Numerical Approximation of Spectrum for Variable Coefficients Euler-Bernoulli Beams Under a Force Control in Position and Velocity

Abstract

Abstract:In this paper, we use asymptotic techniques and the finite differences method to study the spectrum of differential operator arising in exponential stabilization of Euler-Bernoulli beam with nonuniform thickness or density that is clamped at one end and is free at the other. To stabilize the system, we apply at the free end, the following shear force feedback control:We build a numerical scheme and investigate the eigenvalues locus as a function of the positive feedback parameters α and β.

Numerical approximation of the dissipativity of energy and spectrum for a damped Euler-Bernoulli beam with variable coefficients

“…Several books have discussed the numerical analysis of Euler-Bernoulli beams in literature, and there are various ways. It is well known that in literature (see for instance [8,10]) to geometrically describe the spectrum of an operator, the way used is the following: the authors use the finite differences method [6,12] and apply QZ method [7,9]. At this level, we proceed differently.…”