Free Vibration of Line Supported Rectangular Plates Using a Set of Static Beam Functions

Zhou, Di; Cheung, Y.K.

doi:10.1006/jsvi.1998.2043

Cited by 22 publications

(11 citation statements)

References 15 publications

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“…According to the theorem of exponential matrix, the state vector d( 1 ) at a given point = 1 and the state vector d( 2 ) at another point = 2 are related by a transfer equation from Equation (13) into of the following form [40] …”

Section: Boundary Conditions and Solutionmentioning

confidence: 99%

Free vibration of generally supported rectangular Kirchhoff plates: State‐space‐based differential quadrature method

Zhang

Chen

2006

Numerical Meth Engineering

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SUMMARYThe title problem is investigated using the differential quadrature method based on the state-space formalism. The plates, with mixed boundary conditions, may cross over one-way internal rigid line supports that impose zero transverse displacement constraints. Differential quadrature procedure is applied in the direction of line supports, while exact solution is sought in the transfer domain perpendicular to the line supports using the state space method. To avoid numerical instability in the transfer matrix method, joint coupling matrices are introduced, mainly according to the continuity conditions at line joints. Natural frequencies of rectangular Kirchhoff plates with general boundary conditions are calculated and compared with the results from other methods. Effects of location of internal line supports and the mixed boundary conditions on the frequency parameters are discussed.

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Section: Boundary Conditions and Solutionmentioning

confidence: 99%

Free vibration of generally supported rectangular Kirchhoff plates: State‐space‐based differential quadrature method

Zhang

Chen

2006

Numerical Meth Engineering

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“…It is obvious that for an Euler}Bernoulli beam, takes zero value because the e!ect of shear deformation is neglected. In this case, the static Timoshenko beam functions automatically degenerate into the static Euler}Bernoulli beam functions which have been successfully applied to the vibration analysis of rectangular thin plates with internal line supports [12]. In order to demonstrate the low computational cost and high accuracy of the present method, the convergence and comparison studies are carried out.…”

Section: Static Timoshenko Beam Functionsmentioning

confidence: 98%

Free Vibration of Multi-Span Timoshenko Beams Using Static Timoshenko Beam Functions

Zhou

2001

Journal of Sound and Vibration

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“…The eigenfunctions of those bridges three spans in one direction and the single span beam in the other direction were used as inputs for the Rayleigh-Ritz method to determine the natural frequencies of the plate. Zhou and Cheung (1999) used the same static beam functions in the Rayleigh-Ritz method to determine the natural frequencies and mode shapes of thin, orthotropic, rectangular, continuous plates in one and two directions. They showed that this set of static beam functions has advantages in terms of computational cost, application versatility, and numerical accuracy, especially for the plate problem with a large number of intermediate lines supported and/or when higher vibrating modes need to be calculated.…”

Section: Introductionmentioning

confidence: 99%

“…The finite element method approach has been widely adopted for analysis of plates with complex geometries (Zhou and Cheung, 1999;Hrabok and Hrudley, 1984;Smith and William, 1970). Recently Rezaiguia and Laefer (2009) introduced the concept of intermodal coupling for a three-span bridge deck, as will be described below.…”

Section: Introductionmentioning

confidence: 99%

Extension of a semi-analytical approach to determine natural frequencies and mode shapes of a multi-span orthotropic bridge deck

Rezaiguia¹,

Fisli²,

Ellagoune³

et al. 2012

Structural Engineering and Mechanics

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Abstract. This paper extends a single equation, semi-analytical approach for three-span bridges to multispan ones for the rapid and precise determination of natural frequencies and natural mode shapes of an orthotropic, multi-span plate. This method can be used to study the dynamic interaction between bridges and vehicles. It is based on the modal superposition method taking into account intermodal coupling to determine natural frequencies and mode shapes of a bridge deck. In this paper, a four-and a five-span orthotropic roadway bridge decks are compared in the first 10 modes with a finite element method analysis using ANSYS software. This simplified implementation matches numerical modeling within 2% in all cases. The paper verifies that applicability of single formula approach as a simpler alternative to finite element modeling.

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Free Vibration of Line Supported Rectangular Plates Using a Set of Static Beam Functions

Cited by 22 publications

References 15 publications

Free vibration of generally supported rectangular Kirchhoff plates: State‐space‐based differential quadrature method

Free vibration of generally supported rectangular Kirchhoff plates: State‐space‐based differential quadrature method

Free Vibration of Multi-Span Timoshenko Beams Using Static Timoshenko Beam Functions

Extension of a semi-analytical approach to determine natural frequencies and mode shapes of a multi-span orthotropic bridge deck

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