Forced vibro-acoustical analysis for a theoretical model of a passenger compartment with a trunk—Part I: Theoretical part

In this paper, a new analytical model is proposed to investigate interior noise in a passenger compartment of an automobile with a trunk. The new analytical model is a coupled structural–acoustic model, which consists of double cavities connected by a neck and two mechanical harmonic oscillators. Acoustic impedance is calculated at every surface of discontinuity in the cross-sectional area for the forced vibro-acoustical analysis of the coupled system. Evanescent wave as well as standing wave is considered to investigate the neck's effect on modal properties of the coupled system. The evanescent wave with a set of cross-modes is converted to an added length term of the neck. In deriving the characteristic equation of the coupled system, the real length of a neck is replaced by the effective length including the added length. A new coupling parameter, which changes the natural frequencies of the coupled system, is introduced and is compared with other coupling parameters (mass ratio and stiffness ratio) in case studies. The natural frequencies of the coupled system decrease as the value of the new coupling parameter increases, which means that the cross-sectional area of the neck decreases and its position shifts close to the corner. Also, the results in this paper are qualitatively validated by an experimental investigation in a companion paper, Part 2.