Block diagram of the TBEM algorithm for general problems with all types of boundary conditions. A block indicated with z−1 represents the unit delay.
(a) A partially lined, parallelepiped box with a point source at (0.10, 0.15, 0.20) m, (b) the boundary element model composed of 368 nodes and 732 linear triangular elements.
A comparison of the fitted time domain surface impedance in a form of an IIR digital filter (—) and the frequency domain surface impedance (---) for an absorptive liner with a rigid backing.
Magnitudes of eigenvalues that decrease gradually with increasing orders.
A wave vector that describes the time-marching mode shape of the (0,1,1) mode. Each contour plot describes the modal distribution for the real or imaginary part of [λ − i u], in which an index i is related to the time delay.
Magnitudes of eigenvalues and frequencies of all unstable oscillatory wave vectors.
A comparison of the calculated interior field pressure at (0.15, 0.20, 0.30) m excited by an octave-band impulse excitation centered at (a) 250 Hz, (b) 500 Hz: —, TBEM; ---, FBEM.
Time variation of the MAC values between unstable wave vectors corresponding to the largest eigenvalue and the calculated response ⟨Y⟩. The center frequencies of excited octave bands are: (a) fc = 250 Hz, (b) fc = 500 Hz.
A comparison of the stabilized interior field pressure after nullifying unstable oscillatory wave vectors: —, TBEM; ---, FBEM. The center frequencies of excited octave bands are: (a) fc = 250 Hz, (b) fc = 500 Hz.
A comparison of the interior field pressure stabilized at a late time (octave band with fc = 500 Hz): —, TBEM; ---, FBEM. (a) Nullification of unstable oscillatory wave vectors, (b) employment of the same decay rate for two nonoscillatory wave vectors in addition to (a), i.e., after nullifying the unstable oscillatory wave vectors.
Effect of timing in decay application to nonoscillatory wave vectors (octave band with fc = 500 Hz): (a) From the beginning, (b) after the energy of the input excitation was decayed by 25 dB: —, TBEM; ---, FBEM.
A comparison of the calculated interior field pressure within a rigid box (octave band with fc = 500 Hz): —, TBEM; ---, FBEM. Frequency resolutions are: (a) 0.2 Hz (T = 5 s), (b) 2 Hz (T = 0.5 s), (c) 20 Hz (T = 0.05 s).
Filter coefficients of the time domain impedance in Eq. (6) for the surface of a porous liner with a rigid backing.
Characteristics of the wave vectors corresponding to the lowest six modal frequencies.
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