FREE VIBRATION ANALYSIS OF A NONLINEAR BEAM USING HOMOTOPY AND MODIFIED LINDSTEDT-POINCARE METHODS

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AHMADIAN M.T.; MOJAHEDI M.; MOEINFARD H.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: JOURNAL OF SOLID MECHANICS Year:2009 | Volume:1 | Issue:1 Page(s): 29-36

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Information Journal Paper

Title

FREE VIBRATION ANALYSIS OF A NONLINEAR BEAM USING HOMOTOPY AND MODIFIED LINDSTEDT-POINCARE METHODS

Author(s)

AHMADIAN M.T. | MOJAHEDI M. | MOEINFARD H. | Issue Writer Certificate

Keywords

FREE VIBRATION

NONLINEAR BEAM

HOMOTOPY PERTURBATION METHOD

LINDSTEDT-POINCARE METHOD

AXIAL LOAD

Abstract

In this paper, homotopy perturbation and modified LINDSTEDT-POINCARE METHODs are employed for nonlinear FREE VIBRATIONal analysis of simply supported and double-clamped beams subjected to AXIAL LOADs. Mid-plane stretching effect has also been accounted in the model. Gale rkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies of the beams. Effects of design parameters such as AXIAL LOAD and slenderness ratio are investigated. The analytic expressions are valid for a wide range of vibration amplitudes. Comparing the semi-analytic solutions with numerical results, presented in the literature, indicates good agreement. The results signify the fact that HPM is a powerful tool for analyzing dynamic and vibrational behavior of structures analytically

Cites

References

AN APPROXIMATE SOLUTION TECHNIQUE WHICH DOES NOT DEPEND UPON SMALL PARAMETERS: A SPECIAL EXAMPLE

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APA: Copy

AHMADIAN, M.T., MOJAHEDI, M., & MOEINFARD, H.. (2009). FREE VIBRATION ANALYSIS OF A NONLINEAR BEAM USING HOMOTOPY AND MODIFIED LINDSTEDT-POINCARE METHODS. JOURNAL OF SOLID MECHANICS, 1(1), 29-36. SID. https://sid.ir/paper/319199/en

Vancouver: Copy

AHMADIAN M.T., MOJAHEDI M., MOEINFARD H.. FREE VIBRATION ANALYSIS OF A NONLINEAR BEAM USING HOMOTOPY AND MODIFIED LINDSTEDT-POINCARE METHODS. JOURNAL OF SOLID MECHANICS[Internet]. 2009;1(1):29-36. Available from: https://sid.ir/paper/319199/en

IEEE: Copy

M.T. AHMADIAN, M. MOJAHEDI, and H. MOEINFARD, “FREE VIBRATION ANALYSIS OF A NONLINEAR BEAM USING HOMOTOPY AND MODIFIED LINDSTEDT-POINCARE METHODS,” JOURNAL OF SOLID MECHANICS, vol. 1, no. 1, pp. 29–36, 2009, [Online]. Available: https://sid.ir/paper/319199/en

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