Comparison of acoustic complex modes for a set of boundary conditions through the impedance function measurement

Abstract

Complex modes are commonly observed in systems where damping acts locally, i.e., in cases the damping distribution is not uniform. The present work aims to compare the natural modes resultant from different boundary conditions of a cavity, considering a circular duct of rigid walls as the cavity under test. In one end, a volume velocity source was installed. At the other end, were considered four cases: closed end, open end, and two absorbing ends with different thickness. An Acoustic Experimental Modal Analysis was performed, in order to evaluate the mode shapes, using as basis a set of Acoustic Impedance Functions. Quantitative (phase scatter) and qualitative (variation of the node location) analysis were performed to estimate the "complexity" of the mode shapes. The comparison among the resultant complex mode shapes for each boundary condition showed the relation between the level of resistance and its effect in the complex modes.