Low-frequency noise from service equipment in buildings tends to be of a structure-borne nature rather than an airborne nature. The transmission between different building elements can be determined on a power basis. The injected structure-borne sound power by an installation can be determined by multiplying velocities and contact forces in each of the installation's contact points. The velocity can be measured approximately by use of accelerometers close to the contact points, but the measurement of the force is less obvious. Force sensors should be inserted between the installation and the building element, which is often difficult or even impossible. Even when it's not that tedious, it is advisable not to alter the path of sound transmission, since small changes can imply large differences in injected structure-borne sound power. In this paper, contact forces of a fitness vibration plate are estimated through a structural-acoustic reciprocal method. First, the installation in a source room is put into operation and sound pressures in a receiver room are measured at multiple receiver points. Next, a dedicated volume sound source is placed in the receiver points in order to determine the transfer functions of the sound source's volume acceleration to the acceleration of the building element at the position of the contact points. A dedicated volume sound source was used that approximates point source behaviour and produces a high noise level down to very low frequencies (>20Hz). This enables accurate measurement of the structure-borne sound transmission. And, in a second step, it allows inverse estimation of the structural-acoustic contact forces down to these low frequencies. The estimated forces are compared with directly measured forces.
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