scholarly journals Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yaobing Zhao ◽  
Ceshi Sun ◽  
Zhiqian Wang ◽  
Lianhua Wang
Keyword(s):  
Free Vibration ◽  
Analytical Methods ◽  
Initial Conditions ◽  
Detailed Comparison ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Series Solutions ◽  
Nonlinear Free Vibration ◽  
Suspended Cables ◽  
Analytical Approaches

This paper presents approximate series solutions for nonlinear free vibration of suspended cables via the Lindstedt-Poincare method and homotopy analysis method, respectively. Firstly, taking into account the geometric nonlinearity of the suspended cable as well as the quasi-static assumption, a mathematical model is presented. Secondly, two analytical methods are introduced to obtain the approximate series solutions in the case of nonlinear free vibration. Moreover, small and large sag-to-span ratios and initial conditions are chosen to study the nonlinear dynamic responses by these two analytical methods. The numerical results indicate that frequency amplitude relationships obtained with different analytical approaches exhibit some quantitative and qualitative differences in the cases of motions, mode shapes, and particular sag-to-span ratios. Finally, a detailed comparison of the differences in the displacement fields and cable axial total tensions is made.

scholarly journals Coupled Dynamic Analysis for the Riser-Conductor of Deepwater Surface BOP Drilling System

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Kanhua Su ◽  
Stephen Butt ◽  
Jianming Yang ◽  
Hongyuan Qiu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Cross Sections ◽  
Lateral Displacement ◽  
Bending Moment ◽  
Equation Of Motion ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Drilling System ◽  
Natural Frequency Analysis

Deepwater surface BOP (surface blowout prevention, SBOP) drilling differs from conventional riser drilling system. To analyze the dynamic response of this system, the riser-conductor was considered as a beam with varied cross-sections subjected to loads throughout its length; then an equation of motion and free vibration of the riser-conductor string for SBOP was developed. The finite difference method was used to solve the equation of motion in time domain and a semianalytical approach based on the concept of section division and continuation was proposed to analyze free vibration. Case simulation results show that the method established for SBOP system natural frequency analysis is reasonable. The mode shapes of the riser-conductor are different between coupled and decoupled methods. The soil types surrounding the conductor under mudline have tiny effect on the natural frequency. Given that some papers have discussed the response of the SBOP riser, this work focused on the comparison of the dynamic responses on the wellhead and conductor with variable conditions. The dynamic lateral displacement, the bending moment, and the parameters’ sensitivity of the wellhead and the conductor were analyzed.

scholarly journals Free Vibration Analysis of Cable Stayed-Bridge by Finite Element Method

2019 ◽  
Vol 12 (4) ◽  
pp. 67-72
Author(s):  
Haneen A. Mahmood ◽  
Zaid S. Hammoudi ◽  
Ali Laftah Abbas
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Cable Stayed Bridge

A delicate analysis of the natural frequencies and mode shapes of a cable stayed bridge is essential to the solution of its dynamic responses due to seismic, wind and traffic loads. In this paper, a bridge with geometry comparable to the Quincy Bayview Bridge was modelled in order to explore the significance of the three dimensional and free vibration analysis. This paper provides a detail of the bridge and the equivalent cross section of the three-dimensional finite element model implicating cables, the bridge deck and pylons as well as the boundary conditions and free vibration analysis by Ansys15.0. The bridge was analyzed to free vibration to obtaine the natural frequency and mode shape. result of this paper present the natural frequencies and mode shapes of the bridge. The method of modelling cables is also studied. It is found that modelling cables as multi beam elements provides better results than using the traditional (and simpler) method of modeling them as single tensile elements.

Nonlinear free vibration analysis of pre-stressed membranes

2016 ◽  
Vol 231 (2) ◽  
pp. 346-356
Author(s):  
Morteza Ahmadi ◽  
Gholamreza Hashemi ◽  
Milad Jamali ◽  
Morteza R Dehkordi ◽  
Seyed A Razavian
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Vibration Amplitude ◽  
Analytical Approach ◽  
Analytical Procedure ◽  
Initial Conditions ◽  
Free Vibration Analysis ◽  
Nonlinear Frequency ◽  
Nonlinear Free Vibration ◽  
Modern Analytical

This paper is dedicated to investigate the nonlinear free vibration analysis of prestressed orthotropic membranes. The fundamental frequency of the system is obtained asymptotically by employing a modern analytical approach. The effects of different parameters such as vibration amplitude, initial conditions and geometric parameters on the frequency ratio and nonlinear frequency of membrane are investigated. Comparison between the obtained results in the present study, the reported results in the literature, and Runge–Kutta fourth-order numerical method verify the strength of the analytical procedure.

Control of Vibrations due to Moving Loads on Suspension Bridges

2006 ◽  
Vol 11 (3) ◽  
pp. 293-318 ◽  
Author(s):  
M. Zribi ◽  
N. B. Almutairi ◽  
M. Abdel-Rohman
Keyword(s):  
Bridge Deck ◽  
Suspension Bridge ◽  
Lyapunov Theory ◽  
Dynamic Responses ◽  
Suspension Bridges ◽  
Control Force ◽  
Moving Loads ◽  
Hydraulic Actuator ◽  
Long Span ◽  
Suspended Cables

The flexibility and low damping of the long span suspended cables in suspension bridges makes them prone to vibrations due to wind and moving loads which affect the dynamic responses of the suspended cables and the bridge deck. This paper investigates the control of vibrations of a suspension bridge due to a vertical load moving on the bridge deck with a constant speed. A vertical cable between the bridge deck and the suspended cables is used to install a hydraulic actuator able to generate an active control force on the bridge deck. Two control schemes are proposed to generate the control force needed to reduce the vertical vibrations in the suspended cables and in the bridge deck. The proposed controllers, whose design is based on Lyapunov theory, guarantee the asymptotic stability of the system. The MATLAB software is used to simulate the performance of the controlled system. The simulation results indicate that the proposed controllers work well. In addition, the performance of the system with the proposed controllers is compared to the performance of the system controlled with a velocity feedback controller.

Effect of crack on free vibration of a pre-stressed curved plate

2021 ◽  
pp. 095440622199486
Author(s):  
Can Gonenli ◽  
Hasan Ozturk ◽  
Oguzhan Das
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Present Model ◽  
Mode Shapes ◽  
Load Parameter ◽  
Flexible Plate ◽  
Cantilever Plate ◽  
Finite Element Software ◽  
Aspect Ratios

In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

Dynamic Response of the Spectral Element Model by Using the FFT

2007 ◽  
Vol 345-346 ◽  
pp. 845-848
Author(s):  
Joo Yong Cho ◽  
Han Suk Go ◽  
Usik Lee
Keyword(s):  
Fourier Transforms ◽  
Initial Conditions ◽  
Element Model ◽  
Spectral Element ◽  
Dynamic Responses ◽  
Analysis Method ◽  
Euler Beam ◽  
Exact Analytical Solutions ◽  
Simply Supported ◽  
Spectral Analysis Method

In this paper, a fast Fourier transforms (FFT)-based spectral analysis method (SAM) is proposed for the dynamic analysis of spectral element models subjected to the non-zero initial conditions. To evaluate the proposed SAM, the spectral element model for the simply supported Bernoulli-Euler beam is considered as an example problem. The accuracy of the proposed SAM is evaluated by comparing the dynamic responses obtained by SAM with the exact analytical solutions.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

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