A Hybrid System Consisting of Two Flexible Beams Connected by a Point Mass: Spectral Analysis and Well-posedness in Asymmetric Spaces

We consider a hybrid system consisting on two exible beams connected by a point mass. We prove that the presence of the point mass aaects the spectral gap when the inertia term does not vanish. This allows us to show that the system is well-posed in as ymmetric spaces in which solutions have one more degree of regularity to one side of the mass. The proofs combine classical techniques from asymptotic analysis and the theory of non-harmonic Fourier series. 1. Introduction In this paper we study a linear system modeling the vibrations of two exible beams connected by a point mass. We assume that the beams occupy the intervals (-1,0) and (0,1) and that the point mass is