The radiation efficiency of mass-loaded, slender, baffled beams

• Published in: Journal of sound and vibration 1988-02, Vol.120 (3), p.487-498
• Main Authors: Seybert, A.F., Tsui, Y.K.
• Format: Article
• Language: English
• Subjects: Acoustics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Structural acoustics and vibration
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/S0022-460X(88)80221-9

A study of the radiation of sound from mass-loaded, baffled beams which are either simply supported or clamped is described. The Rayleigh-Ritz method is employed to obtain approximate natural frequencies and mode shapes for the mass-loaded beams. A set of comparison functions is selected which are used with the Rayleigh integral to obtain expressions for the radiation efficiency of the mass-loaded beams. The radiation efficiency is determined for simply supported and clamped mass-loaded beams as a function of the location and magnitude of a single added mass. The radiation efficiency is evaluated numerically over a broad frequency range below coincidence. In the region well below coincidence approximate analytical expressions are developed to represent the radiation efficiency. The concept of volume velocity cancellation is used to interpret the radiation efficiency. It is shown that well below coincidence the radiation efficiency of simply supported mass-loaded beams is equivalent to the radiation efficiency produced by a series of in-phase monopoles and a series of dipoles. Two examples are used to illustrate the effect of mass addition to an otherwise uniform beam: a simply supported, mass-loaded beam vibrating in the second mode and a clamped mass-loaded beam vibrating in the third mode.