A hybrid system consisting in two flexible beams connected by a point mass: spectral analysis and well-posedness in asymmetric spaces

We consider a hybrid system consisting in two flexible beams connected by a point mass. We prove that the presence of the point mass affects the spectral gap when the inertia term does not vanish. This allows us to show that the system is well-posed in a symmetric space 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.