
doi: 10.1007/bf00885180
The problem of the motion of an elastic halfspace (Lamb problem) excited at the surface (x-y plane) by a harmonic normal force is studied. Emphasis is layed on analyzing the partition of the energy among the different wave modes (longitudinal, transverse, Rayleigh) thus generated. The amplitude of the surface force is assumed to be distributed along one coordinate, while it is constant along the other axis, e.g. it is a function f(x), and is assumed to be representable by a Fourier integral. Simple asymptotic expressions for the components of the displacement and stress vectors of the wave field are given (for details it is referred to the literature) being the basis for the evaluation of the energy efficiencies of the wave field. By calculating the power flow through the surface - by means of integrating the z-component of the period average pointing vector - the average power produced by the normal forces is obtained. A characteristic feature of this relation is the explicit separation of the power spent in the generation of the surface waves. It is further shown that the other two (logitudinal, transverse) components can be obtained by the calculation of the total power flow through a cylindrical surface of large radius. Finally, specific examples of driving forces with uniform and harmonic distributed amplitudes are considered. The variation of the relative distribution of the power among the modes as a function of the width of the driving zone is shown. The results are of practical interest (for example the excitation of surface acoustic waves is required in acoustooptic switches), because they allow to estimate the proper driving technique for the excitation of the various wave modes in solids.
variation of relative distribution of power, representable by Fourier integral, explicit separation of power spent in generation of surface waves, power flow through surface, Surface waves in solid mechanics, amplitude of surface force distributed along one coordinate, constant along other axis, motion of elastic halfspace, excited at surface, average power, Lamb problem, wave modes (longitudinal, transverse, Rayleigh), cylindrical surface of large radius, uniform and harmonic distributed amplitudes, driving forces, asymptotic expressions for components of displacement and stress vectors of wave field, energy analysis, harmonic normal force, other two components obtained by calculation of total power flow, function of width of driving zone
variation of relative distribution of power, representable by Fourier integral, explicit separation of power spent in generation of surface waves, power flow through surface, Surface waves in solid mechanics, amplitude of surface force distributed along one coordinate, constant along other axis, motion of elastic halfspace, excited at surface, average power, Lamb problem, wave modes (longitudinal, transverse, Rayleigh), cylindrical surface of large radius, uniform and harmonic distributed amplitudes, driving forces, asymptotic expressions for components of displacement and stress vectors of wave field, energy analysis, harmonic normal force, other two components obtained by calculation of total power flow, function of width of driving zone
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