On the Free in-Plane Vibration of Isotropic Rectangular Plates

Bardell, N.S.; Langley, R.S.; Dunsdon, J.M.

doi:10.1006/jsvi.1996.0134

Cited by 85 publications

(48 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The current SDSM results, which are accurate up to the last figures quoted with six significant figures, are intended to serve as benchmark solutions. It can be found that the results computed by GSM [18] and Ritz method [23] have four significant figures which all coincide with the first four digits of the current SDSM results. The dynamic stiffness method based on the superposition method [31] appears to miss the repeated natural frequency for the square plate as denoted by ' * * ' in Table 3.…”

Section: Applications To Plane Stress Problemssupporting

confidence: 80%

“…The notations k (corresponding to x axis) and j (corresponding to y axis) of (k, j) denote symmetric (taking '0') or antisymmetric (taking '1') deformation with respect to the corresponding axes. [18] c Fourier series based analytical method [32] d Ritz method [23] Similar comparison can be made for the free inplane vibration of completely free isotropic plates (ν = 0.3) between the current SDSM results and those available in the literature [18,23,31,32]. All SDSM results have six significant digit accuracy which are more accurate than those available in the literature (the latter methods give no more than three or four significant figures).…”

Section: Applications To Plane Stress Problemsmentioning

confidence: 53%

“…Table 3 compares the first eight natural frequencies computed by the SDSM results with those obtained by other methods wherever available. The comparative methods include dynamic stiffness method based on the superposition method (DSM) [31], Gorman's superposition method (GSM) [18], Fourier series based analytical method (FSA) [32] and the Ritz method [23]. The current SDSM results, which are accurate up to the last figures quoted with six significant figures, are intended to serve as benchmark solutions.…”

Section: Applications To Plane Stress Problemsmentioning

confidence: 99%

“…Xing and Liu [19][20][21] provided closed-form exact solutions for all possible cases of simply supported plates by using the Rayleigh quotient method. The classical dynamic stiffness method [22][23][24][25], first developed for plates in the 70s [22], can be applied to plate assemblies but restricted to cases with two opposite plate edges simply supported. Plates with other boundary conditions are solved resorting to other analytical methods.…”

Section: Introductionmentioning

confidence: 99%

“…Plates with other boundary conditions are solved resorting to other analytical methods. Bardell et al [23] used the Rayleigh-Ritz method to discuss the free inplane vibration of single plates with simply supported, fully clamped and completely free boundary conditions. Dozio [26] used the Ritz method in conjunction with a set of trigonometric functions to study the free inplane vibration of plates with elastic boundaries.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

Xiang

Banerjee

2017

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

Citation: Liu, X. and Banerjee, J. R. (2017). A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems. Mechanical Systems and Signal Processing, 87, doi: 10.1016/j.ymssp.2016.10.017 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractA highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the exact general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J 0 ) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.

show abstract

Section: Applications To Plane Stress Problemssupporting

confidence: 80%