Uniform Exponential Stabilisation of Serially Connected Inhomogeneous Euler-Bernoulli Beams

TL;DR

This paper proves uniform exponential energy decay in a chain of inhomogeneous Euler-Bernoulli beams with spatially varying properties, extending previous results to more general inhomogeneous cases.

Contribution

It generalizes existing stability results to inhomogeneous beams with spatially dependent parameters, under specific boundary conditions.

Findings

Proves exponential energy decay for the coupled beam system.

Extends stability results to spatially inhomogeneous beams.

Provides conditions for dissipative and conservative boundary setups.

Abstract

We consider a chain of Euler-Bernoulli beams with spatial dependent mass density, modulus of elasticity and area moment which are interconnected in dissipative or conservative ways and prove uniform exponential energy decay of the coupled system for suitable dissipative boundary conditions at one end and suitable conservative boundary conditions at the other end. We thereby generalise some results of G. Chen, M.C. Delfour, A.M. Krall and G. Payre from the 1980's to the case of spatial dependence of the parameters.