Exponential Stability Analysis of a Long Chain of Coupled Vibrating Strings with Dissipative Linkage

• Published in: SIAM journal on applied mathematics Vol. 49; no. 6; pp. 1694 - 1707
• Main Authors: Liu, Kang-Sheng, Huang, Fa-Lun, Chen, Goong
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.12.1989
• Subjects: Applied mathematics; Boundary conditions; Boundary points; Classical and quantum physics: mechanics and fields; Classical mechanics of continuous media: general mathematical aspects; Energy; Exact sciences and technology; Hilbert space; Hilbert spaces; Mechanical stabilizers; Ordinary differential equations; Partial differential equations; Physics; Wave equations; Wave equation; Vibrating string; Continuum mechanics; Exponential stability; Hyperbolic equation

Consider a long chain of coupled vibrating strings, where a stabilizer is installed at each internal node and perhaps also at a boundary point. The exponential stability of the stabilizers' arrangement for this large dynamic structure will be determined. Through a careful transformation of the...