The problem of elastic wave resonance scattering from elastic targets is discussed in this paper. A new resonance formalism to extract the elastic resonance information of the target from scattered elastic waves is introduced. The new resonance formalism is an extension of the works developed for acoustic wave scattering problems by the author. The classical resonance scattering theory (RST), which is usually being used for this type of problem, computes reasonable magnitude information of the resonances in each partial wave, but the phase behaves in somewhat irregular way, therefore, is not clearly explainable. The new method has been developed to obtain physically meaningful magnitude and phase of the resonances. As an example problem, elastic wave scattering from an infinitely-long elastic cylinder was analyzed by the proposed new method and compared with the previous studies by RST. In case of no mode conversion, both methods generate identical magnitude. However, the new method computes exact π radian phase shifts through resonances and anti-resonances while RST produces physically unexplainable phases. In case of mode conversion, even magnitudes are slightly different. The phase shifts through resonances and antiresonances obtained by the new method are not exactly π radians due to energy leak by mode conversion. But. the phases by the new method still show more reasonable and intuitive behavior than those by RST.

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