On the simulation of systems governed by partial differential equations

Problems of vibrations are common in engineering applications, and need to be studied so that effective control/vibration suppression techniques can be developed. Part of the solution to problems of this nature is to simulate the systems under consideration. These are essentially governed by partial differential equations that require an excessive computational effort when solved on a digital computer. It is shown how the infinite order of the system modes can be reduced to a finite number, making the simulation easier. Since this modal type of analysis can lead to inaccuracies in the resonant frequencies it is imperative that any online vibration control system includes a strategy for tuning the parameters. It is shown that a suitable solution can be obtained by using a Doppler shift technique to reduce the error between the model and system modal frequencies