The generation of impulses from narrow bandwidth signals using resonant spherical chains

An ultrasonic horn operating at 73 kHz has been used to excite one end of a chain of steel spheres. The signal transmitted along the chain was measured at the far end using a laser vibrometer. Various chain lengths, ranging from 2-10 spheres, have been studied. It was found that a set of solitary wave impulses were generated when a high input amplitude and a minimal pre-compression force was used. Both harmonics and sub-harmonics of the input frequency could be observed. Theoretical models were developed, based on the relevant equations of motion, which modelled the end conditions properly, and their predictions confirmed the experimental observations. Solitary wave impulses were generated only when certain numbers of spheres were used, corresponding to the establishment of resonances in the form of nonlinear normal modes (NNMs). It was found that longer chains led to wider impulse bandwidths. Increased pre-compression tended to damp out this phenomenon, but gave a weakly non-linear state where the time delay of propagation along the chain changed with applied static force. It was thus established that a gated sinusoidal input could be transformed into a set of impulses, of interest in biomedical applications.