Analysis of the forced vibration of geometrically nonlinear cantilever beam with lumping mass by multiple scale Lindstedt-Poincare method

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	Analysis of the forced vibration of geometrically nonlinear cantilever beam with lumping mass by multiple scale Lindstedt-Poincare method
	Du, H.; Er, G. K.; Iu, V. P.
	2017-07-01
Source Publication	Proceedings of 9th European Nonlinear Dynamics Conference
Abstract	The forced vibration of cantilever beam with or without lumping mass can be found in many practical applications. With the variational approach based on extended Hamiltonian principle, the equation of motion and boundary conditions governing a uniform cantilever beam carrying a lumping mass at the free end are formulated under the action of lateral tip concentrated load. After that, the multiple-scales method, multiple-scales Lindstedt-Poincaré method and fourth-order Runge-Kutta method are employed to analyze the forced vibration of the considered cantilever. It is found that the first mode frequency response curve obtained by the multiplescales Lindstedt-Poincaré method agree well with the first mode frequency response curve obtained by the fourth-order Runge-Kutta method. However, the first mode frequency response curve obtained by multiple-scales method deviates from the first mode frequency response curve obtained by the fourth-order Runge-Kutta method when the beam deflection is large. When the excitation frequency is around second or third natural frequency, neither multiple-scales method nor multiple-scales Lindstedt-Poincaré method can give correct frequency response curves comparing to the frequency response curves obtained by the fourth-order Runge-Kutta method.
Keyword	Forced Vibration Geometrically Nonlinear Cantilever Beam Multiple-Scales Lindstedt-Poincaré Method
Language	英語English
The Source to Article	PB_Publication
PUB ID	29898
Document Type	Conference paper
Collection	DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING Faculty of Science and Technology
Recommended Citation GB/T 7714	Du, H.,Er, G. K.,Iu, V. P.. Analysis of the forced vibration of geometrically nonlinear cantilever beam with lumping mass by multiple scale Lindstedt-Poincare method[C], 2017.
APA	Du, H.., Er, G. K.., & Iu, V. P. (2017). Analysis of the forced vibration of geometrically nonlinear cantilever beam with lumping mass by multiple scale Lindstedt-Poincare method. Proceedings of 9th European Nonlinear Dynamics Conference.

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