Solution of the inverse eigenvalue problem of a vibrating continuum with the method of intermediate operators

TLDR: In this paper, the problem of searching into the unknown "shape" of a continuum to have prescribed eigenvalues was identified with an eigenvalue problem belonging to an intermediate problem in the sense of Weinstein, Bazley and Fox.

Abstract: The problem of searching into the unknown “shape” of a continuum to have prescribed eigenvalues will be identified with an eigenvalue problem belonging to an intermediate problem in the sense of Weinstein, Bazley and Fox. Those eigenvalues of this latter are prescribed, which are defined by a linear algebraic eigenvalue problem. A special base operator enables the prescribed m eigenvalues to be the first m ones of the structure to be designed. Unknown parameters of the shape are looked for in an appropriate family of functions. A nonlinear algebraic system of equations is obtained for the unknown coefficients. Method is illustrated with a straight rod performing plane flexural vibration. A numerical example is given.