Finite mechanical proxies for a class of reducible continuum systems

We present the exact finite reduction of a class of nonlinearly perturbed wave equations -typically, a non-linear elastic string- based on the Amann-Conley-Zehnder paradigm. By solving an inverse eigenvalue problem, we establish an equivalence between the spectral finite description derived from A-C-Z and a discrete mechanical model, a well definite finite spring-mass system. By doing so, we decrypt the abstract information encoded in the finite reduction and obtain a physically sound proxy for the continuous problem.