The Modal Superposition Method Using Maple: A Structural Dynamics Application for the Classroom

The objective of the present paper is to illustrate the use of the commercially available mathematical package MAPLE and other computer software for educational purposes. The problem chosen to illustrate the use of the software is the problem of forced vibrations of an elastic plate. The presentation of the topic is made in a simple manner to make it suitable for introductory graduate or undergraduate structural dynamics or vibration courses. The paper illustrates many concepts of structural dynamics in a step by step structured way: from the mathematical formulation, to the generation of a computer animation. The organization of the material and its computer implementation facilitate the introduction of the topic to students without having to resort to black-box type commercial finite element packages like ANSYS, SAP2000, RISA, etc. A very simple finite element (FE) is used to model the plate. The simplicity of the FE model used makes it possible to implement the procedure using high-level computer languages like those available within MATLAB, MAPLE, or even EXCEL. The classical modal superposition method is used to illustrate the concepts. A standard finite element procedure in conjunction with Jacobi’s method is used to solve the eigenvalue problem. A sample numerical problem together with snapshots of the computer animation are presented.