Structure-borne Sound

General description

Vibration of mechanical systems and waves in solid structures in the audible frequency rang are subjects which form an integral part of engineering acoustics. The study of the phenomena of such vibrations and waves are called structure-borne sound, structural acoustics or vibro-acoustics; the three terms can be considered equivalent and interchangeable. Thus, vibro-acoustic is the study of the mechanical waves in structures and how they interact with and radiate into adjacent media.

Although sound waves in structures cannot be heard directly, and only be felt at low frequencies, they play an important role in noise control. Many sound signals are generated or transmitted in structures before they are radiated into the surrounding medium. Examples are musical sound from a string instrument, noise from machines such as pumps in a central heating system or transport vehicles, (unwanted) sound radiation from the cabinet of loudspeakers, or sound transmission and structure-borne noise in buildings, etc.

A fundamental knowledge of structural sound waves and their propagation is necessary for understanding vibro-acoustics. In many ways sound waves in structures and in fluids (gases or liquids) are similar. There are, however, also fundamental differences, which are due to the fact that solids have shear stiffness, whereas gases or liquids show practically none (except for viscosity effects). As a consequence acoustic energy can be transported not only by compressional (longitudinal) waves but also by shear waves and many combinations of compressional and shear waves. For noise control purposes, bending (or flexural or transvers) waves are of primary importance. Bending waves are more complicated than compressional or shear waves and depend not only on material properties but also on geometric properties. Due to this, they are dispersive, which means that the waves travel at different speeds for its different frequency components. When a vibrating structure is in contact with a fluid, the normal particle velocities at the interface must be equal in the two media. This causes some of the energy from the structure to escape into the fluid; some of it radiates away as sound in the far field and some of which stays near the structure as an evanescent near field. Most sound radiation is caused by bending waves, which have most of its motion in the transverse direction.

The finite element method (FEM) can be used to predict the vibration of complex structures. A finite element computer program will assemble the mass, stiffness, and damping matrices based on geometrical and material properties.  The vibration response is then solved based on the excitations applied. The finite element method is deterministic and mainly applicable in the low frequency range (small Helmholtz numbers). Therefore, an exact analysis of large vibro-acoustic systems and complicated structures can be very difficult and time-consuming. Furthermore, when solutions are sought after in the full audible frequency range, then it will nearly always be necessary to use approximate computational methods. The excitation often is broadband, which means that many natural modes will be excited simultaneously, and often these modes overlap. In addition, the very modelling is complicated by the fact that boundary conditions and the exact material properties rarely are sufficiently well known in practice. In order to remedy this problem a strongly simplified method for predicting mean-value responses and sound radiation in connection with complex vibro-acoustic problems has been developed. This method is called statistical energy analysis (SEA), and has its origin in statistical room acoustic and in statistical mechanics.

Research Focus

At ACT and at CAMM, vibro-acoustic research is conducted in the fields mentioned above.  PhD project related to vibro-acoustics are concerned with FE modeling of vocal folds and hearing aids, seismic inversion techniques, miniature loudspeaker modeling and FE modeling of orthotropic plates. Other research activities have been conducted on cross-coupling and source description of vibro-acoustic sources, experimental and theoretical studies of rib-stiffened plates, and radiation and sound transmission of finite plates,  to name a few recent studies.


Jonas Brunskog
Associate Professor
DTU Electrical Engineering
+45 45 25 39 35