Acoustic characteristics analysis of slender cavity system with arbitrary impedance end conditions

A modeling method for the dynamic characteristics analysis of slender acoustical cavity with impedance end conditions is established. In order to satisfy the continuity requirement at impedance ends for the first order differential of sound pressure, filed function is constructed as the standard Fourier series supplemented by boundary smoothed auxiliary polynomials. System characteristic equation is derived by solving governing differential equation and impedance acoustic boundary of slender acoustical cavity system simultaneously, relevant acoustical modal information is obtained via the state space solution procedure. In the numerical simulation, various acoustic variables, such as acoustical modal frequency, sound pressure modal shape, sound pressure frequency response and the particle velocity,are presented for the slender acoustical cavity system with different boundary conditions and compared with those results in the existing literature. The correctness and effectiveness of the proposed method are then fully validated.