SIMPLE ANALYSIS OF EXHAUST NOISE PRODUCED BY A 4 CYLINDER ENGINE

Developing an idea of Laville and Soedel [J. Sound Vib., 60 (1978) 273 1, the noise radiated by the exhaust system of a four cylinder engine is calculated, analytically and numerically, and compared to experimen t. The basic idea is as follows: the effect of the exact shape of the volume velocity signal produced by a cylinder during opening can be co nsidered as a second order effect on the result. The amplitude of ever y harmonic of the radiated noise is shown to be proportional to the fi rst order of certain quantities, the zeroth order being zero. On the o ne hand, the harmonics H-2, H-4, ... are proportional to the deviation of the signal during opening from a square signal and to the ratio of the overlap time of opening of two cylinders to the valve opening dur ation. On the other hand, the other harmonics are proportional to quan tities like the ratios of the length difference between two parallel t ubes of the manifold to the wavelength. The analysis of the amplitude of the radiated noise exhibits the role of the resonances of the admit tance of the whole exhaust as viewed from outside when the cylinders a re closed, and of the resonances of the manifold. Comparison with expe riment confirms the basic hypothesis and the result of the theory, al least qualitatively, but losses seem to cancel the manifold resonances , which are related to the interferences between parallel tubes.