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Characterization of damped linear dynamical systems in free motion
1. | Department of Mathematics, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, United States |
2. | Department of Mechanical Engineering, Rose-Hulman Institute of Technology, Terre Haute, IN 47803, United States |
3. | Department of Mechanical Engineering, University of California, Berkeley, CA 94720, United States |
References:
[1] |
L. Barkwell and P. Lancaster, Overdamped and gyroscopic vibrating systems, ASME Journal of Applied Mechanics, 59 (1992), 176-181.
doi: 10.1115/1.2899425. |
[2] |
A. Bhaskar, Criticality of damping in multi-degree-of-freedom systems, ASME Journal of Applied Mechanics, 64 (1997), 387-393.
doi: 10.1115/1.2787320. |
[3] |
R. M. Bulatović, Non-oscillatory damped multi-degree-of-freedom systems, Acta Mechanica, 151 (2001), 235-244.
doi: 10.1007/BF01246920. |
[4] |
R. M. Bulatović, On the heavily damped response in viscously damped dynamic systems, ASME Journal of Applied Mechanics, 71 (2004), 131-134.
doi: 10.1115/1.1629108. |
[5] |
T. K. Caughey and M. E. J. Okelly, Classical normal modes in damped linear dynamic systems, ASME Journal of Applied Mechanics, 32 (1965), 583-588.
doi: 10.1115/1.3627262. |
[6] |
R. M. Chalasani, Ride performance potential of active suspension systems - part I: simplified analysis based on a quarter-car model, in "ASME Symposium on Simulation and Control of Ground Vehicles and Transportation Systems," AMD-Vol. 80, DSC-Vol. 2, ASME, (1986), 187-204. |
[7] |
G. M. Connell, Asymptotic stability of second-order linear systems with semi-definite damping, AIAA Journal, 7 (1969), 1185-1187.
doi: 10.2514/3.5307. |
[8] |
J. W. Demmel, "Applied Numerical Linear Algebra," Society for Industrial and Applied Mathematics, Philadelphia, 1997.
doi: 10.1137/1.9781611971446. |
[9] |
R. J. Duffin, A minimax theory for overdamped networks, Journal of Rational Mechanics and Analysis, 4 (1955), 221-233. |
[10] |
R. Fletscher, "Practical Methods of Optimization," 2nd edition, Wiley, Hoboken, New Jersey, 2000. |
[11] |
I. Gohberg, P. Lancaster and L. Rodman, "Matrix Polynomials," Academic Press, New York, 1982. |
[12] |
A. J. Gray and A. N. Andry, A simple calculation of the critical damping matrix of a linear multi-degree-of-freedom system, Mechanics Research Communications, 9 (1982), 379-380.
doi: [10.1016/0093-6413(82)90035-0. |
[13] |
P. Hagedorn and S. Otterbein, "Technische Schwingungslehre," Springer, Berlin, Germany, 1987.
doi: 10.1007/978-3-642-83164-5. |
[14] |
K. Huseyin, "Vibrations and Stability of Multiple Parameter Systems," Noordhoff, Leiden, 1978. |
[15] |
D. J. Inman and A. N. Andry, Jr., Some results on the nature of eigenvalues of discrete damped linear systems, ASME Journal of Applied Mechanics, 47 (1980), 927-930.
doi: 10.1115/1.3153815. |
[16] |
D. J. Inman, "Vibration with Control," Wiley, Hoboken, New Jersey, 2006. |
[17] |
D. T. Kawano, M. Morzfeld and F. Ma, The decoupling of defective linear dynamical systems in free motion, Journal of Sound and Vibration, 330 (2011), 5165-5183.
doi: 10.1016/j.jsv.2011.05.013. |
[18] |
P. Lancaster, "Lambda-Matrices and Vibrating Systems," Pergamon Press, Oxford, United Kingdom, 1966. |
[19] |
P. Lancaster and M. Tismenetsky, "The Theory of Matrices," 2nd edition, Academic Press, New York, 1985. |
[20] |
F. Ma, A. Imam and M. Morzfeld, The decoupling of damped linear systems in oscillatory free vibration, Journal of Sound and Vibration, 324 (2009), 408-428.
doi: 10.1016/j.jsv.2009.02.005. |
[21] |
F. Ma, M. Morzfeld and A. Imam, The decoupling of damped linear systems in free or forced vibration, Journal of Sound and Vibration, 329 (2010), 3182-3202.
doi: 10.1016/j.jsv.2010.02.017. |
[22] |
L. Meirovitch, "Methods of Analytical Dynamics," McGraw-Hill, New York, 1970. |
[23] |
M. Morzfeld, F. Ma and B. N. Parlett, The transformation of second-order linear systems into independent equations, SIAM Journal on Applied Mathematics, 71 (2011), 1026-1043.
doi: 10.1137/100818637. |
[24] |
P. C. Müller, Oscillatory damped linear systems, Mechanics Research Communications, 6 (1979), 81-86. |
[25] |
D. W. Nicholson, Eigenvalue bounds for damped linear systems, Mechanics Research Communications, 5 (1978), 147-152. |
[26] |
D. W. Nicholson, Eigenvalue bounds for linear mechanical systems with nonmodal damping, Mechanics Research Communications, 14 (1978), 115-122. |
[27] |
D. W. Nicholson, Overdamping of a linear mechanical system, Mechanics Research Communications, 10 (1983), 67-76. |
[28] |
J. Nocedal and S. T. Wright, "Numerical Optimization," 2nd edition, Springer, New York, 2006. |
[29] |
J. W. Strutt (Lord Rayleigh), "The Theory of Sound, Vol. I," Dover, New York, 1945 (reprint of the 1894 edition). |
[30] |
F. Tisseur and K. Meerbergen, The quadratic eigenvalue problem, SIAM Review, 43 (2001), 235-286. |
[31] |
S. Türkay and H. Akçay, A study of random vibration characteristics of a quarter car model, Journal of Sound and Vibration, 282 (2005), 111-124. |
show all references
References:
[1] |
L. Barkwell and P. Lancaster, Overdamped and gyroscopic vibrating systems, ASME Journal of Applied Mechanics, 59 (1992), 176-181.
doi: 10.1115/1.2899425. |
[2] |
A. Bhaskar, Criticality of damping in multi-degree-of-freedom systems, ASME Journal of Applied Mechanics, 64 (1997), 387-393.
doi: 10.1115/1.2787320. |
[3] |
R. M. Bulatović, Non-oscillatory damped multi-degree-of-freedom systems, Acta Mechanica, 151 (2001), 235-244.
doi: 10.1007/BF01246920. |
[4] |
R. M. Bulatović, On the heavily damped response in viscously damped dynamic systems, ASME Journal of Applied Mechanics, 71 (2004), 131-134.
doi: 10.1115/1.1629108. |
[5] |
T. K. Caughey and M. E. J. Okelly, Classical normal modes in damped linear dynamic systems, ASME Journal of Applied Mechanics, 32 (1965), 583-588.
doi: 10.1115/1.3627262. |
[6] |
R. M. Chalasani, Ride performance potential of active suspension systems - part I: simplified analysis based on a quarter-car model, in "ASME Symposium on Simulation and Control of Ground Vehicles and Transportation Systems," AMD-Vol. 80, DSC-Vol. 2, ASME, (1986), 187-204. |
[7] |
G. M. Connell, Asymptotic stability of second-order linear systems with semi-definite damping, AIAA Journal, 7 (1969), 1185-1187.
doi: 10.2514/3.5307. |
[8] |
J. W. Demmel, "Applied Numerical Linear Algebra," Society for Industrial and Applied Mathematics, Philadelphia, 1997.
doi: 10.1137/1.9781611971446. |
[9] |
R. J. Duffin, A minimax theory for overdamped networks, Journal of Rational Mechanics and Analysis, 4 (1955), 221-233. |
[10] |
R. Fletscher, "Practical Methods of Optimization," 2nd edition, Wiley, Hoboken, New Jersey, 2000. |
[11] |
I. Gohberg, P. Lancaster and L. Rodman, "Matrix Polynomials," Academic Press, New York, 1982. |
[12] |
A. J. Gray and A. N. Andry, A simple calculation of the critical damping matrix of a linear multi-degree-of-freedom system, Mechanics Research Communications, 9 (1982), 379-380.
doi: [10.1016/0093-6413(82)90035-0. |
[13] |
P. Hagedorn and S. Otterbein, "Technische Schwingungslehre," Springer, Berlin, Germany, 1987.
doi: 10.1007/978-3-642-83164-5. |
[14] |
K. Huseyin, "Vibrations and Stability of Multiple Parameter Systems," Noordhoff, Leiden, 1978. |
[15] |
D. J. Inman and A. N. Andry, Jr., Some results on the nature of eigenvalues of discrete damped linear systems, ASME Journal of Applied Mechanics, 47 (1980), 927-930.
doi: 10.1115/1.3153815. |
[16] |
D. J. Inman, "Vibration with Control," Wiley, Hoboken, New Jersey, 2006. |
[17] |
D. T. Kawano, M. Morzfeld and F. Ma, The decoupling of defective linear dynamical systems in free motion, Journal of Sound and Vibration, 330 (2011), 5165-5183.
doi: 10.1016/j.jsv.2011.05.013. |
[18] |
P. Lancaster, "Lambda-Matrices and Vibrating Systems," Pergamon Press, Oxford, United Kingdom, 1966. |
[19] |
P. Lancaster and M. Tismenetsky, "The Theory of Matrices," 2nd edition, Academic Press, New York, 1985. |
[20] |
F. Ma, A. Imam and M. Morzfeld, The decoupling of damped linear systems in oscillatory free vibration, Journal of Sound and Vibration, 324 (2009), 408-428.
doi: 10.1016/j.jsv.2009.02.005. |
[21] |
F. Ma, M. Morzfeld and A. Imam, The decoupling of damped linear systems in free or forced vibration, Journal of Sound and Vibration, 329 (2010), 3182-3202.
doi: 10.1016/j.jsv.2010.02.017. |
[22] |
L. Meirovitch, "Methods of Analytical Dynamics," McGraw-Hill, New York, 1970. |
[23] |
M. Morzfeld, F. Ma and B. N. Parlett, The transformation of second-order linear systems into independent equations, SIAM Journal on Applied Mathematics, 71 (2011), 1026-1043.
doi: 10.1137/100818637. |
[24] |
P. C. Müller, Oscillatory damped linear systems, Mechanics Research Communications, 6 (1979), 81-86. |
[25] |
D. W. Nicholson, Eigenvalue bounds for damped linear systems, Mechanics Research Communications, 5 (1978), 147-152. |
[26] |
D. W. Nicholson, Eigenvalue bounds for linear mechanical systems with nonmodal damping, Mechanics Research Communications, 14 (1978), 115-122. |
[27] |
D. W. Nicholson, Overdamping of a linear mechanical system, Mechanics Research Communications, 10 (1983), 67-76. |
[28] |
J. Nocedal and S. T. Wright, "Numerical Optimization," 2nd edition, Springer, New York, 2006. |
[29] |
J. W. Strutt (Lord Rayleigh), "The Theory of Sound, Vol. I," Dover, New York, 1945 (reprint of the 1894 edition). |
[30] |
F. Tisseur and K. Meerbergen, The quadratic eigenvalue problem, SIAM Review, 43 (2001), 235-286. |
[31] |
S. Türkay and H. Akçay, A study of random vibration characteristics of a quarter car model, Journal of Sound and Vibration, 282 (2005), 111-124. |
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