A Dynamic Model of the Deformation of a Diamond Mesh Cod-End of a Trawl Net

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
F. G. O’Neill ◽  
R. D. Neilson
Keyword(s):  
Dynamic Model ◽  
Harmonic Balance ◽  
Second Harmonic ◽  
Closed Form Solution ◽  
Harmonic Balance Method ◽  
Form Solution ◽  
Body Motion ◽  
Harmonic Series ◽  
Pressure Loading ◽  
Dependent Variables

A dynamic model of a diamond mesh cod-end subject to harmonic forcing is developed. The partial differential equations governing the displacements of the cod-end and the tension in the twine are first derived and then analyzed using the harmonic balance method by substituting a harmonic series for the dependent variables and the forcing term. A closed-form solution is derived for the case of rigid-body motion, where there is no deformation of the cod-end geometry, along with the conditions for the forcing under which this motion occurs. A pressure loading, which varies linearly over a portion of the cod-end and varies harmonically with time, is then introduced as a first representation of the loading on the cod-end that results from the pressure and acceleration forces on the catch due to surge motion of the towing vessel. The resulting sets of equations for the static and the first and second harmonic terms are solved numerically in a sequential manner, and the results presented for a number of cases. These results show that, due to the nonlinearity of the system, the oscillatory motion of the cod-end is asymmetric, and that the deformation of the net and the amplitude of oscillation increases as the region over which the forcing is applied increases. The model is the basis for a more complete coupled catch/cod-end model.

Toward a Minimal Dynamic Model of a 6-DOF Parallel Robot

1997 ◽  
Author(s):  
L. Beji ◽  
M. Pascal ◽  
P. Joli
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Parallel Robot ◽  
Form Solution ◽  
Lagrangian Formalism ◽  
Inverse Kinematic Problem ◽  
Geometrical Properties

Abstract In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.

Analysis of the Periodic Damping Coefficient Equation Based on Floquet Theory

2017 ◽  
Author(s):  
Fatemeh Afzali ◽  
Gizem D. Acar ◽  
Brian F. Feeny
Keyword(s):  
Approximate Solution ◽  
Harmonic Balance ◽  
Floquet Theory ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Damping Coefficient ◽  
Harmonic Series ◽  
Periodic Part ◽  
Damped System ◽  
Linear Differential

In this paper, we study the response of a linear differential equation, for which the damping coefficient varies periodically in time. We use Floquet theory combined with the harmonic balance method to find the approximate solution and capture the stability criteria. Based on Floquet theory the approximate solution includes the exponential part having an unknown exponent, and a periodic part, which is expressed using a truncated series of harmonics. After substituting the assumed response in the equation, the harmonic balance method is applied. We use the characteristic equation of the truncated harmonic series to obtain the Floquet exponents. The free response and stability characteristics of the damped system for a set of parameters are shown.

Large Deflection Behavior of Composite Laminated Plates under End-Shortening and Normal Pressure Loading Using a Semi-Energy Finite Strip Method

2011 ◽  
Vol 471-472 ◽  
pp. 432-437
Author(s):  
Hamid Reza Ovesy ◽  
Mohammad Homayoun Sadr-Lahidjani ◽  
Mohammad Hajikazemi ◽  
Hassan Assaee
Keyword(s):  
Large Deflection ◽  
Closed Form Solution ◽  
Normal Pressure ◽  
Form Solution ◽  
Laminated Plates ◽  
Pressure Loading ◽  
Finite Strip ◽  
Composite Laminated Plates ◽  
Strip Method ◽  
Finite Strip Method

In this paper, the application of previously the semi energy finite strip method (FSM) for the non-linear post-buckling analysis of rectangular anti-symmetric laminates is extended to include the effects of normal pressure loading in addition to the progressive end-shortening. One of the main advantages of the semi-energy FSM is that it is based on the closed form solution of von Kármán’s compatibility equation. The developed finite strip method is applied to analyze the large deflection behavior of anti-symmetric angle ply composite laminated plates with simply supported boundary conditions at its loaded ends. To validate the results, they are compared with those obtained from finite element method (FEM) of analysis.

scholarly journals A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1017
Author(s):  
Dong Mei ◽  
Jun-Yi Sun ◽  
Zhi-Hang Zhao ◽  
Xiao-Ting He
Keyword(s):  
Boundary Value Problem ◽  
Closed Form ◽  
Boundary Value ◽  
Closed Form Solution ◽  
Form Solution ◽  
Gas Pressure ◽  
Circular Membrane ◽  
Rigid Plate ◽  
Pressure Loading ◽  
Numerical Example

In this paper, the static problem of equilibrium of contact between an axisymmetric deflected circular membrane and a frictionless rigid plate was analytically solved, where an initially flat circular membrane is fixed on its periphery and pressurized on one side by gas such that it comes into contact with a frictionless rigid plate, resulting in a restriction on the maximum deflection of the deflected circular membrane. The power series method was employed to solve the boundary value problem of the resulting nonlinear differential equation, and a closed-form solution of the problem addressed here was presented. The difference between the axisymmetric deformation caused by gas pressure loading and that caused by gravity loading was investigated. In order to compare the presented solution applying to gas pressure loading with the existing solution applying to gravity loading, a numerical example was conducted. The result of the conducted numerical example shows that the two solutions agree basically closely for membranes lightly loaded and diverge as the external loads intensify.

scholarly journals A Closed-Form Solution without Small-Rotation-Angle Assumption for Circular Membranes under Gas Pressure Loading

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2269
Author(s):  
Xiao-Ting He ◽  
Xue Li ◽  
Bin-Bin Shi ◽  
Jun-Yi Sun
Keyword(s):  
Closed Form ◽  
Rotation Angle ◽  
Closed Form Solution ◽  
Form Solution ◽  
Gas Pressure ◽  
Pressure Loading ◽  
Large Rotation ◽  
Closed Form Solutions ◽  
Film Substrate ◽  
Small Rotation

The closed-form solution of circular membranes subjected to gas pressure loading plays an extremely important role in technical applications such as characterization of mechanical properties for freestanding thin films or thin-film/substrate systems based on pressured bulge or blister tests. However, the only two relevant closed-form solutions available in the literature are suitable only for the case where the rotation angle of membrane is relatively small, because they are derived with the small-rotation-angle assumption of membrane, that is, the rotation angle θ of membrane is assumed to be small so that “sinθ = 1/(1 + 1/tan2θ)1/2” can be approximated by “sinθ = tanθ”. Therefore, the two closed-form solutions with small-rotation-angle assumption cannot meet the requirements of these technical applications. Such a bottleneck to these technical applications is solved in this study, and a new and more refined closed-form solution without small-rotation-angle assumption is given in power series form, which is derived with “sinθ = 1/(1 + 1/tan2θ)1/2”, rather than “sinθ = tanθ”, thus being suitable for the case where the rotation angle of membrane is relatively large. This closed-form solution without small-rotation-angle assumption can naturally satisfy the remaining unused boundary condition, and numerically shows satisfactory convergence, agrees well with the closed-form solution with small-rotation-angle assumption for lightly loaded membranes with small rotation angles, and diverges distinctly for heavily loaded membranes with large rotation angles. The confirmatory experiment conducted shows that the closed-form solution without small-rotation-angle assumption is reliable and has a satisfactory calculation accuracy in comparison with the closed-form solution with small-rotation-angle assumption, particularly for heavily loaded membranes with large rotation angles.

scholarly journals Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1238
Author(s):  
Bin-Bin Shi ◽  
Jun-Yi Sun ◽  
Ting-Kai Huang ◽  
Xiao-Ting He
Keyword(s):  
Closed Form ◽  
Plane Stress ◽  
Large Deflection ◽  
Closed Form Solution ◽  
Form Solution ◽  
Gas Pressure ◽  
Circular Membrane ◽  
Pressure Loading ◽  
Out Of Plane ◽  
Large Deflection Problem

The large deflection phenomenon of an initially flat circular membrane under out-of-plane gas pressure loading is usually involved in many technical applications, such as the pressure blister or bulge tests, where a uniform in-plane stress is often present in the initially flat circular membrane before deflection. However, there is still a lack of an effective closed-form solution for the large deflection problem with initial uniform in-plane stress. In this study, the problem is formulated and is solved analytically. The initial uniform in-plane stress is first modelled by stretching or compressing an initially flat, stress-free circular membrane radially in the plane in which the initially flat circular membrane is located, and based on this, the boundary conditions, under which the large deflection problem of an initially flat circular membrane under in-plane radial stretching or compressing and out-of-plane gas pressure loading can be solved, are determined. Therefore, the closed-form solution presented in this paper can be applied to the case where the initially flat circular membrane may, or may not, have a uniform in-plane stress before deflection, and the in-plane stress can be either tensile or compressive. The numerical example conducted shows that the closed-form solution presented has satisfactory convergence.

scholarly journals A WEIGHTED CLOSED-FORM SOLUTION FOR RGB-D DATA REGISTRATION

2016 ◽  
Vol XLI-B3 ◽  
pp. 403-409 ◽  
Author(s):  
K. M. Vestena ◽  
D. R. Dos Santos ◽  
E. M. Oilveira Jr. ◽  
N. L. Pavan ◽  
K. Khoshelham
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Form Solution ◽  
Body Motion ◽  
Random Errors ◽  
Scale Invariant ◽  
Loop Closure ◽  
Dual Number ◽  
Data Registration

Existing 3D indoor mapping of RGB-D data are prominently point-based and feature-based methods. In most cases iterative closest point (ICP) and its variants are generally used for pairwise registration process. Considering that the ICP algorithm requires an relatively accurate initial transformation and high overlap a weighted closed-form solution for RGB-D data registration is proposed. In this solution, we weighted and normalized the 3D points based on the theoretical random errors and the dual-number quaternions are used to represent the 3D rigid body motion. Basically, dual-number quaternions provide a closed-form solution by minimizing a cost function. The most important advantage of the closed-form solution is that it provides the optimal transformation in one-step, it does not need to calculate good initial estimates and expressively decreases the demand for computer resources in contrast to the iterative method. Basically, first our method exploits RGB information. We employed a scale invariant feature transformation (SIFT) for extracting, detecting, and matching features. It is able to detect and describe local features that are invariant to scaling and rotation. To detect and filter outliers, we used random sample consensus (RANSAC) algorithm, jointly with an statistical dispersion called interquartile range (IQR). After, a new RGB-D loop-closure solution is implemented based on the volumetric information between pair of point clouds and the dispersion of the random errors. The loop-closure consists to recognize when the sensor revisits some region. Finally, a globally consistent map is created to minimize the registration errors via a graph-based optimization. The effectiveness of the proposed method is demonstrated with a Kinect dataset. The experimental results show that the proposed method can properly map the indoor environment with an absolute accuracy around 1.5% of the travel of a trajectory.

Aerodynamics of Airfoils with Porous Trailing Edges

1979 ◽  
Vol 30 (2) ◽  
pp. 387-399 ◽  
Author(s):  
C. Samuel Ventres ◽  
Richard Barakat
Keyword(s):  
Supersonic Flow ◽  
Complex Variable ◽  
Closed Form Solution ◽  
Form Solution ◽  
Pressure Loading ◽  
Trailing Edge ◽  
Variable Theory ◽  
Complex Variable Theory ◽  
Trailing Edges ◽  
Special Case

SummaryThe aerodynamics of a thin airfoil of arbitrary camber having a porous trailing edge in steady, subsonic, compressible potential flow is investigated. In the special case of a flat plate airfoil with a porous trailing edge, an exact, closed form solution is obtained using complex variable theory. The pressure loading on the airfoil, the lift and pitching moments are exhibited explicitly along with typical numerical results. The corresponding situation in supersonic flow is also considered.

scholarly journals A WEIGHTED CLOSED-FORM SOLUTION FOR RGB-D DATA REGISTRATION

2016 ◽  
Vol XLI-B3 ◽  
pp. 403-409
Author(s):  
K. M. Vestena ◽  
D. R. Dos Santos ◽  
E. M. Oilveira Jr. ◽  
N. L. Pavan ◽  
K. Khoshelham
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Form Solution ◽  
Body Motion ◽  
Random Errors ◽  
Scale Invariant ◽  
Loop Closure ◽  
Dual Number ◽  
Data Registration

Existing 3D indoor mapping of RGB-D data are prominently point-based and feature-based methods. In most cases iterative closest point (ICP) and its variants are generally used for pairwise registration process. Considering that the ICP algorithm requires an relatively accurate initial transformation and high overlap a weighted closed-form solution for RGB-D data registration is proposed. In this solution, we weighted and normalized the 3D points based on the theoretical random errors and the dual-number quaternions are used to represent the 3D rigid body motion. Basically, dual-number quaternions provide a closed-form solution by minimizing a cost function. The most important advantage of the closed-form solution is that it provides the optimal transformation in one-step, it does not need to calculate good initial estimates and expressively decreases the demand for computer resources in contrast to the iterative method. Basically, first our method exploits RGB information. We employed a scale invariant feature transformation (SIFT) for extracting, detecting, and matching features. It is able to detect and describe local features that are invariant to scaling and rotation. To detect and filter outliers, we used random sample consensus (RANSAC) algorithm, jointly with an statistical dispersion called interquartile range (IQR). After, a new RGB-D loop-closure solution is implemented based on the volumetric information between pair of point clouds and the dispersion of the random errors. The loop-closure consists to recognize when the sensor revisits some region. Finally, a globally consistent map is created to minimize the registration errors via a graph-based optimization. The effectiveness of the proposed method is demonstrated with a Kinect dataset. The experimental results show that the proposed method can properly map the indoor environment with an absolute accuracy around 1.5% of the travel of a trajectory.

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