## On the isospectral beams

### Summary

Summary: The free undamped infinitesimal transverse vibrations of a thin straight beam are modelled by a forth-order differential equation. This paper investigates the families of fourth-order systems which have one spectrum in common, and correspond to four different sets of end-conditions. The analysis is based on the transformation of the beam operator into a fourth-order self-adjoint linear differential operator. This operator is factorized as a product $L=H^{*}H$, where $H$ is a second-order differential operator of the form $H=D^2+rD+s$, and $H^{*}$ is its adjoint operator.

34B05, 34B10

### Keywords/Phrases

isospectral, Euler-Bernoulli equation for the vibrating beam, beam operator