A piecewise computational scheme for the vibro-acoustic modeling in mid-to-high frequency range

Abstract

This thesis presents a computational method for the mid-to-high frequency vibro-acoustic system modeling. The Vibro-acoustic analysis in the mid-to-high frequency range is technically challenging due to the complex wavelength composition and the large numbers of the degrees of freedom involved. Conventional low-frequency methods like Finite Element Method (FEM) require enormous computational time and calculation capability while high-frequency methods like Statistical Energy Analysis (SEA) are not always suitable, because of the difficulty in meeting the basic assumptions in some long wavelength sub-systems, or the little information provided. Therefore, this thesis is aiming at establishing a simulation methodology that can balance the efficiency and the richness of the information obtained. The structure of the thesis is as follows. Preliminary investigations are first conducted on the modeling of a typical plate-cavity system, which is widely used as a simplified benchmark model for the sound insulation problems in building/structural acoustics. Through the exploration of the modal method and the wave method, the well-recognized existing convergence difficulties of the former at the vicinity of the vibro-acoustic interface are investigated. A criterion to accelerate the convergence speed of the modal method close to the cavity-plate interface is proposed. By improving the reliability of the modal method, this part paves the way forward by providing a reference solution to the mid-to-high frequency modeling analysis. Then, a so-called Condensed Transfer Function (CTF) method is proposed, in which the uncoupled sub-systems are modeled individually by decomposing the force and velocity over the interface into a set of functions, namely the Condensation Functions (CFs). Then the subsets obtained from each sub-system are assembled following the velocity continuity and force equilibrium conditions. The focus is fixed on how to increase the calculation efficiency of the CTF method by properly selecting the Condensation Functions (CFs). Owing to the spatial wavy features, the complex exponential functions are expected to better match the structural wavelength variations in a given frequency band. It is shown that the complex exponential functions outperform the previously developed Patch Transfer Function (PTF) methods using gate functions. Numerical analyses reveal a piecewise convergence behavior of the calculation in different frequency bands. This property is further exploited in a plate-cavity system for establishing a criterion for further truncation of the CFs, referred to as the piecewise scheme. The piecewise scheme is then extended to systems with an increasing coupling strength. To this end, a coupling strength factor (CSP) is defined to quantify the coupling strength between two sub-systems. Parameters that determine the coupling strength between the sub-systems are then discussed. Using the defined CSP, the previously established piecewise scheme is re-examined and validated using an acoustic system comprising two mutually connected sub-cavities. The effect of the coupling strength on the computational error of the piecewise scheme is systematically quantified. The piecewise scheme, alongside the CTF approach itself, is then experimentally validated. Finally, the piecewise scheme is applied to a simplified Double Skin Façade system (DSF). It is shown that the proposed modeling methodology allows a fine and detailed description of this complex vibro-acoustic system with a relatively complex and large dimension in the entire frequency range including the mid-to-high one.