Prediction of high-frequency responses in the time domain by a transient scaling approach

Many engineering structures are subject to excitations with large amplitudes over a short time duration. These impulsive excitations can cause structural failure or unwanted noise especially in the high-frequency band. This paper presents a transient scaling approach to predict the high-frequency vibration of impulsively excited structures. General scaling laws are derived from the transient statistical energy analysis (TSEA). The similitude between the scaled model and the original system is demonstrated by the equivalence of the TSEA governing equations. Specific forms of the general scaling laws are formulated for a two-oscillator system and a coupled beam system. Computational speedup is achieved from both the reduced order of the original system and the accelerated energy evolution in the scaled model. Numerical validation demonstrates that time domain responses can be obtained efficiently by the transient scaling approach.