1994
DOI: 10.1006/jsvi.1994.1088
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Non-Linear Free Vibrations of Beams By the Finite Element and Continuation Methods

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Cited by 55 publications
(39 citation statements)
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“…Often, particularly in analyses of slender beams, this force is approximated by its mean value over the element [14].…”
Section: Equations Of Motionmentioning
confidence: 99%
“…Often, particularly in analyses of slender beams, this force is approximated by its mean value over the element [14].…”
Section: Equations Of Motionmentioning
confidence: 99%
“…This approach to considered particular problem is more adequate than very popular modal ones because the influence of more then one mode of vibration can be taken into account in an easy way. As shown in many papers (see, for example references [19][20][21][22]), the interaction of two or more modes of vibration could be very important if nonlinear systems are considered. Moreover, beams with the non-uniform spatial distribution of the beam bending stiffness, the mass per unit length or the cross-section characteristic dimension can be modelled more accurately.…”
Section: Description Of Computational Modelmentioning
confidence: 99%
“…As stated above, terms that give rise to secular terms may occur on the right-hand side of equation (19). To eliminate these terms we introduce two time-scales, t "t and t " t, and assume that q L can be expanded in a formal power series in , that is,…”
Section: The Construction Of Formal Approximations*general Casementioning
confidence: 99%
“…We substitute this into equation (19) WEAKLY NON-LINEAR ELASTIC BEAM and collect equal powers in . The O( )-problem becomes…”
Section: The Construction Of Formal Approximations*general Casementioning
confidence: 99%
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