In-plane free vibration and response analysis of isotropic rectangular plates using the dynamic stiffness method

Nefovska-Danilović, Marija; Petronijević, Mira

doi:10.1016/j.compstruc.2015.02.001

Cited by 66 publications

(64 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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: 89%

“…This might be due to the reason that determinant method rather than the WW algorithm was applied as the solution technique in this method [31]. (Although WW algorithm was mentioned briefly in the context of [31], it is apparent that the WW algorithm was after all not applied in its calculation, let alone how the important issue in the WW algorithm, the J 0 count, could be solved.) The first eight natural mode shapes for a fully clamped square isotropic plate (a/b = 1) are plotted in Fig.…”

Section: Applications To Plane Stress Problemsmentioning

confidence: 99%

“…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. This might be due to the reason that determinant method rather than the WW algorithm was applied as the solution technique in this method [31].…”

Section: Applications To Plane Stress Problemsmentioning

confidence: 99%

“…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. This might be due to the reason that determinant method rather than the WW algorithm was applied as the solution technique in this method [31]. (Although WW algorithm was mentioned briefly in the context of [31], it is apparent that the WW algorithm was after all not applied in its calculation, let alone how the important issue in the WW algorithm, the J 0 count, could be solved.)…”

Section: Applications To Plane Stress Problemsmentioning

confidence: 99%

“…Gorman employed a systematic superposition method to study the free inplane vibration of completely free [30] and fully clamped [18] plates. Nefovska-Danilovic et al [31] developed the dynamic stiffness method for isotropic rectangular plates based on Gorman's superposition method. Du et al [32,33] used a Fourier series based analytical method to examine the free inplane vibration of plates with different boundary conditions.…”

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