The one-dimensional bending wave counterpart to the acoustic horn and the semi-infinite wedge

The implications of spatially varying structural properties for flexural vibrations have been addressed for one-dimensional waveguides. A solution of the governing differential equation, based on Bessel functions, enables closed form expressions to be obtained for the point and transfer dynamic characteristics of finite length, tapered beams. Also, under the assumption of pure bending, a closed form expression has been derived for the semi-infinite wedge, which is valid under the same conditions as the finite case solution and which can be simply extended to encompass spatial variations obeying non-integer power laws. The influence of tapering on the energy flow is analysed for the flexural wave counterpart to the acoustic horn, constituted by a finite length taper attached to a semi-infinite, uniform beam. It is found that the main distinction to the uniform case is a comparatively broad-banded transition from flexural vibrations governed by the properties of the deep part of the system to vibrations governed by those of the slender part. The transition region is featured by a stiffness controlled initial part, followed by a resonant one. It is also found that the transition in itself involves a global resonance on which is superimposed the constructive and destructive interferences due to reflections from the discontinuity between the two structural members. On the basis of the complete expressions for the configurations studied, an estimation procedure for the mobility is proposed, which is experimentally confirmed to describe correctly the parameter influence. (C) 1998 Academic Press Limited.