Analysis of small oscillations of a rigid body elastically suspended and containing an almost-homogeneous incompressible liquid
Hilal Essaouini, Larbi Elbakkali, Pierre Capodanno · 2014
We consider a 2d model for a rigid body with a cavity completely filled by a liquid and suspended by means of an elastic beam. The liquid is assumed to be “almost-homogeneous” and incompressible inviscid. From the equations of the system beam-container-liquid, we deduce the variational equation of the problem, and then two operatorial equations in a suitable Hilbert space. We show that the spectrum of the system is real and consists of a countable set of eigenvalues and an essential continuous spectrum filling an interval. The existence and uniqueness of the associated evolution problem are then proved using the weak formulation.