Free Vibration Analysis of Arbitrarily Shaped Plates With Clamped Edges Using Wave-Type Functions

Kang, Sang-Wook; Lee, J.M.

doi:10.1006/jsvi.2000.3347

Cited by 72 publications

(45 citation statements)

References 30 publications

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“…The governing equation of transverse vibration motion of the plate, on the basis of Kirchhoff's classical small deflection theory, has the form [1] p. 134, [2] p. 1238, [13,14],…”

Section: Active Vibration Reduction Of the Plate With Actuatorsmentioning

confidence: 99%

Evaluation of the Active Plate Vibration Reduction by the Parameter of the Acoustic Field

Brański¹,

Szela

2011

Acta Phys. Pol. A

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Effectiveness of the active vibration reduction of triangular plate is evaluated by way of the analysis of acoustical field. The active vibration reduction is performed with actuators. The effect is measured by the analysis of the acoustical field both far distance and near one from the plate. As the control parameter, the difference between acoustical pressures is considered. The first pressure and the second one are radiated by the plate without and with the vibration reduction, respectively. The control parameter is calculated for two reduction cases. First case, when actuators are attached at so-called quasi-optimal places and second one, when they are shifted. The numerical calculations show that the acoustical field is sensitive to change of the plate active vibration reduction. It responds to even little changes of the plate vibrations in both active reduction cases mentioned above. So that it is handy indirect control parameter of the active vibration reduction.

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“…The governing equation of transverse vibration motion of the plate, on the basis of Kirchhoff's classical small deflection theory, has the form [1] p. 134, [2] p. 1238, [13,14],…”

Section: Active Vibration Reduction Of the Plate With Actuatorsmentioning

confidence: 99%

Evaluation of the Active Plate Vibration Reduction by the Parameter of the Acoustic Field

Brański¹,

Szela

2011

Acta Phys. Pol. A

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“…1, F P = F P (x, y,t) -control force due to PZTs. The P-F-F boundary conditions imposed on the plate are defined in [11,16,20], Fig. 2.…”

Section: Formulation Of Plate Theorymentioning

confidence: 99%

Quasi-optimal PZT distribution in active vibration reduction of the triangular plate with P-F-F boundary conditions

Brański¹,

Szela²

2010

Archives of Control Sciences

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An active reduction of transverse vibration of the triangular plate with P-F-F boundary conditions is considered. The cracked plate is idealized research model as partially clamped on one edge with varying clamped length. The active reduction is realised with PZTs. In the paper, assuming the detached base clamped length, the influence of PZTs distribution on the bending moment and the shearing force at the clamped edge is investigated. To realize the purpose two cases are considered. At the former the PZTs are attached at points in which the curvatures of the surface locally take their maximum (MC sub-areas or quasi-optimal ones). At the latter, the PZTs are somewhat shifted. The plate is excited with harmonic plane acoustic wave. The second mode is considered only.The active vibration reduction study with a finite element method (FEM) is carried out. The numerical calculations show that better results are obtained for MC distribution of the PZTs.

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“…Later, the authors extended the NDIF method to membranes with high concavity [3] and plates with various boundary conditions [4][5][6][7]. In the NDIF method, as in the boundary element method (BEM) [8], a field problem is solved on its boundary along which nodes are distributed.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, the NDIF method [1][2][3][4][5][6][7], which was developed by the authors, offers much more accurate eigenvalues than FEM. For acoustic cavities with simple shapes having no exact solution, a great deal of analytical or semianalytical research has been performed to increase the accuracy of eigenvalues and eigenmodes.…”

Section: Introductionmentioning

confidence: 99%

Application of Nondimensional Dynamic Influence Function Method for Eigenmode Analysis of Two-Dimensional Acoustic Cavities

Kang

Atluri

2014

Advances in Mechanical Engineering

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This paper establishes an improved NDIF method for the eigenvalue extraction of two-dimensional acoustic cavities with arbitrary shapes. The NDIF method, which was introduced by the authors in 1999, gives highly accurate eigenvalues despite employing a small number of nodes. However, it needs the inefficient procedure of calculating the singularity of a system matrix in the frequency range of interest for extracting eigenvalues and mode shapes. The paper proposes a practical approach for overcoming the inefficient procedure by making the final system matrix equation of the NDIF method into a form of algebraic eigenvalue problem. The solution quality of the proposed method is investigated by obtaining the eigenvalues and mode shapes of a circular, a rectangular, and an arbitrarily shaped cavity.

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Free Vibration Analysis of Arbitrarily Shaped Plates With Clamped Edges Using Wave-Type Functions

Cited by 72 publications

References 30 publications

Evaluation of the Active Plate Vibration Reduction by the Parameter of the Acoustic Field

Evaluation of the Active Plate Vibration Reduction by the Parameter of the Acoustic Field

Quasi-optimal PZT distribution in active vibration reduction of the triangular plate with P-F-F boundary conditions

Application of Nondimensional Dynamic Influence Function Method for Eigenmode Analysis of Two-Dimensional Acoustic Cavities

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