Top

Published in:

2021 | OriginalPaper | Chapter

4. Selected Applications

Authors : Rubens Gonçalves Salsa Junior, Fai Ma

Published in: Advances in the Theory of System Decoupling

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This chapter outlines applications for which the method of decoupling by phase synchronization can be used as the main theoretical tool. The applications include: computation of invariant of motion, derivation of a canonical form of the equation of motion, characterization of oscillatory behavior in free vibration and modal reduction of a system under base excitation. Several illustrative examples are supplied for theoretical developments.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Decoupling of Linear Systems by Phase Synchronization

Eigenvectors have been normalized in accordance with the scheme depicted in Appendix B.

Rayleigh, J.W.S.: The Theory of Sound, vol. 1, reprint of the 1894 edn. Dover, New York (1945)

Genta, G.: Vibration Dynamics and Control. Springer, New York (2009)CrossRef

Chopra, A.K.: Dynamics of Structures: Theory and Applications to Earthquake Engineering, 5th edn. Pearson, Hoboken (2017)

Humar, J.L.: Dynamics of Structures, 3rd edn. CRC Press, Boca Raton (2012)CrossRef

30.

Morzfeld, M., Ma, F., Parlett, B.N.: The transformation of second-order linear systems into independent equations. SIAM J. Appl. Math. 71(4), 1026–1043 (2011). https://doi.org/10.1137/100818637 MathSciNetCrossRef

59.

Tisseur, F., Meerbergen, K.: The quadratic eigenvalue problem. SIAM Rev. 43(2), 235–286 (2001). https://doi.org/10.1137/S0036144500381988 MathSciNetCrossRef

66.

Clough, R.W., Mojtahedi, S.: Earthquake response analysis considering non-proportional damping. Earthq. Eng. Struct. Dyn. 4(5), 489–496 (1976). https://doi.org/10.1002/eqe.4290040506 CrossRef

67.

Tsai, H.C., Kelly, J.M.: Non-classical damping in dynamic analysis of base-isolated structures with internal equipment. Earthq. Eng. Struct. Dyn. 16(1), 29–43 (1988). https://doi.org/10.1002/eqe.4290160104 CrossRef

68.

Tsai, H.C., Kelly, J.M.: Seismic response of the superstructure and attached equipment in a base-isolated building. Earthq. Eng. Struct. Dyn. 18(4), 551–564 (1989). https://doi.org/10.1002/eqe.4290180409 CrossRef

69.

Itoh, T.: Damped vibration mode superposition method for dynamic response analysis. Earthq. Eng. Struct. Dyn. 2(1), 47–57 (1973). https://doi.org/10.1002/eqe.4290020105 CrossRef

71.

Horn, R.A., Johnson, C.R.: Matrix Analysis, 2nd edn. Cambridge University Press, New York (2013)MATH

82.

Kawano, D.T., Salsa, R.G., Jr., Ma, F., Morzfeld, M.: A canonical form of the equation of motion of linear dynamical systems. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 471, 20170809 (2018). https://doi.org/10.1098/rspa.2017.0809

84.

Morzfeld, M., Kawano, D.T., Ma, F.: Characterization of damped linear dynamical systems in free motion. Numer. Algebra Control Optim. 3(1), 49–62 (2013). https://doi.org/10.3934/naco.2013.3.49 MathSciNetCrossRef

85.

Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products, 17th edn., p. 1060. Academic Press, San Diego (2007)

86.

Duffin, R.L., Duffin, R.J.: A minimax theory for overdamped networks. J. Rational Mech. Anal. 4, 221–233 (1955). http://www.jstor.org/stable/24900361 MathSciNetMATH

87.

Barkwell, L., Lancaster, P.: Overdamped and gyroscopic vibrating systems. ASME J. Appl. Mech. 59(1), 176–181 (1992). https://doi.org/10.1115/1.2899425 MathSciNetCrossRef

88.

Bulatović, R.M.: Non-oscillatory damped multi-degree-of-freedom systems. Acta Mech. 151(3), 235–244 (2001). https://doi.org/10.1007/BF01246920 CrossRef

89.

Bulatović, R.M.: On the heavily damped response in viscously damped dynamic systems. ASME J. Appl. Mech. 71(1), 131–134 (2004). https://doi.org/10.1115/1.1629108 MathSciNetCrossRef

90.

Bhaskar, A.: Criticality of damping in multi-degree-of-freedom systems. ASME J. Appl. Mech. 64(2), 387–393 (1997). https://doi.org/10.1115/1.2787320 CrossRef

91.

Inman, D.J., Andry, A.N., Jr.: Some results on the nature of eigenvalues of discrete damped linear systems. ASME J. Appl. Mech. 47(4), 927–930 (1980). https://doi.org/10.1115/1.3153815 CrossRef

92.

Müller, P.C.: Oscillatory damped linear systems. Mech. Res. Commun. 6(2), 81–85 (1979). https://doi.org/10.1016/0093-6413(79)90017-X MathSciNetCrossRef

93.

Nicholson, D.W.: Overdamping of a linear mechanical system. Mech. Res. Commun. 10(2), 67–76 (1983). https://doi.org/10.1016/0093-6413(83)90075-7 MathSciNetCrossRef

94.

Nicholson, D.W.: Eigenvalue bounds for linear mechanical systems with nonmodal damping. Mech. Res. Commun. 14(2), 115–122 (1987). https://doi.org/10.1016/0093-6413(87)90028-0 CrossRef

95.

Silvester, J.R.: Determinants of block matrices. Math. Gaz. 84(501), 460–467 (2000). https://doi.org/10.2307/3620776 CrossRef

96.

Ince, L.E.: Ordinary Differential Equations, pp. 394–395. Dover, New York (1956)

97.

Zwillinger, D.: Handbook of Differential Equations, pp. 95–96. Academic Press, San Diego (1989)

98.

Hill, J.M.: Solution of Differential Equations by Means of One-Parameter Groups, pp. 42–43. Pitman Publishing, Boston (1982)

99.

Xu, J.: A synthesis formulation of explicit damping matrix for non-classically damped systems. Nucl. Eng. Des. 227(2), 125–132 (2004). https://doi.org/10.1016/j.nucengdes.2003.08.005 CrossRef

100.

Thomson, W.T., Calkins, T., Caravani, P.: A numerical study of damping. Earthq. Eng. Struct. Dyn. 3(1), 97–103 (1974). https://doi.org/10.1002/eqe.4290030108 CrossRef

101.

Angeles, J., Ostrovskaya, S.: The proportional-damping matrix of arbitrarily damped linear mechanical systems. ASME J. Appl. Mech. 69(5), 649–656 (2002). https://doi.org/10.1115/1.1483832 MathSciNetCrossRef

102.

Felszeghy, S.F.: On uncoupling and solving the equations of motion of vibrating linear discrete systems. ASME J. Appl. Mech. 60(2), 456–462 (1993). https://doi.org/10.1115/1.2900815 CrossRef

103.

Shahruz, S.M., Ma, F.: Approximate decoupling of the equations of motion of linear underdamped systems. ASME J. Appl. Mech. 55(3), 716–720 (1988). https://doi.org/10.1115/1.3125855 CrossRef

104.

Shahruz, S.M.: Approximate decoupling of the equations of motion of damped linear systems. J. Sound Vib. 136(1), 51–64 (1990). https://doi.org/10.1016/0022-460X(90)90937-U MathSciNetCrossRef

105.

Udwadia, F.E.: Inverse problem of Lagrangian mechanics for classically damped linear multi-degrees-of-freedom systems. ASME J. Appl. Mech. 83(10), 104501 (2016). https://doi.org/10.1115/1.4034012 CrossRef

106.

Salsa, R.G., Jr., Kawano, D.T., Ma, F., Leitmann, G.: The inverse problem of linear Lagrangian dynamics. ASME J. Appl. Mech. 85(3), 031002 (2018). https://doi.org/10.1115/1.4038749 CrossRef

107.

Pars, L.A.: A Treatise on Analytical Dynamics. Wiley, New York (1965)MATH

Title: Selected Applications
Authors: Rubens Gonçalves Salsa Junior
Fai Ma
Publisher: Springer International Publishing
Book: Advances in the Theory of System Decoupling
Print ISBN: 978-3-030-60845-3

Electronic ISBN: 978-3-030-60846-0

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-60846-0_4

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partners