Theory of Noise and Vibration Insulation of a System with Many Resonances

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Abstract
The results obtained in a previous paper, Part I of this study, are summarized and used to derive the theory of vibration and sound insulation of systems with many natural frequencies, such as machines with more than one resonance mounted on resonating springs, a motor spring-mounted on a shell, or plates at higher frequencies. At lower frequencies, the quality of the insulation is a function of the ratio of the square of the lowest fully excited resonant frequency to that of the frequency of the force. Weakly excited natural modes cause spikes in the transmission curve. Resonances in the vibrating masses may annihilate completely the effect of the vibrator mounting, whereas resonances in the springs are harmless as long as the mass is small in comparison to that of the machinery. Spring mounting a vibrator on a shell or plate reduces the noise level considerably. Any measure that increases the fundamental natural frequency to the housing helps to improve vibration insulation. Mounting the vibrator in a rigid cage or onto a rigid girder seems to be expedient; and welding these along a whole circumference or along their whole length onto the housing, to simulate a one-dimensional vibration pattern, is expedient. The noise radiation of a shell or plate to greater distances can be reduced by increasing the mass of the radiating shell or plate and by decreasing its size sufficiently to reduce the number of modes that radiate sound. Damping diminishes the sound radiation at lower frequencies, but has very little effect on it at higher frequencies.

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