Abstract
A novel family of infinite “wave envelope” elements is proposed for the solution of transient wave problems in unbounded regions. The elements are formed by applying an inverse Fourier transformation to a discrete wave envelope model in the frequency domain. This gives a coupled system of second-order equations which are readily integrated in time to yield transient pressure histories at nodal points on the surface of the radiating body and — in retarded form — at discrete points within the infinite domain. The infinite elements formed in this way can be applied quite generally to two-dimensional and three-dimensional problems and are fully compatible with conventional finite acoustical elements. They can be used to model radiating bodies of arbitrary shape but are demonstrated in the current instance in application to test problems which involve sound fields generated by spherical surfaces excited from rest, the exterior region being modeled by finite and infinite elements with explicit transverse interpolation. The computed transient solutions obtained from this formulation are compared to analytic solutions and shown to yield accurate results over a full range of exciting frequencies. The utility of the method for problems which involve broadband excitation is confirmed by comparisons of computed and analytic surface impedances for the steady harmonic case. These indicate that the accuracy of the scheme is limited only by a requirement to match element order to the highest order multi-pole component present in the radiated field. That is to say, elements of radial order 1 give an exact solution for monopole fields at all frequencies; elements of order 2 give an exact solution for dipole fields; elements of order 3 give an exact solution for quadrupole fields and so on. Similar results are presented for the fully three dimensional case. These support the extension of this hypothesis to three dimensional transient solutions subject only to the normal limitations imposed by spatial resolution in the transverse direction.