On nonlinear perturbation analysis of a structure carrying a circular cylindrical liquid tank under horizontal excitation

The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system ar...

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Veröffentlicht in:Journal of vibration and control 2019-03, Vol.25 (5), p.1058-1079
Hauptverfasser: Attari, N. K. A., Rofooei, F. R., Waezi, Z.
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creator Attari, N. K. A.
Rofooei, F. R.
Waezi, Z.
description The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode response with respect to the excitation amplitude. The saturation phenomenon is observed in the decoupled modes of the system; however, the structural mode and the first anti-symmetric mode of liquid are a combination of the saturated mode and another mode whose scale factor is crucial for the structural response. The results of perturbation analysis are in good agreement with results obtained from numerical methods.
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K. A. ; Rofooei, F. R. ; Waezi, Z.</creator><creatorcontrib>Attari, N. K. A. ; Rofooei, F. R. ; Waezi, Z.</creatorcontrib><description>The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode response with respect to the excitation amplitude. The saturation phenomenon is observed in the decoupled modes of the system; however, the structural mode and the first anti-symmetric mode of liquid are a combination of the saturated mode and another mode whose scale factor is crucial for the structural response. 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The obtained results reveal an increase in the stability region for a single-mode response with respect to the excitation amplitude. The saturation phenomenon is observed in the decoupled modes of the system; however, the structural mode and the first anti-symmetric mode of liquid are a combination of the saturated mode and another mode whose scale factor is crucial for the structural response. 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subjects Cylindrical tanks
Differential equations
Earthquakes
Equations of motion
Excitation
Liquid sloshing
Mathematical analysis
Nonlinear analysis
Nonlinear differential equations
Nonlinear equations
Numerical methods
Perturbation methods
Seismic activity
Seismic engineering
title On nonlinear perturbation analysis of a structure carrying a circular cylindrical liquid tank under horizontal excitation
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