## P. Computation of the Pressure Field Radiated by a Vibrating Surface with a Known Displacement Field (HAR3)

In this analysis, the structure radiates an acoustic wave inan infinite medium and it is assumed that the displacement field is known foreach frequency. The system of equations is thus expressed in the form:

The Y vector definesthe radiation condition applied on the external surface S limiting the fluid domain:

where R is the radius of the boundary surface S. [D] and [D'] are obtained by assembling the damping elements on that surface. n equals 1 for axisymmetric or 3D meshes, 2 forplain-strain meshes. The first term is the monopolar contribution associatedwith a spherical (n=1) or cylindrical (n=2) wave impedance condition, and the second term is thedipolar contribution. The damping term can be written:

where [G] represents a complex linear operator that is frequency dependent. Consequently:

The user must provide U andthe excitation frequency. The code computes P. The radiating surface on which [G] is computed is a spherical (n=1) or cylindrical (n=2)surface, the center of which corresponds to the acoustical center of theradiation field. Its radius is determined by the user to ensure theconvergence of the computation. If the damping elements are monopolar, theboundary surface must be in the far field. If the elements are dipolar, theboundary surface can be in the near field. In this case, the information onthe far field is not available until an appropriate post-processing is done bythe TDIP2 program (see Section V.F).

To define U, the EXCITATIONS entry must be used (see Section III.D) to specify the values of the displacement for each interface degree-of-freedom on the solid. The matrices are assembled and stored to file by columns. Gaussian algorithms are used to solve the problem, in single or in double precision. Internal losses can be taken into account.