A Theoretical Analysis of Dynamic Elastic Response of a Circular Ring to Water Waves

2007 ◽  
Vol 129 (3) ◽  
pp. 211-218 ◽  
Author(s):  
G. H. Dong ◽  
S. H. Hao ◽  
Z. Zong ◽  
Y. N. Zheng
Keyword(s):  
Elastic Deformation ◽  
Water Waves ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Fish Farming ◽  
Circular Ring ◽  
Open Ocean ◽  
Elastic Response ◽  
Superposition Method ◽  
Dominant Form

Fish farming in the open ocean is becoming a dominant form of fishery aquaculture due to the dramatic drop of fishery resources in near shore. Deep water anti-stormy fish cages are the most important tool for fish farming in the open ocean. The floatation ring, as a pivotal component of the fish cage, undergoes large deformations and it has been found that the floatation ring oscillates when moving in water waves. In the most serious cases, its deformation is so large it can be damaged. The floatation ring is simplified as a free circular ring, and the governing equations of motion and deformation of the ring can be built up according to the force equilibrium and curved beam theory. The numerical calculation is carried out in terms of the modal superposition method. The motion and the deformation of the ring are analyzed, and two corresponding equations in which the elastic deformations are neglected and considered are given, respectively. By comparing the results of the above two equations, we get the resonant frequencies and the frequency scope influenced by the elastic deformation. It is concluded that the influence of the deformation of the ring is very important for the oscillation of the ring, particularly the former three modes of the elastic deformation which cannot be neglected.

In-Plane Free Vibration of Curved Beams Using Finite Element Method

2007 ◽  
Author(s):  
F. Yang ◽  
R. Sedaghati ◽  
E. Esmailzadeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Central Line ◽  
Circular Ring ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Element Method

Curved beam-type structures have many applications in engineering area. Due to the initial curvature of the central line, it is complicated to develop and solve the equations of motion by taking into account the extensibility of the curve axis and the influences of the shear deformation and the rotary inertia. In this study the finite element method is utilized to study the curved beam with arbitrary geometry. The curved beam is modeled using the Timoshenko beam theory and the circular ring model. The governing equation of motion is derived using the Extended-Hamilton principle and numerically solved by the finite element method. A parametric sensitive study for the natural frequencies has been performed and compared with those reported in the literature in order to demonstrate the accuracy of the analysis.

Numerical Analysis of the Flotation Ring of a Gravity-Type Fish Cage

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Guo-hai Dong ◽  
Shuang-hu Hao ◽  
Yun-peng Zhao ◽  
Zhi Zong ◽  
Fu-kun Gui
Keyword(s):  
Water Waves ◽  
Plane Deformation ◽  
Beam Theory ◽  
Superposition Method ◽  
Motion Equations ◽  
Modal Superposition Method ◽  
Waves Propagation ◽  
Elastic Responses ◽  
Increasing Demand ◽  
The Waves

The gravity-type fish cage is extensively applied with the increasing demand for fishery products. The flotation ring is its main load-bearing component and supports the whole cage. So it is essential to study the hydroelasticity of the flotation ring for the safety of a fish cage. An analytical method is proposed to study the elastic deformation of a simplified flotation ring subjected to water waves. The equations governing in-plane deformations are obtained according to curved beam theory, in which the modal superposition method is used to represent the in-plane deformation of an element of the ring. Then, the motion equations of the ring are built up coupled with deformation equations. The correlation between the predicted results and the experimental data is acceptable to validate the numerical modeling. Then the effect of Young’s module, radius of the ring, and wave conditions on elastic responses is discussed in terms of the prototype scale of a flotation ring. It is concluded that the deformations over the ring in the direction of waves’ propagation are the largest, and that the mooring point in the head-on direction of the waves is critical for reliability of the ring. Large deformations of the flotation ring may induce the failure of the fish cage when the storm covers it. So more attention to the hydroelasticity of the flotation ring should be paid in the design for a fish cage.

Solution of Impact-Induced Flexural Waves in a Circular Ring by the Method of Characteristics

1998 ◽  
Vol 65 (3) ◽  
pp. 569-579 ◽  
Author(s):  
V. P. W. Shim ◽  
S. E. Quah
Keyword(s):  
Numerical Scheme ◽  
Method Of Characteristics ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Circular Ring ◽  
Higher Order ◽  
Flexural Waves ◽  
The Method Of Characteristics ◽  
Finite Difference Equations ◽  
Generalized Displacements

A study of elastic wave propagation in a curved beam (circular ring) is presented. The governing equations of motion are formulated in two forms based on Timoshenko beam theory. Solutions are obtained using the method of characteristics, whereby a numerical scheme employing higher-order interpolation is proposed for the finite difference equations. Results obtained are verified by experiments; it is found that use of the higher-order numerical scheme improves correlation with experimental results. Comparison of the relative accuracy between the two mathematical formulations—one in terms of generalized forces and velocities and the other in terms of generalized displacements—shows the former to be mathematically simpler and to yield more accurate results.

scholarly journals Shallow water waves in a rotating rectangular basin

2000 ◽  
Vol 24 (10) ◽  
pp. 649-661 ◽  
Author(s):  
Mohamed Atef Helal
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Equations Of Motion ◽  
System Of Nonlinear Equations ◽  
System Of Equations ◽  
Order Of Approximation ◽  
Shallow Water Waves ◽  
Nonlinear System Of Equations ◽  
Rectangular Basin ◽  
Shallow Water Approximation

This paper is mainly concerned with the motion of an incompressible fluid in a slowly rotating rectangular basin. The equations of motion of such a problem with its boundary conditions are reduced to a system of nonlinear equations, which is to be solved by applying the shallow water approximation theory. Each unknown of the problem is expanded asymptotically in terms of the small parameterϵwhich generally depends on some intrinsic quantities of the problem of study. For each order of approximation, the nonlinear system of equations is presented successively. It is worthy to note that such a study has useful applications in the oceanography.

Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

2012 ◽  
Vol 28 (3) ◽  
pp. 513-522 ◽  
Author(s):  
H. M. Khanlo ◽  
M. Ghayour ◽  
S. Ziaei-Rad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Behavior ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Disk System ◽  
Partial Differential ◽  
Rayleigh Beam ◽  
Flexible Shaft

AbstractThis study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

In-plane hydroelastic response of a circular ring in water waves

2008 ◽  
Vol 30 (3) ◽  
pp. 208-214 ◽  
Author(s):  
Z. Zong ◽  
S.H. Hao ◽  
Y.P. Zhao ◽  
G.H. Dong ◽  
F.K. Gui
Keyword(s):  
Water Waves ◽  
Circular Ring ◽  
Hydroelastic Response

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

Experimental Study on a 3-Dimensional Hydro-Elastic Deformation of “Underwater Platform” With Multi-Towers in Waves

2016 ◽  
Author(s):  
Ken Haneda ◽  
Motohiko Murai ◽  
Jun Yamanoi
Keyword(s):  
Elastic Deformation ◽  
Body Motion ◽  
Offshore Wind ◽  
Elastic Response ◽  
Experimental Result ◽  
Elastic Model ◽  
Mooring Lines ◽  
3 Dimensional ◽  
Floating Offshore Wind Turbines ◽  
Head Waves

Underwater platform was proposed in OMAE 2015 for the purpose of enhancing productivity of various types of renewable energy converter on the sea and its feasibility study was carried out through 2 types of tank experiment [1]. The underwater platform which is a very large frame shape structure connects several floaters under the sea to share power cables and mooring lines and to keep relative distances between the floaters. In the experiment, 1/200 scale elastic model with three spar buoys was used. The buoys imitated spar type floating offshore wind turbines (FOWTs). From the experiment, it was shown that the platform with large draft can reduce its response in waves. In this paper, we report new result and knowledge obtained by additional model experiments use the 1/200 model. In the experiment, we changed the arrangement and draft of the model and measured hydro-elastic deformation of the underwater platform in waves. From the last experiment, relationship between draft settings and response was shown. In the experiment, relationship between wave angles and response was surveyed. From the experiment, we have confirmed followings: 1. Rigid-body motion is remarkable in beam waves, 2. Elastic response is remarkable in head waves, and 3. Remarkable torsional motion is occurred in 45 degrees’ waves. The more important thing, however, is that the experimental result indicated that the platform of large draft decreases its motion in the all the wave angles.

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

Seismic Analysis of Structures With Coulomb Friction

1983 ◽  
Vol 105 (2) ◽  
pp. 171-178 ◽  
Author(s):  
V. N. Shah ◽  
C. B. Gilmore
Keyword(s):  
Rigid Body ◽  
Coulomb Friction ◽  
Seismic Event ◽  
Seismic Analysis ◽  
Equations Of Motion ◽  
Relative Displacement ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Superposition Method ◽  
Modal Superposition Method

A modal superposition method for the dynamic analysis of a structure with Coulomb friction is presented. The finite element method is used to derive the equations of motion, and the nonlinearities due to friction are represented by pseudo-force vector. A structure standing freely on the ground may slide during a seismic event. The relative displacement response may be divided into two parts: elastic deformation and rigid body motion. The presence of rigid body motion necessitates the inclusion of the higher modes in the transient analysis. Three single degree-of-freedom problems are solved to verify this method. In a fourth problem, the dynamic response of a platform standing freely on the ground is analyzed during a seismic event.

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