirms the potential of this design parameter.D etailed instructions for assembling apanel with adequate thin vertical supports on arigid frame are then given. Finally,three laboratory cases are described which illustrate possible experimental vibroacoustic applications using ap anel assembled following previous guidelines. The design parameter viability is experimentally confirmed, and all obtained results depicted good agreement with analytical solutions and numerical predictions.

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Section: Simulations Fora Pproaching Actual Boundary Conditions Of Asmentioning

confidence: 99%

Section: Simulations Fora Pproaching Actual Boundary Conditions Of Asmentioning

confidence: 99%

Section: Simulations Fora Pproaching Actual Boundary Conditions Of Asmentioning

confidence: 99%

See 1 more Smart Citation

A Plane and Thin Panel with Representative Simply Supported Boundary Conditions for Laboratory Vibroacoustic Tests

Robin¹,

Chazot²,

Boulandet³

et al. 2016

Acta Acustica united with Acustica

View full text Add to dashboard Cite

show abstract

“…This problem will become much more serious for plates that are elastically restrained along its edges. This is probably the reason why the previous investigations have been mostly focused on the problems that involve some kind of simplifications with respect to the arrangement of elastic restraints (Carmichael, 1959;Warburton and Edney, 1984;Gorman, 1980;Bapat et al, 1988). To substitute for the beam functions, one can use other forms of admissible functions such as simple or orthogonal polynomials, trigonometric functions and their combinations (Cupial, 1997;Bhat, 1985;Dickinson 1986;Filipich and Rosales, 2000;Beslin and Nicolas, 1997;Zhou, 1996;Hurlebaus and Gaul, 2001;Ramkumar et al, 1987).…”

Section: Introductionmentioning

confidence: 98%

The Influence of edge restraining stiffness on the transverse vibrations of rectangular plate structures

Jin

Hao

et al. 2010

J. Marine. Sci. Appl.

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This paper presents an analytical study on the influence of edge restraining stiffness on the transverse vibrations of rectangular plate structure. An improved Fourier series method was employed to analyze the transverse vibration of plate structure with general elastically restrained boundary conditions. A linear combination of a double Fourier series and eight auxiliary terms was sought as the admissible function of the flexural displacement of the plate, each term being a combination of a polynomial function and a single cosine series expansion. The auxiliary terms were introduced to ensure and improve the smoothness of the original displacement function and its derivatives at the boundaries. Several numerical examples were given to demonstrate the validity and accuracy of the current solution. The influences of translational and rotational stiffness on the natural frequencies and mode shapes of plate were analyzed by numerical results. The results show that the translational stiffness has bigger influence on the natural frequencies than the rotational stiffness. It is generally well known that little change of the rotational stiffness has little influence on the mode shapes of plate. However, the current work shows that a very little change of rotational stiffness value may lead to a large change of the mode shapes of a square plate structure.

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“…Gorman used the superposition technique to solve approximately free vibration problems of plates for various geometries and boundary conditions, like in Gorman (1980) and Gorman (1982). A set of static beam functions was used to determine the natural frequencies of elastically restrained plates, like in Bapat et al (1988) and Zhou (1996). Hurlebaus et al (2001) have extended the Fourier series solution to the problems with more complicated boundary conditions than the simply supported one.…”

Section: Introductionmentioning

confidence: 99%

Vibration of plate on foundation with four edges free by finite cosine integral transform method

Zhong

Zhao

Liu

2014

Lat. Am. j. solids struct.

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The analytical solutions for the natural frequencies and mode shapes of the rectangular plate on foundation with four edges free is presented by using the finite cosine integral transform method. In the analysis procedure, the classical Kirchhoff rectangular plate is considered and the foundation is modelled as the Winkler elastic foundation. Because only are the basic dynamic elasticity equations of the thin plate on elastic foundation adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by present paper is reasonable and theoretical. In order to illuminate the correction of formulations, the numerical results are also presented to comparing with that of the other references.

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Simulation of classical edge conditions by finite elastic restraints in the vibration analysis of plates

Cited by 27 publications

References 14 publications

A Plane and Thin Panel with Representative Simply Supported Boundary Conditions for Laboratory Vibroacoustic Tests

A Plane and Thin Panel with Representative Simply Supported Boundary Conditions for Laboratory Vibroacoustic Tests

The Influence of edge restraining stiffness on the transverse vibrations of rectangular plate structures

Vibration of plate on foundation with four edges free by finite cosine integral transform method

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