High frequency vibration analysis by the complex envelope vectorization

Abstract

The complex envelope displacement analysis (CEDA) is a procedure to solve high frequency vibration and vibro-acoustic problems, providing the envelope of the physical solution. CEDA is based on a variable transformation mapping the high frequency oscillations into signals of low frequency content and has been successfully applied to one-dimensional systems. However, the extension to plates and vibro-acoustic fields met serious difficulties so that a general revision of the theory was carried out, leading finally to a new method, the complex envelope vectorization (CEV). In this paper the CEV method is described, underlying merits and limits of the procedure, and a set of applications to vibration and vibro-acoustic problems of increasing complexity are presented.

Vibroacoustic: The challenges of a mission impossible?

“…CEDA (Complex Envelope Displacement Analysis) [52] transforms the wave equation of a wave guide by a variable, defined through the Hilbert transform, that maps the fast oscillating response of high frequency problems into an envelope response characterized by a low wavenumber content. The Complex Envelope Vectorization (CEV) [53] (see Appendix A) is an evolution of CEDA: it uses a discrete formulation of a complex vibrating problem so that the response of the system is described by a vector. This vector can be regarded as the discrete counterpart of a one-dimensional variable to which the standard definitions and rules used in the one-dimensional CEDA are applied.…”

A direct hybrid finite element – Wave based modelling technique for efficient coupled vibro-acoustic analysis

“…As a result, the required discretisation sizes to control the interpolation errors decrease proportionally. Moreover, since the pollution rule (17) shows a more than linear dependency on the physical wavenumber, the number of elements (and the subsequent FE model sizes and associated computational cost) needed to retain an acceptable prediction accuracy grows very fast.…”

“…Other techniques approximate the equations of motion by smoothing the short-wavelength response in some frequency band. This allows for a coarse mesh to be used in an FE-like manner to predict the long-wavelength amplitude variation of the response, like in the Complex Envelope Vectorization approach [17]. Another class of techniques which is part of this family is based on the Trefftz [18] approach in which the field variable expansion functions satisfy the governing dynamic equations a priori, like e.g.…”