Exact solutions for dynamic response of a periodic spring and mass structure

This paper derives exact analytical solutions for the dynamic response of a periodic structure for which the unit cell consists of one mass and one spring. The solutions cover arbitrary initial conditions and both polynomial and harmonic external forces. They involve Bessel, Lommel, Weber and hyperg...

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Veröffentlicht in:	Journal of sound and vibration 2012-02, Vol.331 (5), p.1183-1190
Hauptverfasser:	Gao, Q., Wu, F., Zhang, H.W., Zhong, W.X., Howson, W.P., Williams, F.W.
Format:	Artikel
Sprache:	eng
Schlagworte:	Dynamic response Exact sciences and technology Exact solutions Fundamental areas of phenomenology (including applications) Initial conditions Mathematical analysis Physics Solid mechanics Springs Springs (elastic) Structural and continuum mechanics Unit cell Vibration Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Beschreibung
Zusammenfassung:	This paper derives exact analytical solutions for the dynamic response of a periodic structure for which the unit cell consists of one mass and one spring. The solutions cover arbitrary initial conditions and both polynomial and harmonic external forces. They involve Bessel, Lommel, Weber and hypergeometric functions. ► Exact solutions for the dynamic response of a special periodic structure are derived. ► Arbitrary initial conditions and both polynomial and harmonic external forces treated. ► The solutions involve Bessel, Lommel, Weber and hypergeometric functions.
ISSN:	0022-460X 1095-8568
DOI:	10.1016/j.jsv.2011.10.020