Application Of Asymptotic Waveform Evaluation (AWE) Method In Solving Thermal And Vibration Problems - Loh, Jit Seng (Universiti Sains Malaysia, 2003)
Asymptotic Waveform Evaluation (AWE), which has been used in transient circuit simulation, is extended for solving mechanical engineering problems. AWE is based on the concept of approximating the original system with a reduced order system. Thus, it is efficient and powerful than conventional numerical method because it requires much less computational time but also produces the same accuracy. AWE is capable of solving first, second, third and even higher order linear differential equation. AWE can handle one or even a set of linear differential equations. Thus, AWE is suitably used with Finite Element Method (FEM), where the final equation is usually reduced to a set of linear differential equations that is to be solved for its transient solution. However, AWE is known for producing unstable response even for stable system. Higher order approximation also will not always guarantee a more accurate and stable solution. Thus, some modification has to be made to stabilize its solution. In this project, AWE has proved its capability in solving transient thermal and vibration problems. AWE, together with FEM, is used to solve one dimensional fin problem with varying or constant temperature boundary condition imposed at the base. Then, it is also used to solve hyperbolic (Non-Fourier) heat conduction equation on two and three dimensional finite element model. The accuracy and instability of AWE are also discussed and two stability schemes are introduced to address this problem. Nevertheless, AWE is also used in vibration analysis of beam, where dynamic force such as impulse, step or sinusoidal force, is imposed. Lastly, AWE is used to solve third order differential equation. AWE has proved to produce transient solution as accurate as Crank-Nicolson, Rungge-Kutta and also Ansys software. However, AWE can produce the solution much faster than these three methods.