“…1 are periodic, one can assume the following Fourier expansions for the coefficients that appear in Eqs. (1) and (2):…”
Section: The Plane Wave Expansion Methods For the In-plane Wave Equationmentioning
confidence: 99%
“…There are several recent significant theoretical and numerical contributions to the study of the in-plane vibrations of plates [1,2,3,5,6,7,8,9,10,11,12]. However, experimental results have been, until recently, very scarce [4,13].…”
Theoretical and experimental results for in-plane vibrations of a uniform rectangular plate with free boundary conditions are obtained. The experimental setup uses electromagnetic-acoustic transducers and a vector network analyzer. The theoretical calculations were obtained using the plane wave expansion method applied to the in-plane thin plate vibration theory. The agreement between theory and experiment is excellent for the lower 95 modes covering a very wide frequency range from DC to 20 kHz. Some measured normal-mode wave amplitudes were compared with the theoretical predictions; very good agreement was observed. The excellent agreement of the classical theory of in-plane vibrations confirms its reliability up to very high frequencies Keywords: rectangular plate, in-plane vibrations, plane wave expansion method * Corresponding author, Tel. +52 55 562 27788; Fax: +52 55 562 27775. Email addresses: arreolaarturo@gmail.com (A. Arreola-Lucas), jofravil@fis.unam.mx (J. A. Franco-Villafañe), gbaez@correo.azc.uam.mx (G. Báez), mendez@fis.unam.mx (R. A. Méndez-Sánchez)
“…1 are periodic, one can assume the following Fourier expansions for the coefficients that appear in Eqs. (1) and (2):…”
Section: The Plane Wave Expansion Methods For the In-plane Wave Equationmentioning
confidence: 99%
“…There are several recent significant theoretical and numerical contributions to the study of the in-plane vibrations of plates [1,2,3,5,6,7,8,9,10,11,12]. However, experimental results have been, until recently, very scarce [4,13].…”
Theoretical and experimental results for in-plane vibrations of a uniform rectangular plate with free boundary conditions are obtained. The experimental setup uses electromagnetic-acoustic transducers and a vector network analyzer. The theoretical calculations were obtained using the plane wave expansion method applied to the in-plane thin plate vibration theory. The agreement between theory and experiment is excellent for the lower 95 modes covering a very wide frequency range from DC to 20 kHz. Some measured normal-mode wave amplitudes were compared with the theoretical predictions; very good agreement was observed. The excellent agreement of the classical theory of in-plane vibrations confirms its reliability up to very high frequencies Keywords: rectangular plate, in-plane vibrations, plane wave expansion method * Corresponding author, Tel. +52 55 562 27788; Fax: +52 55 562 27775. Email addresses: arreolaarturo@gmail.com (A. Arreola-Lucas), jofravil@fis.unam.mx (J. A. Franco-Villafañe), gbaez@correo.azc.uam.mx (G. Báez), mendez@fis.unam.mx (R. A. Méndez-Sánchez)
“…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.…”
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.
“…The studies on the in-plane vibration of plates have basically focused on isotropic rectangular plates solved numerically by various methods [1][2][3][4][5][6][7][8][21][22][23][24][25]. As far as the author knows the unique paper examining the inplane vibration of rectangular plates with intermediate point-supports was submitted by Kobayashi et al [1].…”
Free in-plane vibration of super-elliptical plates of uniform thickness was investigated by the Ritz method. A large variety of plate shapes ranging from an ellipse to a rectangle were examined. Two cases were considered: (1) a completely free, and (2) a point-supported plate. The geometrical boundary conditions were satisfied by the Lagrange multipliers. The results were compared with those of rectangular plates. Basically good agreement was obtained. Matching results were reported, and the discrepancies were highlighted.
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