Concentrated force excitation of deep beams - In memory of Professor Manfred Heckl

The influence of the shear-tensional near field on the dynamic characterist ics of force-excited deep beams is addressed. From a transform solution, ap proximations are derived and analysed for several configurations. The dynam ic characteristics are examined in terms of the "point" mobility, establish ed on a complex power basis. It is found that both the real and imaginary p arts are significantly influenced by the shear-tensional nearfield in an in termediate region between a slender beam behaviour and an asymptotic wavegu ide behaviour. The influence manifests itself in an elevated real part owin g to "leakage" from the evanescent field to the propagating one for real ma terials possessing losses and in a logarithmic weighting of the stiffness c ontrolled imaginary part. No explicit dependence on the size of the indente r is identified. The estimation procedures developed, distinguishing betwee n moderately deep and deep beams, are physically valid in a qualitative sen se but furnish conservative estimates for the real part of the force mobili ty, while those for the corresponding imaginary part slightly over-estimate the antiresonant region and either give the overall trend or an approximat e influence of the excitation distribution in the upper range of Helmholtz numbers for moderately deep and deep beams respectively. (C) 1999 Academic Press.