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Applicable Analysis
An International Journal
Volume 29, 1988 - Issue 1-2
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Original Articles

On linear vibrational systems with one dimensional damping

Krešimir Veselić Lehrg. Mathematische Physik, FERNUNIVERSITÄT -GHS-, Postfach 940, Hagen, D-5800, Germany
Pages 1-18 | Received 17 Sep 1987, Published online: 02 May 2007

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Seyf Eddine Ghenimi & Abdelmouhcene Sengouga. (2023) Exponential stability estimates for an axially travelling string damped at one end. Applicable Analysis 0:0, pages 1-20.
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Olga Martynuk, Vyacheslav Pivovarchik & Christiane Tretter. (2015) Inverse problem for a damped Stieltjes string from parts of spectra. Applicable Analysis 94:12, pages 2605-2619.
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Articles from other publishers (34)

Seyf Eddine Ghenimi & Abdelmouhcene Sengouga. (2024) Boundary stabilization of a vibrating string with variable length. Journal of Mathematical Analysis and Applications 532:1, pages 127910.
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Zoran Tomljanović. (2023) Damping optimization of the excited mechanical system using dimension reduction. Mathematics and Computers in Simulation 207, pages 24-40.
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Ninoslav Truhar & Maja Petrač. (2022) Damping Optimization of Linear Vibrational Systems with a Singular Mass Matrix. Mathematics 10:11, pages 1854.
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Lu Yang, Yongxia Guo & Guangsheng Wei. (2020) Inverse eigenvalue problems for a damped Stieltjes string with mixed data. Linear Algebra and its Applications 601, pages 55-71.
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Lu Yang, Yongxia Guo & Guangsheng Wei. (2020) Inverse Problem for a Stieltjes String Damped at an Interior Point. Integral Equations and Operator Theory 92:4.
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Ivica Nakić, Zoran Tomljanović & Ninoslav Truhar. (2019) Mixed control of vibrational systems. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 99:9.
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Ninoslav Truhar, Zoran Tomljanović & Matea Puvača. (2019) Approximation of damped quadratic eigenvalue problem by dimension reduction. Applied Mathematics and Computation 347, pages 40-53.
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Anastasia Dudko & Vyacheslav Pivovarchik. (2019) Three spectra problem for Stieltjes string equation and Neumann conditions. Proceedings of the International Geometry Center 12:1, pages 41-55.
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O. P. Boyko, O. M. Martynyuk & V. M. Pivovarchik. (2017) On the Relationship Between the Multiplicities of Eigenvalues in Finite- and Infinite-Dimensional Problems on Graphs. Ukrainian Mathematical Journal 69:4, pages 521-533.
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M. Möller & V. Pivovarchik. (2016) Damped star graphs of Stieltjes strings. Proceedings of the American Mathematical Society 145:4, pages 1717-1728.
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Vojin Jovanovic & Sergiy Koshkin. (2013) D’Alembert sums for a vibrating bar with viscous ends. Journal of Engineering Mathematics 85:1, pages 99-114.
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Olga M. Martynyuk & Vyacheslav M. Pivovarchik. (2011) The inverse spectral problem for a Stieltjes eight-shaped string. Journal of Mathematical Sciences 178:1, pages 84-96.
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F.S.V. Bazán. (2010) Chebyshev pseudospectral method for wave equation with absorbing boundary conditions that does not use a first order hyperbolic system. Mathematics and Computers in Simulation 80:11, pages 2124-2133.
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Ninoslav Truhar & Krešimir Veselić. (2009) An Efficient Method for Estimating the Optimal Dampers' Viscosity for Linear Vibrating Systems Using Lyapunov Equation. SIAM Journal on Matrix Analysis and Applications 31:1, pages 18-39.
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O Boyko & V Pivovarchik. (2008) The inverse three-spectral problem for a Stieltjes string and the inverse problem with one-dimensional damping. Inverse Problems 24:1, pages 015019.
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Ninoslav Truhar & Krešimir Veselić. (2007) Bounds on the trace of a solution to the Lyapunov equation with a general stable matrix. Systems & Control Letters 56:7-8, pages 493-503.
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V. N. Pivovarchik. (2007) On spectra of a certain class of quadratic operator pencils with one-dimensional linear part. Ukrainian Mathematical Journal 59:5, pages 766-781.
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Yury Arlinskiĭ & Eduard Tsekanovskiĭ. (2006) Non-self-adjoint Jacobi matrices with a rank-one imaginary part. Journal of Functional Analysis 241:2, pages 383-438.
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Dionisio Bernal. (2005) Closely Spaced Roots and Defectiveness in Second-Order Systems. Journal of Engineering Mechanics 131:3, pages 276-281.
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M.I. Friswell, U. Prells & S.D. Garvey. (2005) Low-rank damping modifications and defective systems. Journal of Sound and Vibration 279:3-5, pages 757-774.
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Y.M. Ram & G.Z. Voyiadjis. (2004) Material characterization of a Kelvin chain from dynamic response. ZAMM 84:12, pages 807-817.
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Steven J. Cox, Ivica Nakić, Annette Rittmann & Krešimir Veselić. (2004) Lyapunov optimization of a damped system. Systems & Control Letters 53:3-4, pages 187-194.
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Ninoslav Truhar. (2004) An efficient algorithm for damper optimization for linear vibrating systems using Lyapunov equation. Journal of Computational and Applied Mathematics 172:1, pages 169-182.
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M. Dilena & A. Morassi. (2003) Detecting cracks in a longitudinally vibrating beam with dissipative boundary conditions. Journal of Sound and Vibration 267:1, pages 87-103.
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Uwe Prells & Michael I. Friswell. (2000) A Relationship Between Defective Systems and Unit-Rank Modification of Classical Damping. Journal of Vibration and Acoustics 122:2, pages 180-183.
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Beresford N. Parlett. (1998) Spectral sensitivity of products of bidiagonals. Linear Algebra and its Applications 275-276, pages 417-431.
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Yitshak M. Ram. (2016) Pole-Zero Assignment of Vibratory Systems by State Feedback Control. Journal of Vibration and Control 4:2, pages 145-165.
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Moody T. Chu. (1998) Inverse Eigenvalue Problems. SIAM Review 40:1, pages 1-39.
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Lloyd N. Trefethen. (1997) Pseudospectra of Linear Operators. SIAM Review 39:3, pages 383-406.
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Steven Cox & Roger Knobel. (1996) An inverse spectral problem for a nonnormal first order differential operator. Integral Equations and Operator Theory 25:2, pages 147-162.
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Tobin A. Driscoll & Lloyd N. Trefethen. (1996) Pseudospectra for the wave equation with an absorbing boundary. Journal of Computational and Applied Mathematics 69:1, pages 125-142.
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M. Gürgöze & P.C. Müller. (1992) Optimal positioning of dampers in multi-body systems. Journal of Sound and Vibration 158:3, pages 517-530.
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K. Veseli?. (1990) On linear vibrational systems with one dimensional damping II. Integral Equations and Operator Theory 13:6, pages 883-897.
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A. C. M. Ran & L. Rodman. (1989) Semidefinite perturbations of analytic Hermitian matrix functions. Integral Equations and Operator Theory 12:5, pages 739-745.
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