New Wall Design for High Transmission Loss or High Damping

Abstract

739This frequency equation was derived by Mirsky and Herrmann •7 but since they were interested in cylindrical shells no frequency calculations were made. Table VIII includes a tabulation of the frequency coefficients for this case. D. Hollow Circular Bar Clamped along Its Outer Surface The boundary conditions, Eqs. (14a) and (14b), result in the following frequency equation' J,•(f2nr•) It.' •2. --J,•' •2,.,• r•(gnm) = 0. (19)A typical single wall is characterized by a free flexural wave speed, cB, which increases with cot. When cB approaches co (the speed of sound waves in the surrounding medium) the impedance of the wall to incident sound wave ceases to be mass-like because of the coincidence effect and the transmission loss will be less than that given by mass law. Since ½•= (B/M)t(co)• for homogeneous walls, the deleterious effects of the coincidence of the flexural wave speed with the phase velocity of sound in the medium can be avoided for homogeneous walls by reducing the ratio of B/M. (B is the dynamic bending stiffness of the wall; M is the mass per unit area of the wall.) Thus the problem of good acoustical performance in homogeneous walls is seen to be in essential conflict with the need for structural rigidity.A new wall design has been found in which the ratio of the static to the dynamic stiffness can be in excess of 1000:1 and where the stiffness changes from the static to the dynamic value in such a way that the acoustical behavior is nearly that of a perfectly limp wall. If desired, the loss tangent of the wall can be made large and nearly constant over a wide range of frequencies. INTRODUCTIONHE sound transmission loss (TL) of fairly large, single solid walls is essentially determined by the following physical characteristics•.2: 1. The mass per unit area of the wall. 2. The dynamic bending stiffness of the wall. 3. The internal damping or loss tangent of the wall material. An alternative set of physical properties which can be related to the above set is: 1. The mass per unit area. 2. The speed of propagation of free transverse waves on the wall. The decay, or damping of these free waves per unit distance along the wall.It is generally accepted that a high value of mass per unit area is required for high TL. The role of the bending stiffness of the wall (or equivalently, the speed of transverse waves) is not so well known but is fully as important as that of the mass. When the dynamic stiffness of a wall is great enough (or when the speed of transverse waves is high enough) then the wall tends to lose its massive character and the TL is reduced. The amount of internal damping of the wall material generally is of less importance than the mass or stiffness as far as the TL is concerned.Other, equally annoying "side effects" also occur in the case of a relatively stiff wall which are largely absent in a relatively limp wall of the same weight. For example, structure-borne vibrations transmitted from a distant point (e.g., machinery noise, heel clicks, etc.) will radiate much more efficiently from ...

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