Numerical modeling of 1-dimensional wave equation using finite modal synthesis

Syahidatul Syahira , Abdul Rahman (2013) Numerical modeling of 1-dimensional wave equation using finite modal synthesis. Project Report. UTeM, Melaka. (Submitted)

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Abstract

This project is to perform numerical modelling of behavior of 1-dimensional wave equation and investigate the behavior through the variation of the system’s parameters. The study of wave is useful nowadays to improve world achievement in order to settle down problems regarding physical phenomena. This is because some physical phenomena happened are based on the principles of wave motion. For information, the simplest example of physical phenomena is a vibrating string. From this project the 1-dimensional wave equation needed to be study using Finite Modal Synthesis method to model the wave equation in the form of numerical modeling. Finite Modal Synthesis is a real-time synthesis as the stimulus of the (virtual) objects before they occur. The vibrating object is modeled by a bank of damped harmonic oscillators which are excited by an external stimulus. The frequency and damping of the oscillators are determined by the geometry and material properties, while the coupling gains are determined by the location of the force applied to the object. This method is a linear partial differential equation for a vibrating system with its boundary conditions. The advantages of this method are the feasibility of analysis of each component separately and it simplifies the test and analysis of the models. Hence, all the parameters that needed to simulate the equation are identified using Matlab. All the parameters needed to be understood more in effort to relate with the method used. Then the selected parameters are manipulated to study and discuss the behavior of the wave.

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