Flexural free vibrations of rectangular plates with complex support conditions

Fan, S.C.; Cheung, Y.K.

doi:10.1016/0022-460x(84)90352-3

Cited by 114 publications

(38 citation statements)

References 11 publications

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“…It can be seen that this result is very close to the value obtained by using equation (13). An even better comparison between these two values can be obtained by using more spline sections.…”

Section: One-dimensional Beam Analysissupporting

confidence: 82%

“…One way to construct such a B-spline displacement ÿeld is suggested by inspection of the Timoshenko beam mode functions. 13 These functions satisfy equation (16) Let us consider an isotropic Timoshenko beam. The two equilibrium equations are…”

Section: One-dimensional Beam Analysismentioning

confidence: 99%

“…First we use equation (13) to calculate the fundamental frequency parameter of the beam. For all slenderness ratios h=L this equation gives the same which is presented at the bottom of Table I.…”

Section: One-dimensional Beam Analysismentioning

confidence: 99%

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A Unified Timoshenko Beam B-Spline Rayleigh-Ritz Method for Vibration and Buckling Analysis of Thick and Thin Beams and Plates

Wang

1997

Int. J. Numer. Meth. Engng.

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SUMMARYFirst, the shear-locking phenomenon in the w B k SRRM 1-3 is investigated and the shear-locking terms are identiÿed in both one-dimensional beam and two-dimensional plate analyses. Subsequently the shear-locking free conditions are proposed and under the guidance of these conditions the Timoshenko beam B-spline Rayleigh-Ritz method, designated as TB k SRRM, is formulated for vibration analysis of beams based on Timoshenko beam theory and vibration and buckling analysis of isotropic plates or ÿbre-reinforced composite laminates based on the ÿrst-order shear deformation plate theory (SDPT). In TB k SRRM the number of degrees of freedom is exactly the same as that when the Bernoulli-Euler beam theory or classical plate theory (CPT) is used. However, the TB k SRRM includes the through-thickness shearing and rotary inertia e ects in full. Several numerical applications are presented and they show that this uniÿed approach is extremely e cient for both thick and thin beams and plates.

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Section: One-dimensional Beam Analysissupporting

confidence: 82%

Section: One-dimensional Beam Analysismentioning

confidence: 99%

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A Unified Timoshenko Beam B-Spline Rayleigh-Ritz Method for Vibration and Buckling Analysis of Thick and Thin Beams and Plates

Wang

1997

Int. J. Numer. Meth. Engng.

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“…Gorman (1981) introduced an auxiliary plate for which accurate solution is easily available to the original problem and the combined solution satisfies the governing differential equation, the boundary and support conditions. Since there is no exact solution in general, various numerical approaches, such as the finite difference method (Nishimura, 1953;Cox, 1955;Johns and Nataraja, 1972), the Rayleigh-Ritz method (Nowacki, 1953;Dowell, 1974;Narita, 1984;Laura and Cortinez, 1985), the Galerkin method (Yamada et al, 1985), the modal constraint method (Kerstens, 1979;Gorman, 1981), the finite element method (Mirza and Petyt, 1971;Rao et al, 1973;Rao et al, 1975;Utjes et al, 1984), the spline finite strip method (Fan and Cheung, 1984) and the flexibility function method (Bapat and Suryanarayan, 1989), are utilized for these problems. Recently, Liew et al (1994a) and Kitipornchai et al (1994) employed their pb-2 Ritz method to treat plates with point supports with success.…”

Section: Introductionmentioning

confidence: 99%

Plate vibration under irregular internal supports

Zhao

Wang

Xiang

2002

International Journal of Solids and Structures

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This paper studies the problem of plate vibration under complex and irregular internal support conditions. Such a problem has its widely spread industrial applications and has not been addressed in the literature yet, partially due to the numerical difficulties. A novel computational method, discrete singular convolution (DSC), is introduced for solving this problem. The DSC algorithm exhibits controllable accuracy for approximations and shows excellent flexibility in handling complex geometries, boundary conditions and internal support conditions. Convergence and comparison studies are carried out to check the validity and accuracy of the DSC method. Case studies are considered to the combination of a few different boundary conditions and irregular internal supports. The latter are generated by using an image processing algorithm. Completely independent verifications are conducted by using the established pb-2 Ritz method, which is available for two relatively simpler support patterns. The morphology of the first few eigenmodes is found to be localized to largest support-free spatial regions. Ó

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“…The general study to vibration characteristics of rectangular plates with arbitrarily located point-supports came from Fan and Cheung [2] using the spline finite strip. Kim and Dickinson [3] used the Lagrangian multiplier method combining with the orthogonally generated polynomials to study the rectangular plates with point-supports.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Rectangular Plates with Attached Discrete Sprung Masses

Zhou

2012

Shock and Vibration

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Abstract.A direct approach is used to derive the exact solution for the free vibration of thin rectangular plates with discrete sprung masses attached. The plate is simply supported along two opposite edges and elastically supported along the two other edges. The elastic support can represent a range of boundary conditions from free to clamped supports. Considering only the compatibility of the internal forces between the plate and the sprung masses, the equations of the coupled vibration of the plate-spring-mass system are derived. The exact expressions for mode and frequency equations of the coupled vibration of the plate and sprung masses are determined. The solutions converge steadily and monotonically to exact values. The correctness and accuracy of the solutions are demonstrated through comparison with published results. A parametric study is undertaken focusing on the plate with one or two sprung masses. The results can be used as a benchmark for further investigation.The solution provided in the paper is general and includes several special cases, such as the plate with classical boundary conditions, the plate attached with discrete rigid masses, the plate supported by discrete springs and the plate restricted by rigid vertical point-supports.

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Flexural free vibrations of rectangular plates with complex support conditions

Cited by 114 publications

References 11 publications

A Unified Timoshenko Beam B-Spline Rayleigh-Ritz Method for Vibration and Buckling Analysis of Thick and Thin Beams and Plates

A Unified Timoshenko Beam B-Spline Rayleigh-Ritz Method for Vibration and Buckling Analysis of Thick and Thin Beams and Plates

Plate vibration under irregular internal supports

Free Vibration of Rectangular Plates with Attached Discrete Sprung Masses

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