Asymptotics of the eigenmodes and stability of an elastic structure with general feedback matrix

• Published in: IMA journal of applied mathematics Vol. 84; no. 5; pp. 873 - 911
• Main Authors: Shubov, Marianna A, Kindrat, Laszlo P
• Format: Journal Article
• Language: English
• Published: Oxford University Press 11.10.2019
• Subjects: Kantorovich’s theorem; asymptotic approximation; matrix differential operator; discrete spectrum; eigenvalues

Abstract The distribution of natural frequencies of the Euler–Bernoulli beam subject to fully non-dissipative boundary conditions is investigated. The beam is clamped at the left end and equipped with a 4-parameter ($\alpha ,\beta ,k_1,k_2$) linear boundary feedback law at the right end. The $2 \tim...