Approximate dynamics using Hamilton's principle, including applications to non-conservative and constrained systems

Townend, M. Stewart; Kerr, Andrew H

doi:10.1016/0094-114x(82)90007-6

Cited by 3 publications

(1 citation statement)

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“…Townend simulated the dynamic behavior of a mechanical system using approximate techniques based on Hamilton's principle and showed that the method could be suitable for both multidegrees of freedom and constrained systems [13]. nagai derived the governing equations and the boundary conditions by using Hamilton's principle and presented the analytical results on nonlinear vibrations of a cantilevered beam [14].…”

Section: Introductionmentioning

confidence: 99%

The primary resonance of laminated piezoelectric rectangular plates

Zhao

Shi

Xiang

2009

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Based on Hamilton's principle and the Rayleigh-Ritz method, a model of a nonlinear dynamic laminated piezoelectric rectangular plate was established, and the governing equations were derived and solved for both the thin-plate and thick-plate models. In the present investigation, the nonlinear constitutive relations of piezoelectric materials were considered and the effects of the nonlinearity on the response of the plate were discovered. The primary resonance of rectangular plate is investigated with the use of the method of multiple scales. The results obtained in the present paper agree very well with the experiment results.

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Section: Introductionmentioning

confidence: 99%