Wavelet transformation induced multi-time scaling (WATMUS) model for coupled transient electro-magnetic and structural dynamics finite element analysis

Multi-functional devices that integrate electromagnetic and mechanical fields are gaining importance in a wide variety of applications. The combined mechanical and electromagnetic regimes, encompassed in these structures, make it necessary to develop effective multi-physics analysis tools at a range of temporal scales. An important consideration is that the different fields governing multi-physics response may have large frequency discrepancies, e.g. the ultra-high electromagnetic frequencies and moderate vibration frequencies. Computational analyses of these discrepant frequency problems using conventional time integration schemes can become intractable. This paper develops a framework for coupling transient electromagnetic and dynamic fields to predict the evolution of electric and magnetic fields and their fluxes in a vibrating substrate undergoing finite deformation. It addresses the issue of time integration with large frequency ratios, by introducing a novel wavelet transformation induced multi-time scaling (WATMUS) method in the finite element framework. The method significantly enhances the computational efficiency in comparison with conventional single time scale integration methods. An adaptive enhancement of WATMUS scheme allows for the optimal wavelet bases in the transformation and integration step sizes. The accuracy and efficiency of the proposed WATMUS scheme is verified by comparing the results with the single time-scale simulations of the coupled transient electromagnetic nonlinear vibration problems.