Nonlinear Vibration Model for Initially Stressed Beam-Foundation System

In this study, the nonlinear vibration model of structure with cross support is established. The conventional structure without cross support is linear and easy to be investigated. Unfortunately, its dynamic stability and vibration due to earthquake excitation are usually not acceptable. For suppressing the structural vibration the cross support composed of the elastic connecting bar and damper is considered here. This is a passive control design. Beside, due to the supporting arrangement, the mathematical model of the structure is highly nonlinear. In this study, the analytical solution for this system is derived. Further, the effects of control parameters on the vibration response are investigated.

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The Research on Single-Disc Rotor Nonlinear Vibration Model and Mechanism

Advanced Engineering Forum ◽

10.4028/www.scientific.net/aef.2-3.954 ◽

2011 ◽

Vol 2-3 ◽

pp. 954-959 ◽

Cited By ~ 2

Author(s):

Min Wu ◽

Jin Fu Yang

Keyword(s):

Frequency Response ◽

Nonlinear Vibration ◽

Duffing Equation ◽

Resonance Amplitude ◽

Vibration Model ◽

Engineering Problems ◽

Characteristics Analysis ◽

Response Equation ◽

New Research ◽

Nonlinear Components

Based on mechanical properties of rotor nonlinear vibration and the assumption of large deformation, the rotor nonlinear vibration model in the form of Duffing equation is constructed from typical engineering problems. According to analytical solutions of Duffing equation, system’s equivalent frequency and frequency response equation are derived. Furthermore, the influences of stiffness, damping and nonlinear components are studied. The single-disc rotor nonlinear vibration experimental results verify the rationality and efficiency of nonlinear vibration model’s construction and Duffing equation’s analytical solution and frequency response equation. The mechanisms of resonance, amplitude jump and hysteresis are also revealed. It provides a new research method for rotor vibration characteristics analysis.

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Bi-nonlinear vibration model of tubing string in oil & gas well and its experimental verification

Applied Mathematical Modelling ◽

10.1016/j.apm.2019.09.057 ◽

2020 ◽

Vol 81 ◽

pp. 50-69 ◽

Cited By ~ 5

Author(s):

Jun Liu ◽

Xiaoqiang Guo ◽

Guorong Wang ◽

Qingyou Liu ◽

Dake Fang ◽

...

Keyword(s):

Nonlinear Vibration ◽

Experimental Verification ◽

Gas Well ◽

Vibration Model ◽

Tubing String ◽

Oil Gas

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A NOVEL TECHNIQUE FOR NONLINEAR ANALYSIS OF BEAMS ON TWO-PARAMETER ELASTIC FOUNDATIONS

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455411004440 ◽

2011 ◽

Vol 11 (06) ◽

pp. 999-1014 ◽

Cited By ~ 45

Author(s):

HUI-SHEN SHEN

Keyword(s):

Nonlinear Vibration ◽

Perturbation Technique ◽

Nonlinear Behavior ◽

Exact Expression ◽

Initial Stresses ◽

Nonlinear Bending ◽

Elastic Foundations ◽

End Conditions ◽

Beam Foundation ◽

Two Parameter

Postbuckling, nonlinear bending, and nonlinear vibration analyses are presented for a simply supported Euler–Bernoulli beam resting on a two-parameter elastic foundation. The nonlinear model is introduced by using the exact expression of the curvature. Two kinds of end conditions, namely movable and immovable, are considered. The nonlinear equation of motion, including beam–foundation interaction, is derived separately for these two kinds of end conditions. The analysis uses a two-step perturbation technique to determine the postbuckling equilibrium paths of an axially loaded beam, the static large deflections of a bending beam subjected to a uniform transverse pressure, and the nonlinear frequencies of a beam with or without initial stresses. The numerical results confirm that the foundation stiffness has a significant effect on the nonlinear behavior of Euler–Bernoulli beams. The results also reveal that the end condition has a great effect on the nonlinear bending and nonlinear vibration behaviors of Euler–Bernoulli beams with or without elastic foundations.

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Three-Dimensional Nonlinear Vibration Model and Fatigue Failure Mechanism of Deep-Water Test Pipe

10.21203/rs.3.rs-866437/v1 ◽

2021 ◽

Author(s):

Xiaoqiang Guo ◽

Yuxin Nie ◽

Jun Liu ◽

Yufa He ◽

Liangjie Mao ◽

...

Keyword(s):

Fatigue Life ◽

Flow Velocity ◽

Nonlinear Vibration ◽

Fatigue Failure ◽

Deep Water ◽

Three Dimensional ◽

Internal Flow ◽

Outflow Velocity ◽

Vibration Model ◽

Water Test

Abstract In deep-water test conditions, the riser-test pipe system (RTS) is subject to the vortex induced effect on riser, flow induced effect on test pipe and longitudinal/transverse coupling effect, which is prone to buckling deformation, fatigue fracture and friction perforation. To resolve this, the three-dimensional (3D) nonlinear vibration model of deep-water RTS is established using the micro-finite method, energy method and Hamilton variational principle. Based on the elastic-plastic contact collision theory, the nonlinear contact load calculation method between riser and test pipe is proposed. Compared with experimental measurement results, calculation results of the proposed vibration model in this study and the single tubing vibration model in our recent work, the correctness and effectiveness of the proposed vibration model of the deep-water RTS are verified. Meanwhile, the cumulative damage theory is used to establish the fatigue life prediction method of test pipe. Based on that, the influences of outflow velocity, internal flow velocity, significant wave height, as well as top tension coefficient on the fatigue life of test pipe are systematically analyzed. The results demonstrate that, first, with the increase of outflow velocity, the maximum alternating stress, the annual fatigue damage rate increased and the service life decreased significantly. The locations where fatigue failure of the test tube is easy to occur are mainly distributed at the upper “one third” and the bottom of test pipe. Second, with the increase of internal flow velocity, the “one third effect” of the test pipe will decrease, and is shown “the bottom damage effect”, which needs the attention of field operators. Third, during field operation, it is necessary to properly configure the top tension coefficient so that there can be a certain relaxation between the riser and the test pipe, so as to cause transverse vibration and consume some axial energy and load. The study led to the formulation of a theoretical method for safety evaluation and a practical approach for effectively improving the fatigue life of deep-water test pipe.

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Effect of rolling bearing parameters on the nonlinear dynamics of offset rotor

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220912274 ◽

2020 ◽

Vol 234 (15) ◽

pp. 2968-2978

Author(s):

Mingxuan Liang ◽

Tianhong Yan ◽

Jianhong Hu ◽

Zhongli Chen

Keyword(s):

Nonlinear Vibration ◽

High Speed ◽

Rolling Bearing ◽

Dynamic Responses ◽

Rolling Bearings ◽

Nonlinear Parameters ◽

Rotating Speed ◽

Effect Mechanism ◽

Vibration Model ◽

Experimental Rig

Nonlinear vibration of rotating machinery induced by rolling bearings has gradually become a research issue. In many cases, the rotor discs are not always installed in middle of shaft in actual rotor system, and the influence of disc offset on nonlinear vibration needs to be studied in depth as rotating speed increases. This study deals with the effect mechanism of rotor offset on nonlinear dynamic responses. Nonlinear vibration model of offset rotor is established based on finite element method, and the disc offset position along rotor shaft is concerned. The responses are calculated by Newmark-β integration method, which are also validated by an experimental rig, and the influences of nonlinear parameters of rolling bearings are investigated. The results indicate that disc offset is a crucial factor that can induce more complex nonlinearity coupled with rolling bearing under high-speed conditions.

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