Application of joint time–frequency representation method in transient analysis of semi-infinite media
University of Tokyo, Institute of Industrial Science, 4–6–1 Komaba, Meguro-ku 153–8505, Tokyo, Japan
ABSTRACT
Many methods have been developed for the analysis of semi-infinite media in highly idealized situations where either nonlinear behavior of the near field was neglected or a full nonlinear analysis was conducted with heavy computational efforts. In this work, to model a half-space medium with various irregularities, a combination of finite and infinite elements has been used. More problems arise when nonlinearities are going to be included in the system. The impedance matrix of an infinite element is frequency dependent [1,2] while for nonlinear analyses the equations of motion should be solved in time domain [3]. To overcome this difficulty the time-frequency representation of signals is utilized [4,5] to investigate the behavior and frequency content of infinite elements' responses and obtain the dominant frequencies of their ends' vibrations at each time interval. Using the weighted average approach, the effective stiffness, mass and damping matrices of infinite elements are then assembled into the matrices of the system at each time interval. The matrices of infinite elements will be piecewise constant, and hence they can be transferred easily into time domain.
Keywords:
Infinite elements; Time–frequency representation; nonlinear analysis; Adaptive optimal kernel; Short time ambiguity function