Stability of a non-uniform Rayleigh beam with general boundary conditions

Abstract

This paper investigates the stability of a Rayleigh beam with variable coefficients, clamped at one end and subject to general control laws at its free end. Based on the governing equations, we derive asymptotic expressions for the eigenvalues of the associated operator by means of a spectral method. Furthermore, we show that the optimal energy decay rate is determined by the spectral abscissa of the semigroup generator. We then show that exponential stability is maintained under a specific balance condition on the boundary control coefficients. Finally, numerical simulations are presented to illustrate the theoretical results.

https://doi.org/10.70974/mat10126177