scholarly journals Vortex-Induced Vibration of a Cable-Stayed Bridge

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
M. T. Song ◽  
D. Q. Cao ◽  
W. D. Zhu
Keyword(s):  
Differential Equations ◽  
Dynamic Response ◽  
Galerkin Method ◽  
Vortex Shedding ◽  
Rectangular Cross Section ◽  
Mode Shapes ◽  
Vortex Induced Vibration ◽  
Cable Stayed Bridge ◽  
Geometric Nonlinear ◽  
Bridge Model

The dynamic response of a cable-stayed bridge that consists of a simply supported four-cable-stayed deck beam and two rigid towers, subjected to a distributed vortex shedding force on the deck beam with a uniform rectangular cross section, is studied in this work. The cable-stayed bridge is modeled as a continuous system, and the distributed vortex shedding force on the deck beam is modeled using Ehsan-Scanlan’s model. Orthogonality conditions of exact mode shapes of the linearized undamped cable-stayed bridge model are employed to convert coupled governing partial differential equations of the original cable-stayed bridge model with damping to a set of ordinary differential equations by using Galerkin method. The dynamic response of the cable-stayed bridge is calculated using Runge-Kutta-Felhberg method in MATLAB for two cases with and without geometric nonlinear terms. Convergence of the dynamic response from Galerkin method is investigated. Numerical results show that the geometric nonlinearities of stay cables have significant influence on vortex-induced vibration of the cable-stayed bridge. There are different limit cycles in the case of neglecting the geometric nonlinear terms, and there are only one limit cycle and chaotic responses in the case of considering the geometric nonlinear terms.

scholarly journals Dynamic analysis of a cable-stayed bridge subjected to a continuous sequence of moving forces

2016 ◽  
Vol 8 (12) ◽  
pp. 168781401668172
Author(s):  
Mitao Song ◽  
Dengqing Cao ◽  
Weidong Zhu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Response ◽  
Galerkin Method ◽  
Mode Shapes ◽  
Partial Differential ◽  
Cable Stayed Bridge ◽  
Stay Cables ◽  
Continuous Sequence ◽  
The Galerkin Method

In this work, an eigenfunction expansion approach is used to study the dynamic response of a cable-stayed bridge excited by a continuous sequence of identical, equally spaced moving forces. The nonlinear dynamic response of the cable-stayed bridge is obtained by simultaneously solving nonlinear and linear partial differential equations that govern transverse and longitudinal vibrations of stay cables and transverse vibrations of segments of the deck beam, respectively, along with their boundary and matching conditions. Orthogonality conditions of exact mode shapes of the linearized cable-stayed bridge model are employed to convert the coupled nonlinear partial differential equations of the original nonlinear model to a set of ordinary differential equations by using the Galerkin method. The dynamic response of the cable-stayed bridge is numerically solved. Convergence of the dynamic response from the Galerkin method is investigated. Effects of close natural frequencies, mode localization, the distance between any two neighboring forces, and geometric nonlinearities of stay cables on the forced dynamic response of the cable-stayed bridge are captured using a convergent modal truncation.

Experimental Analysis of Vortex Induced Vibration in the Bladeless Small Wind Turbine

2019 ◽  
Author(s):  
Micha Premkumar Thomai ◽  
Lasoodawanki Kharsati ◽  
Nakandhrakumar Rama Samy ◽  
Seralathan Sivamani ◽  
Hariram Venkatesan
Keyword(s):  
Energy Conversion ◽  
Wind Turbine ◽  
Natural Frequency ◽  
Cross Section ◽  
Vortex Shedding ◽  
Rectangular Cross Section ◽  
The Body ◽  
Test Facility ◽  
Vortex Induced Vibration ◽  
Small Wind Turbine

Abstract Vortex-induced vibration is one of the predominant fundamental concepts for forced oscillation which attracts considerable practical engineering application for energy conversion. In this work, an oscillation of a mast arising as a result of wind force is utilized for energy conversion. The paradigm for energy conversion from vortex-induced vibration in the mast is the bladeless wind turbine. It consists of a rigid mass known as a mast, fixed in the spring of stiffness (k) and allowed to oscillate along the direction of the flow. In this work, four different types of mast have been fabricated and tested. The first is uniform tapered hollow conical mast (MAST1), the cross-section of the second is uniform tapered plus symbol (MAST2), the third is uniform tapered inversed plus symbol (MAST3) and the fourth is uniform tapered simple rectangular cross-section (MAST4). All the masts were fabricated using fiber carbon. The experiments were conducted in a versatile small wind turbine testing facility of Hindustan Institute of Technology and Science, Chennai. This test facility contained an open jet wind tunnel with variable frequency drive and other measuring instruments. The vibration sensor was located in the mast where it experienced a large oscillation in a free stream. In this experiment, an increase in wind velocity led to a terrible change in the amplitude of vibration. A vigorous oscillation was experienced in this mast at this critical frequency, when the natural frequency of the mast was synchronized with the frequency of the vortex shedding and the frequency of the oscillation of the mast. The total force in this oscillation was a summation of the body force due to the mass of the mast and vorticity force that is mainly which was the result of the shedding of the vortices. In this work, extensive studies have been carried out for Reynolds number ranging from 2.5 × 105 to 5.0 × 105. The mast length to diameter ratio of 13 was exposed to various speeds of wind and response was measured. The occurrence of the maximum oscillation in a simple rectangular mast was seen where vortex shedding due to the bluff body was large for constant mass and spring stiffness. The frequency of the oscillation at maximum amplitude of the rectangular cross-section mast was equal to the natural frequency, due to vortices shedding at critical velocity. This demonstrated the appropriateness of the simple rectangular cross-section for harnessing the low rated wind energy and its suitability for renewable energy conversion in the small bladeless wind turbine.

scholarly journals On Solving One-Dimensional Partial Differential Equations With Spatially Dependent Variables Using the Wavelet-Galerkin Method

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Simon Jones ◽  
Mathias Legrand
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Frequency Response ◽  
Natural Frequencies ◽  
Basis Functions ◽  
Mode Shapes ◽  
Response Functions ◽  
Partial Differential ◽  
Frequency Response Functions

The discrete orthogonal wavelet-Galerkin method is illustrated as an effective method for solving partial differential equations (PDE's) with spatially varying parameters on a bounded interval. Daubechies scaling functions provide a concise but adaptable set of basis functions and allow for implementation of varied loading and boundary conditions. These basis functions can also effectively describe C0 continuous parameter spatial dependence on bounded domains. Doing so allows the PDE to be discretized as a set of linear equations composed of known inner products which can be stored for efficient parametric analyses. Solution schemes for both free and forced PDE's are developed; natural frequencies, mode shapes, and frequency response functions for an Euler–Bernoulli beam with piecewise varying thickness are calculated. The wavelet-Galerkin approach is shown to converge to the first four natural frequencies at a rate greater than that of the linear finite element approach; mode shapes and frequency response functions converge similarly.

Dynamic Response of a Fluid-Conveying Riser Subject to Vortex-Induced Vibration: Integral Transform Solution

2014 ◽  
Author(s):  
Jijun Gu ◽  
Zhenhua Song ◽  
Kang Zhang ◽  
Liguo Su ◽  
Menglan Duan
Keyword(s):  
Differential Equations ◽  
Dynamic Response ◽  
Integral Transform ◽  
Fluid Velocity ◽  
Critical Evaluation ◽  
Cross Flow ◽  
Coupled System ◽  
Vortex Induced Vibration ◽  
Wake Oscillator ◽  
Line Force

Analysis of dynamic response of a fluid-conveying riser is an important aspect in subsea production system. In the present paper, dynamic response of a pinned-pinned riser subject to external fluid force was solved by the generalized integral transform technique (GITT). A nonlinear wake oscillator models was used to represent the cross-flow and in-line force acting on the riser, leading to a coupled system of second-order Partial Differential Equations (PDEs). The GITT approach was used to transform the system of PDEs to a system of Ordinary Differential Equations (ODEs), which was numerically solved by using the Adams-Moulton and Gear method (DIVPAG) developed by the International Mathematics and Statistics Library (IMSL). Numerical results were presented for comparison to those given by the numerical and experimental results, allowing a critical evaluation of the technique performance. The influence of conveying fluid velocity and mean top tension were evaluated to show that they should not be negligible in numerical simulation of Vortex-Induced Vibration of a long flexible riser.

Dynamic Analysis of a Micro-Resonator Driven by Electrostatic Combs

2011 ◽  
Author(s):  
M. T. Song ◽  
D. Q. Cao ◽  
W. D. Zhu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Response ◽  
Natural Frequencies ◽  
Nonlinear Partial Differential Equations ◽  
Rigid Bodies ◽  
Mode Shapes ◽  
Flexible Beams ◽  
Global Mode ◽  
Micro Resonator

The dynamic response of a micro-resonator driven by electrostatic combs is investigated in this work. The micro-resonator is assumed to consist of eight flexible beams and three rigid bodies. The nonlinear partial differential equations that govern the motions of the flexible beams are obtained, as well as their boundary and matching conditions. The natural matching conditions for the flexible beams are the governing equations for the rigid bodies. The undamped natural frequencies and mode shapes of the linearized model of the micro-resonator are determined, and the orthogonality relation of the undamped global mode shapes is established. The modified Newton iterative method is used to simultaneously solve for the frequency equation and identify repeated natural frequencies that can occur in the micro-resonator and their multiplicities. The Gram-Schmidt orthogonalization method is extended to orthogonalize the mode shapes of the continuous system corresponding to the repeated natural frequencies. The undamped global mode shapes are used to spatially discretize the nonlinear partial differential equations of the microresonator. The simulation results show that the geometric nonlinearities of the flexible beams can have a significant effect on the dynamic response of the micro-resonator.

Parametric Study of the Dynamic Response a Cable-Stayed Bridge

2001 ◽  
Vol 84 (7) ◽  
pp. 99-106
Author(s):  
Sven Mayer ◽  
Steven L. McCabe
Keyword(s):  
Dynamic Response ◽  
Parametric Study ◽  
Cable Stayed Bridge

Dynamic response of cable-stayed bridge under blast load

2016 ◽  
Vol 127 ◽  
pp. 719-736 ◽  
Author(s):  
S.K. Hashemi ◽  
M.A. Bradford ◽  
H.R. Valipour
Keyword(s):  
Dynamic Response ◽  
Blast Load ◽  
Cable Stayed Bridge

Experimental Study on the Continuous Type Three-Dimensional Control of the Cable-Stayed Bridge

2011 ◽  
Vol 71-78 ◽  
pp. 1933-1937
Author(s):  
Jia Yun Xu ◽  
Ji Chen ◽  
Xian Wei Qu ◽  
Wen Kai Gong
Keyword(s):  
Angular Displacement ◽  
Three Dimensional ◽  
Wind Tunnel Test ◽  
Highway Bridge ◽  
Changjiang River ◽  
Continuous Type ◽  
Torsional Response ◽  
Cable Stayed Bridge ◽  
Bridge Model ◽  
Wind Induced Vibration

This paper takes a Chinese Changjiang River highway bridge as engineering background, and a kind of continuous three-dimensional (vertical, lateral and torsion)controllers which can apply in the large span cable-stayed bridge is presented. The controllers can control vertical, lateral and torsional response of bridge wind-induced vibration at the same time. Through comparative wind tunnel test of the bridge model with and without controllers, some important conclusions are made as follows: when the continuous three-dimensional controllers are installed on the bridge model, its flutter critical wind speed increases significantly (mostly increases 33.36%); Meanwhile, there is a certain degree of reduction in its RMS values of vertical, lateral and torsional angular displacement response.

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