This paper is part of research work whose the main objectives are to model ground vibration induced by rail traffic on the surface or underground, and to predict the acoustic radiation caused by vibration in building structures, using the Boundary Elements Method (BEM). This paper proposes a BEM formulation which is implemented to model the propagation of waves in an elastic homogeneous halfspace confined by a fluid (air), where the waves are produced by steady state, spatially sinusoidal, harmonic line structure-borne loads at low frequencies.
The BEM model is formulated in the frequency domain and fully accounts for the air-solid interaction. The required two-and-a-half-dimension fundamental solution (Green’s functions) and stress functions in Cartesian co-ordinates for the elastic and fluid media can be found in [
]. The BEM integrations are performed analytically for the loaded element [
], whereas a Gaussian quadrature scheme is used when the element to be integrated is not the loaded element.
This paper describes the analysis as carried out in the frequency domain, for waves that travel perpendicularly to the z-axis (pure 2D problem). The results show the influence of: the impact source position; the wall material stiffness, and the impact source direction - vertical (y) or horizontal (x). The relationship between the normal vibration velocity of the vibrating structure and the acoustic energy radiated by this same structure (vertical wall) is also analyzed.
At this early stage of the research the authors modeled a homogeneous elastic flat half-space, excited by an applied impact line load, and studied the acoustic radiation provided by a simple structure (vertical wall). The future developments will include a railway tunnel and also a more realistic (complex) building structure. Comparison of the numerical results with some experimental data is another future objective.