An Improved Finite Difference Type Numerical Method for Structural Dynamic Analysis

Article type: Research Article

Authors: Kim, Sung-Hoon | Park, Youn-sik

Affiliations: Center for Noise and Vibration Control (NOVIC), Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Science Town, Taejon 305-707, Korea

Abstract: An improved finite difference type numerical method to solve partial differential equations for one-dimensional (1-D) structure is proposed. This numerical scheme is a kind of a single-step, second-order accurate and implicit method. The stability, consistency, and convergence are examined analytically with a second-order hyperbolic partial differential equation. Since the proposed numerical scheme automatically satisfies the natural boundary conditions and at the same time, all the partial differential terms at boundary points are directly interpretable to their physical meanings, the proposed numerical scheme has merits in computing 1-D structural dynamic motion over the existing finite difference numeric methods. Using a numerical example, the suggested method was proven to be more accurate and effective than the well-known central difference method. The only limitation of this method is that it is applicable to only 1-D structure.

DOI: 10.3233/SAV-1994-1607

Journal: Shock and Vibration, vol. 1, no. 6, pp. 569-583, 1994