Computation of the homogeneous and forced solutions of a finite length, line-driven, submerged plate
| Autor: | Daniel T. DiPerna, Xingguang Diperna, William K. Blake |
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| Rok vydání: | 2007 |
| Předmět: |
Constant coefficients
Models Statistical Acoustics and Ultrasonics Differential equation Physics Mathematical analysis Bending of plates Acoustics Finite element method Physics::Fluid Dynamics symbols.namesake Mathieu function Arts and Humanities (miscellaneous) Ordinary differential equation Plate theory symbols Humans Boundary value problem Mathematics |
| Zdroj: | The Journal of the Acoustical Society of America. 120(6) |
| ISSN: | 0001-4966 |
| Popis: | A formulation is developed to predict the vibration response of a finite length, submerged plate due to a line drive. The formulation starts by describing the fluid in terms of elliptic cylinder coordinates, which allows the fluid loading term to be expressed in terms of Mathieu functions. By moving the fluid loading term to the right-hand side of the equation, it is considered to be a force. The operator that remains on the left-hand side is the same as that of the in vacuo plate: a fourth-order, constant coefficient, ordinary differential equation. Therefore, the problem appears to be an inhomogeneous ordinary differential equation. The solution that results has the same form as that of the in vacuo plate: the sum of a forced solution, and four homogeneous solutions, each of which is multiplied by an arbitrary constant. These constants are then chosen to satisfy the structural boundary conditions on the two ends of the plate. Results for the finite plate are compared to the infinite plate in both the wave number and spatial domains. The theoretical predictions of the plate velocity response are also compared to results from finite element analysis and show reasonable agreement over a large frequency range. |
| Databáze: | OpenAIRE |
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