Complex envelope displacement analysis: a quasi static approach to vibrations

A new model to analyze high frequency vibrations is presented. Instead of using the physical oscillating displacement, the problem is described in terms of a complex envelope, generated by an appropriate use of the Hilbert transform. The model can be put in the category of those methods that try to describe some representative characteristic of the oscillating solution (average energy level, thermal trend, etc.) rather than the solution itself, avoiding the computational problems connected with high frequency problems. Although the envelope solution, by itself, is sufficient and convenient to deal with structural-acoustic coupling, the proposed model presents the twofold advantage of avoiding computational problem connected with high frequency vibrations while keeping the capability of recovering the oscillating response, when required.