Time integration of rectangular membrane free vibration using spline-based differential quadrature

Document Type: Research Paper

Authors

1 Bachelor’s degree student of department of marine engineering, Khorramshahr university of marine science and technology

2 Department of Marine Engineering, Khorramshahr University of Marine Science & Technology

3 3Assistant professor of department of marine engineering, Khorramshahr university of marine science and technology

Abstract

In this paper, numerical spline-based differential quadrature is presented for solving the boundary and initial value problems, and its application is used to solve the fixed rectangular membrane vibration equation. For the time integration of the problem, the Runge–Kutta and spline-based differential quadrature methods have been applied. The Runge–Kutta method was unstable for solving the problem, with large errors in its results, but the spline-based differential quadrature method obtained results that agree with the exact solution. The relative errors were calculated and investigated for different values of time and spatial nodes of discretisation. It seems that the spline-based differential quadrature method is proper for the full simulation of membrane vibration in both spatial and temporal solutions. For the time solving of the membrane vibration, conventional methods, such as the Runge–Kutta method, are not useful even if the time steps are considered too small.

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Main Subjects

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