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2019 | OriginalPaper | Buchkapitel

4. Qualitative Properties of Vibration and Static Deformation Associated with Discrete Systems of Beams

verfasst von : Dajun Wang, Qishen Wang, Beichang (Bert) He

Erschienen in: Qualitative Theory in Structural Mechanics

Verlag: Springer Singapore

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Abstract

The focus of the first six sections of this chapter is on qualitative properties of the finite difference model or the related physical model of a beam. We will set up the governing equations of motion and boundary conditions associated with the finite difference system; derive various modal qualitative properties of the discrete model under different boundary constraints, by applying the theory of oscillatory matrices and the concept of conjugate beams; and establish qualitative properties in static deformation of the finite difference system of a well-constrained beam.

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Literatur
1.
Zurück zum Zitat Gantmacher FP, Krein MG (1961) Oscillation matrices and kernels and small vibrations of mechanical systems. U. S. Atomic Energy Commission, Washington Gantmacher FP, Krein MG (1961) Oscillation matrices and kernels and small vibrations of mechanical systems. U. S. Atomic Energy Commission, Washington
2.
Zurück zum Zitat Gladwell GML (1985) Qualitative properties of vibrating systems. Proc Roy Soc Lond A 401:299–315CrossRef Gladwell GML (1985) Qualitative properties of vibrating systems. Proc Roy Soc Lond A 401:299–315CrossRef
3.
Zurück zum Zitat Gladwell GML (2004) Inverse problems in vibration, 2nd edn. Springer, Dordrecht (1986, 1st edn, Martinus Nijhoff Publishers, Dordrecht) Gladwell GML (2004) Inverse problems in vibration, 2nd edn. Springer, Dordrecht (1986, 1st edn, Martinus Nijhoff Publishers, Dordrecht)
4.
Zurück zum Zitat Gladwell GML, England AH, Wang DJ (1987) Examples of reconstruction of an Euler-Bernoulli beam from spectral data. J Sound Vibr 19(1):81–94CrossRef Gladwell GML, England AH, Wang DJ (1987) Examples of reconstruction of an Euler-Bernoulli beam from spectral data. J Sound Vibr 19(1):81–94CrossRef
5.
Zurück zum Zitat Gladwell GML (1991) Qualitative properties of finite-element models II: the Euler-Bernoulli beam. Q J Mech Appl Math 44(2):267–284CrossRef Gladwell GML (1991) Qualitative properties of finite-element models II: the Euler-Bernoulli beam. Q J Mech Appl Math 44(2):267–284CrossRef
6.
Zurück zum Zitat He BC, Wang DJ, Low KH (1989) Inverse problem for a vibrating beam using a finite difference model. In: Proceedings international conference on noise & vibration, Singapore, B, pp 92–104 He BC, Wang DJ, Low KH (1989) Inverse problem for a vibrating beam using a finite difference model. In: Proceedings international conference on noise & vibration, Singapore, B, pp 92–104
7.
Zurück zum Zitat He BC, Wang DJ, Wang QS (1989) Inverse problem for the finite difference model of Euler beam in vibration. J Vibr Eng 2(2):1–9 (in Chinese) He BC, Wang DJ, Wang QS (1989) Inverse problem for the finite difference model of Euler beam in vibration. J Vibr Eng 2(2):1–9 (in Chinese)
8.
Zurück zum Zitat He BC, Wang DJ, Wang QS (1991) The single mode inverse problem of Euler-Bernoulli beam. Acta Mech Solida Sin 12(1):85–89 (in Chinese) He BC, Wang DJ, Wang QS (1991) The single mode inverse problem of Euler-Bernoulli beam. Acta Mech Solida Sin 12(1):85–89 (in Chinese)
9.
Zurück zum Zitat Wang DJ, He BC, et al (1990) Inverse problems of the finite difference model of a vibrating Euler beam. In: Proceedings international conference on vibration problems in engineering, June 1990, China, vol 1(1), pp 21–26. International Academic Publishers, Singapore Wang DJ, He BC, et al (1990) Inverse problems of the finite difference model of a vibrating Euler beam. In: Proceedings international conference on vibration problems in engineering, June 1990, China, vol 1(1), pp 21–26. International Academic Publishers, Singapore
10.
Zurück zum Zitat Wang DJ, He BC, Wang QS (1990) On the construction of the Euler-Bernoulli beam via two sets of modes and the corresponding frequencies. Acta Mech Sin 22(4):479–483 (in Chinese) Wang DJ, He BC, Wang QS (1990) On the construction of the Euler-Bernoulli beam via two sets of modes and the corresponding frequencies. Acta Mech Sin 22(4):479–483 (in Chinese)
11.
Zurück zum Zitat Wang QS, He BC, Wang DJ (1990) Some qualitative properties of frequencies and modes of Euler beams. J Vibr Eng 3(4):58–66 (in Chinese) Wang QS, He BC, Wang DJ (1990) Some qualitative properties of frequencies and modes of Euler beams. J Vibr Eng 3(4):58–66 (in Chinese)
12.
Zurück zum Zitat Wang QS, Wang DJ, He BC (1991) Construction of the difference discrete system for the simple-support beam from the spectra data. Eng Mech 8(4):10–19 (in Chinese)CrossRef Wang QS, Wang DJ, He BC (1991) Construction of the difference discrete system for the simple-support beam from the spectra data. Eng Mech 8(4):10–19 (in Chinese)CrossRef
13.
Zurück zum Zitat Wang QS, Wang DJ (2006) Difference discrete system of the Euler beam with arbitrary supports and sign oscillatory property of stiffness matrices. Appl Math & Mech 27(3):393–398CrossRef Wang QS, Wang DJ (2006) Difference discrete system of the Euler beam with arbitrary supports and sign oscillatory property of stiffness matrices. Appl Math & Mech 27(3):393–398CrossRef
14.
Zurück zum Zitat Wang QS, Wu L, Wang DJ (2009) Some qualitative properties of frequency spectrum and modes of difference discrete system of multi-bearing beam. Chin J Theor Appl Mech 41(6):61–68 (in Chinese) Wang QS, Wu L, Wang DJ (2009) Some qualitative properties of frequency spectrum and modes of difference discrete system of multi-bearing beam. Chin J Theor Appl Mech 41(6):61–68 (in Chinese)
15.
Zurück zum Zitat Wang QS, Wang DJ, Wu L et al (2009) Sign-oscillating property of stiffness matrix of difference discrete system and qualitative property of beam with overhang. J Vibr Shock 28(6):113–117 (in Chinese) Wang QS, Wang DJ, Wu L et al (2009) Sign-oscillating property of stiffness matrix of difference discrete system and qualitative property of beam with overhang. J Vibr Shock 28(6):113–117 (in Chinese)
16.
Zurück zum Zitat Wang QS, Wang DJ, Wu L et al (2011) Qualitative properties of frequencies and modes of vibrating multi-span beam. Q J Mech Appl Math 64(1):75–86CrossRef Wang QS, Wang DJ, Wu L et al (2011) Qualitative properties of frequencies and modes of vibrating multi-span beam. Q J Mech Appl Math 64(1):75–86CrossRef
17.
Zurück zum Zitat Wang QS, Zhang LH, Wang DJ (2012) Some qualitative properties of modes of discrete system of beam with overhang. Chin J Theor Appl Mech 44(6):1071–1074 (in Chinese) Wang QS, Zhang LH, Wang DJ (2012) Some qualitative properties of modes of discrete system of beam with overhang. Chin J Theor Appl Mech 44(6):1071–1074 (in Chinese)
18.
Zurück zum Zitat Wang QS, Wang DJ (2014) Supplementary proof of some oscillation property for discrete systems of rod and beam having rigid modes. Chin Q Mech 35(2):262–269 (in Chinese) Wang QS, Wang DJ (2014) Supplementary proof of some oscillation property for discrete systems of rod and beam having rigid modes. Chin Q Mech 35(2):262–269 (in Chinese)
19.
Zurück zum Zitat Zheng ZJ, Chen P, Wang DJ (2012) Oscillation property of modes for FE models of bars and beams. J Vibr Shock 31(20):79–83 (in Chinese) Zheng ZJ, Chen P, Wang DJ (2012) Oscillation property of modes for FE models of bars and beams. J Vibr Shock 31(20):79–83 (in Chinese)
20.
Zurück zum Zitat Zheng ZJ, Chen P, Wang DJ (2013) Oscillation property of the vibrations for finite element models of Euler beam. Q J Mech Appl Math 66(4):587–608CrossRef Zheng ZJ, Chen P, Wang DJ (2013) Oscillation property of the vibrations for finite element models of Euler beam. Q J Mech Appl Math 66(4):587–608CrossRef
21.
Zurück zum Zitat Zheng ZJ, Chen P, Wang DJ (2014) A unified proof to oscillation property of discrete beam models. Appl Math Mech 35(5):621–636CrossRef Zheng ZJ, Chen P, Wang DJ (2014) A unified proof to oscillation property of discrete beam models. Appl Math Mech 35(5):621–636CrossRef
22.
Zurück zum Zitat Zheng ZJ (2014) The qualitative vibrational property and modal inverse problems of rods and Euler beams [D]. Department of Mechanics and Engineering Science, College of Engineering, Peking University (in Chinese) Zheng ZJ (2014) The qualitative vibrational property and modal inverse problems of rods and Euler beams [D]. Department of Mechanics and Engineering Science, College of Engineering, Peking University (in Chinese)
Metadaten
Titel
Qualitative Properties of Vibration and Static Deformation Associated with Discrete Systems of Beams
verfasst von
Dajun Wang
Qishen Wang
Beichang (Bert) He
Copyright-Jahr
2019
Verlag
Springer Singapore
DOI
https://doi.org/10.1007/978-981-13-1376-9_4

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