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We derive the elastic field generated by multiple small-scaled inclusionsdistributed in a bounded set of $\mathbb{R}^3$. These inclusions are modeledwith moderate values of the Lam\'e coefficients while they have a largerelative mass density. These properties allow them to enjoy a sequences ofresonant frequencies that can be computed via the eigenvalues of the volumeintegral operator having the Navier fundamental matrix as a kernel, i.e. theNavier volume operator. The dominant field, i.e. the Foldy-Lax field, modelsthe multiple interactions between the inclusions with scattering coefficientsthat are inversely proportional to the difference between the used incidentfrequency and the already mentioned resonances. We show, in particular, that toreconstruct remotely the scattered field generated after $N$ interactionsbetween the inclusions, one needs to use an incident frequency appropriatelyclose to the proper resonance of the inclusions. We provide an explicit linkbetween the order $N$ of interactions and the distance from the incidentfrequency to the resonance. Finally, if the cluster of the inclusions isdensely distributed in a given bounded domain, then the expression of theinduced dominant field suggests that the equivalent homogenized mass densitycan change sign depending if the used incident frequencies is smaller or largerthan a certain threshold (which is explicitly given in terms of the resonantfrequencies of the inclusions).

Elastic fields generated by multiple small inclusions with high mass density at nearly resonant frequencies