AIRBORNE PATH FREQUENCY BASED SUBSTRUCTURING METHOD AND ITS APPLICATIONS

Frequency based substructuring (FBS) is routinely used to model structural dynamics. It provides a framework for connecting structural subsystems together, assessing path contributions, determining the effect of mount modification, and identifying inverse forces. In this work, FBS methods are extended to include acoustic subsystems and connecting pipes and ducts. Connecting pipes or ducts are modeled using the transfer matrix approach which is commonly used for modeling mufflers and silencers below the plane wave cutoff frequency. The suggested approach is validated using boundary element method (BEM) simulation. Applications of the procedure include determining airborne path contributions, the effect of treating ducts and apertures, and the effect of making lumped acoustic impedance modifications to a subsystem. The method can be simplified and used for determining the effect of design changes on the insertion loss of enclosures

Gaussian dynamics equation in normal product form

In this paper, we discuss the normal product form of the density operator of multimode Gaussian states, and obtain the correlation equation between the kernel matrix R of the Gaussian density operator in the normal product form and its kernel matrix G in the standard quadratic form. Further, we explore the time evolution mechanism of R and obtain the Gaussian dynamical equation under the normal product R=i(RJH-HJR). Our work is devoted to searching for another mechanism for Gaussian dynamics. By exploring the description of the normal ordered density matrix under the coherent state representation, we find that our mechanism is feasible and easy to operate