Optimum design of wave transmitting joints

Transmission of wave energy through a one-dimensional wave transmitting system (e.g. a nonuniform elastic rod) is considered. The wave transmitting system consists of an input section with constant impedence, a joint with variable impedance and an output section with constant impedance. A given incident wave is to be transmitted through a joint of given length and mass connecting the input and output sections of given (constant) impedances. The efficiency of energy transmission (defined as the ratio of transmitted to incident wave energy) is maximized by seeking the optimum impedance function for the joint, i.e., the optimum distribution of the joint mass over its length. Efficiencies corresponding to the optimum joints are compared with those obtained for joints with constant impedance and it is found that significant improvements in the efficiency can be achieved. For a case studied in detail, improvements of up to 30 per cent are obtained. The optimum joint shapes turn out to be consisting of segments with very large and very small impedances. Experiments are reported which confirm these results and support the validity of the one-dimensional model.