APPLICATION OF PERTURBATION THEORY TO THE NON-LINEAR VIBRATION ANALYSIS OF A STRING INCLUDING THE BENDING MOMENT EFFECTS

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ESMAEILZADEH KHADEM S.; REZAEE M.

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

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Journal: AMIRKABIR Year:2001 | Volume:12 | Issue:48 Page(s): 347-359

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Title

APPLICATION OF PERTURBATION THEORY TO THE NON-LINEAR VIBRATION ANALYSIS OF A STRING INCLUDING THE BENDING MOMENT EFFECTS

Author(s)

ESMAEILZADEH KHADEM S. | REZAEE M. | Issue Writer Certificate

Keywords

NON-LINEAR VIBRATIONQ3

WIREQ4

STRINGQ4

PERTURBATION THEORYQ2

BENDING MOMENTQ4

Abstract

In this paper the large amplitude and non - linear vibration of a STRING is considered. The initial tension, lateral vibration amplitude, diameter and the modulus of elasticity of the STRING have main effects on its natural frequencies. Increasing the lateral vibration amplitude makes the assumption of constant initial tension invalid. In this case, therefore, it is impossible to use the classical equation of STRING with small amplitude transverse motion assumption. On the other hand, by increasing the STRING diameter, the BENDING MOMENT effect will increase dramatically, and acts as an impressive restoring moment.Considering the effects of the BENDING MOMENTs, the nonlinear equation governing the large amplitude transverse vibration of a STRING is derived. The time dependent portion of the governing equation has the from of Doffing equation. This equation is solved using the PERTURBATION THEORY. The results of the analysis are shown in appropriate graphs, and the natural frequencies of the STRING due to the non-linear factors are compared with the natural frequencies of the linear vibration of a STRING without BENDING MOMENT effects.

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APA: Copy

ESMAEILZADEH KHADEM, S., & REZAEE, M.. (2001). APPLICATION OF PERTURBATION THEORY TO THE NON-LINEAR VIBRATION ANALYSIS OF A STRING INCLUDING THE BENDING MOMENT EFFECTS . AMIRKABIR, 12(48), 347-359. SID. https://sid.ir/paper/789/en

Vancouver: Copy

ESMAEILZADEH KHADEM S., REZAEE M.. APPLICATION OF PERTURBATION THEORY TO THE NON-LINEAR VIBRATION ANALYSIS OF A STRING INCLUDING THE BENDING MOMENT EFFECTS . AMIRKABIR[Internet]. 2001;12(48):347-359. Available from: https://sid.ir/paper/789/en

IEEE: Copy

S. ESMAEILZADEH KHADEM, and M. REZAEE, “APPLICATION OF PERTURBATION THEORY TO THE NON-LINEAR VIBRATION ANALYSIS OF A STRING INCLUDING THE BENDING MOMENT EFFECTS ,” AMIRKABIR, vol. 12, no. 48, pp. 347–359, 2001, [Online]. Available: https://sid.ir/paper/789/en

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