Free in-plane vibration of isotropic non-rectangular plates

Singh, Anand; Muhammad, T.

doi:10.1016/s0022-460x(03)00496-6

Cited by 40 publications

(28 citation statements)

References 9 publications

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“…Kim et al [14] presented exact frequency equations and mode functions to study the in-plane vibration of a circular plate with its outer edge being restrained elastically. Singh and Muhammad [15] presented a numerical method to study the free in-plane vibration of the on-rectangular plate including parallelogram plate and circular annular plate with three sets of boundary conditions, i.e. CCCC, CCCF and CFCF.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

A unified solution for free in-plane vibration of orthotropic circular, annular and sector plates with general boundary conditions

Wang

Shi

Liang

et al. 2016

Applied Mathematical Modelling

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To study the free in-plane vibration for the orthotropic circular, annular and sector plates with general boundary conditions, a modified Fourier-Ritz approach is developed. In this approach, several auxiliary closed-form functions are added to the standard Fourier cosine series to obtain a robust function. The introduction of these auxiliary functions can eliminate all the potential discontinuities of the original displacement function and its derivatives in whole domain and then effectively improve the convergence of the results. All the displacements are expressed with the modified Fourier series expansion and the arbitrary boundary conditions and the appropriate continuity conditions along the radial edges are realized by introducing the artificial boundary spring technique and artificial coupling spring technique. In addition, the Ritz procedure based on the energy functions of the plates is adopted to obtain the accurate solution since the constructed displacement field is adequately smooth in the whole solution domain. By numerical examples involving the plates of various shapes and with different boundary conditions, the reliability, accuracy and versatility of the current method get fully demonstrated. On this basis, some new results for the free in-plane vibration problem of orthotropic circular, annular and sector plates with

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Section: Accepted Manuscriptmentioning

confidence: 99%

A unified solution for free in-plane vibration of orthotropic circular, annular and sector plates with general boundary conditions

Wang

Shi

Liang

et al. 2016

Applied Mathematical Modelling

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show abstract

“…Additionally, Seok et al [7] performed an FIV analysis of a cantilevered rectangular plate by using a variational approximation procedure, wherein the differential equations and tractionfree conditions on two opposite edges are satisfied exactly and the remaining conditions are satisfied variationally. Singh et al [8] investigated the FIV of isotropic non-rectangular plates according to the variational method, wherein the displacement fields are represented by much higher order polynomials than the ones used for the geometric representation. And Woodcock et al [9] studied the effects of the ply orientation on in-plane vibrations based on the Rayleigh-Ritz formulation in conjunction with Hamilton principle.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions for the free in-plane vibrations of rectangular plates

Xing

Liu

2009

International Journal of Mechanical Sciences

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“…Based on Eqs. (11) and (13), the spatial distribution of a waveguide mode is described by a collection of coefficients of the uncoupled modes. The waveguide modes of the four branches in Fig The normalized coefficients of the waveguide mode corresponding to the first branch in Fig.…”

Section: Decomposition Of In-plane Waveguide Modesmentioning

confidence: 99%

“…Their energy can be generated by various kinds of in-plane forces including the tangential stresses on the flow structural interface, 5 and when reaching the structural material and geometric discontinuities, it can also be transformed into the energy of flexural waves which are directly responsible for structural sound radiation. 6 Many of the recent studies [7][8][9][10][11][12][13][14][15][16][17][18][19] on the free and forced responses of in-plane wave in finite plates have been motivated by this recognition. Although brief reviews of the progress in this area over the last two decades have been given by Dozio, 16 and by Liu and Xing,17 of particular interest is the series of papers by Gorman 5,10,12,13,15 on the semianalytical solution of the free in-plane vibration in finite plates, and by Xing and Liu [17][18][19] on exact solution for inplane vibrations of plates.…”

Section: Introductionmentioning

confidence: 99%

Waveguide characteristics of coupled in-plane waves

Lü

Qiu

2012

The Journal of the Acoustical Society of America

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In-plane waves in a waveguide made from a thin plate are described by a superposition of a set of orthogonal functions that satisfy the edge conditions of the waveguide. Due to the Poisson and shear effects, the displacement components of the in-plane waves along the two in-plane orthogonal coordinates are coupled and this coupling affects the propagation and spatial properties of the waveguide modes. The orthogonal functions and their associated wavenumbers represent the characteristics of the uncoupled modes of the waveguide where the above mentioned couplings are ignored. This study demonstrates that the characteristics of the waveguide modes are determined by the couplings of the uncoupled mode pairs, which become significant when the pairs satisfy the conditions of spatial coincidence. At some frequencies, certain waveguide modes can be determined by a single pair of uncoupled modes. For this case, the analytical solution for the waveguide modes exists and provides both a qualitative and quantitative interpretation of the characteristics of the waveguide mode.

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Free in-plane vibration of isotropic non-rectangular plates

Cited by 40 publications

References 9 publications

A unified solution for free in-plane vibration of orthotropic circular, annular and sector plates with general boundary conditions

A unified solution for free in-plane vibration of orthotropic circular, annular and sector plates with general boundary conditions

Exact solutions for the free in-plane vibrations of rectangular plates

Waveguide characteristics of coupled in-plane waves

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