scholarly journals Nonlinear Dynamic and Kinematic Model of a Spar-Buoy: Parametric Resonance and Yaw Numerical Instability

2020 ◽  
Vol 8 (7) ◽  
pp. 504 ◽  
Author(s):  
Giuseppe Giorgi ◽  
Josh Davidson ◽  
Giuseppe Habib ◽  
Giovanni Bracco ◽  
Giuliana Mattiazzo ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Parametric Resonance ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Kinematic Model ◽  
Numerical Instability ◽  
Floating Structure ◽  
Operational Conditions ◽  
Power Extraction

Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assumptions are normally required, usually implying linear kinematics and hydrodynamics. However, while the assumption of linear, small amplitude motion fits traditional offshore problems, in normal operational conditions (it is desirable to stabilize ships, boats, and offshore platforms), large motion and potential dynamic instability may arise (e.g., harsh sea conditions). Furthermore, such nonlinearities are particularly evident in wave energy converters, as large motions are expected (and desired) to enhance power extraction. The inadequacy of linear models has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received very little attention, as few models yet consider six degrees of freedom and large rotations. This paper implements a nonlinear hydrodynamic and kinematic model for an archetypal floating structure, commonplace in offshore applications: an axisymmetric spar-buoy. The influence of nonlinear dynamics and kinematics causing coupling between modes of motion are demonstrated. The nonlinear dynamics are shown to cause parametric resonance in the roll and pitch degrees of freedom, while the nonlinear kinematics are shown to potentially cause numerical instability in the yaw degree of freedom. A case study example is presented to highlight the nonlinear dynamic and kinematic effects, and the importance of including a nominal restoring term in the yaw DoF presented.

Parametric Resonance Characteristics of Woven Fiber Metal Laminated Plates

2019 ◽  
Vol 11 (04) ◽  
pp. 1950034 ◽  
Author(s):  
Elluri Venkata Prasad ◽  
Shishir Kumar Sahu
Keyword(s):  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Parametric Instability ◽  
Laminated Plates ◽  
Load Factor ◽  
Harmonic Loading ◽  
Resonance Behavior ◽  
Fiber Metal ◽  
Ply Orientation

The present investigation deals with the assessment of parametric resonance behavior of new aircraft material, i.e., woven fiber metal laminated (FML) plates subjected to in-plane static and harmonic loading using finite element (FE) technique and Bolotin’s method. In this analysis, a four-node isoparametric element with five degrees of freedom per node is adopted. Based on the first-order Reissner–Mindlin theory, the parametric instability of FML plate subjected to in-plane harmonic loading is examined. A MATLAB code is developed for the parametric study on the dynamic stability of FML plates. The reliability of present formulation is checked by comparing numerical results obtained from present FE analysis with the published researches in the field. The influences of several factors, viz. static load factor, aspect ratio, length-to-thickness ratio, number of layers, ply orientation and boundary conditions on the dynamic instability regions are discussed. Significant variations of these factors on dynamic instability zones of FML plates are observed. The instability zones can be used as guidelines for the prediction of the dynamic behavior of FML plates.

scholarly journals A New Approach of Soft Joint Based on a Cable-Driven Parallel Mechanism for Robotic Applications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1468
Author(s):  
Luis Nagua ◽  
Carlos Relaño ◽  
Concepción A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Humanoid Robots ◽  
Inverse Kinematic ◽  
Element Analysis ◽  
New Approach ◽  
Flexible Polymer ◽  
The Mathematical Model

A soft joint has been designed and modeled to perform as a robotic joint with 2 Degrees of Freedom (DOF) (inclination and orientation). The joint actuation is based on a Cable-Driven Parallel Mechanism (CDPM). To study its performance in more detail, a test platform has been developed using components that can be manufactured in a 3D printer using a flexible polymer. The mathematical model of the kinematics of the soft joint is developed, which includes a blocking mechanism and the morphology workspace. The model is validated using Finite Element Analysis (FEA) (CAD software). Experimental tests are performed to validate the inverse kinematic model and to show the potential use of the prototype in robotic platforms such as manipulators and humanoid robots.

Experimental and analytical investigation on the in-plane dynamic instability of arches owing to parametric resonance

2017 ◽  
Vol 24 (19) ◽  
pp. 4419-4432 ◽  
Author(s):  
Airong Liu ◽  
Zhicheng Yang ◽  
Hanwen Lu ◽  
Jiyang Fu ◽  
Yong-Lin Pi
Keyword(s):  
Parametric Resonance ◽  
Dynamic Instability ◽  
Damping Ratio ◽  
Analytical Investigation ◽  
Engineering Practice ◽  
Test Results ◽  
Periodic Load ◽  
Shallow Arches ◽  
Excitation Frequencies ◽  
Critical Regions

When an arch is subjected to a periodic load, it may lose in-plane stability dynamically owing to parametric resonance. Previous investigations have been concentrated on in-plane dynamic buckling of pin-ended shallow arches. However, in engineering practice, fixed arches with different rise-to-span ratios are often encountered. Little research on in-plane dynamic instability of deep fixed arches has been reported in the literature. This paper is concerned with experimental and analytical investigations for in-plane dynamic instability of fixed circular arches with rise-to-span ratios 1/8–1/2 under a central periodic load owing to parametric resonance. Experiments are carried out to determine the in-plane frequency and damping ratio of arches, to investigate critical regions of frequencies and amplitudes of the periodic load for in-plane dynamic instability of arches, and to explore effects of the rise-to-span ratio and additional weights on dynamic instability. The analytical method for determining the region of excitation frequencies and amplitudes of the periodic load causing in-plane instability of the arch is established using the Hamilton’s principle by accounting for effects of additional concentrated weights. Comparisons of analytical solutions with test results show that they agree with each other quite well. These results show that the rise-to-span ratio significantly influences the bandwidth of regions of critical excitation frequencies for in-plane dynamic instability of arches. The critical frequencies of the periodic load and their bandwidth increase with a decrease of the rise–span ratio of the arch, whereas the corresponding amplitude of the periodic load decreases at the same time. It is also found that the central concentrated weight influences in-plane dynamic instability of arches significantly. As the weight increases, the critical frequencies of excitation and their bandwidth for in-plane dynamic instability of arches decreases, whereas the corresponding amplitude of excitation increases.

Cooperation and Null-Space Control of Networked Omni-Directional Mobile Manipulators

2020 ◽  
Author(s):  
Michael John Chua ◽  
Yen-Chen Liu
Keyword(s):  
Degrees Of Freedom ◽  
Null Space ◽  
Kinematic Model ◽  
Mobile Manipulator ◽  
Main Task ◽  
Mobile Manipulators ◽  
Robot Arm ◽  
Task Space ◽  
End Effector ◽  
Mobile Base

Abstract This paper presents cooperation and null-space control for networked mobile manipulators with high degrees of freedom (DOFs). First, kinematic model and Euler-Lagrange dynamic model of the mobile manipulator, which has an articulated robot arm mounted on a mobile base with omni-directional wheels, have been presented. Then, the dynamic decoupling has been considered so that the task-space and the null-space can be controlled separately to accomplish different missions. The motion of the end-effector is controlled in the task-space, and the force control is implemented to make sure the cooperation of the mobile manipulators, as well as the transportation tasks. Also, the null-space control for the manipulator has been combined into the decoupling control. For the mobile base, it is controlled in the null-space to track the velocity of the end-effector, avoid other agents, avoid the obstacles, and move in a defined range based on the length of the manipulator without affecting the main task. Numerical simulations have been addressed to demonstrate the proposed methods.

A Model of the Human Spine: Forward and Inverse Kinematics

1992 ◽  
Author(s):  
Sunil Kumar Agrawal ◽  
Siyan Li ◽  
Glen Desmier
Keyword(s):  
Range Of Motion ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Joint Angles ◽  
Human Spine ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degrees Of Freedom ◽  
Adjacent Vertebra

Abstract The human spine is a sophisticated mechanism consisting of 24 vertebrae which are arranged in a series-chain between the pelvis and the skull. By careful articulation of these vertebrae, a human being achieves fine motion of the skull. The spine can be modeled as a series-chain with 24 rigid links, the vertebrae, where each vertebra has three degrees-of-freedom relative to an adjacent vertebra. From the studies in the literature, the vertebral geometry and the range of motion between adjacent vertebrae are well-known. The objectives of this paper are to present a kinematic model of the spine using the available data in the literature and an algorithm to compute the inter vertebral joint angles given the position and orientation of the skull. This algorithm is based on the observation that the backbone can be described analytically by a space curve which is used to find the joint solutions..

Nonlinear Dynamics of One-Way Clutches in Belt-Pulley Systems

2003 ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Excitation Amplitude ◽  
Relative Displacement ◽  
Second Primary ◽  
Arc Length ◽  
The One

One-way clutches are frequently used in the serpentine belt accessory drives of automobiles and heavy vehicles. The clutch plays a role similar to a vibration absorber in order to reduce belt/pulley vibration and noise and increase belt life. This paper analyzes a two-pulley system where the driven pulley has a one-way clutch between the pulley and accessory shaft that engages only for positive relative displacement between these components. The belt is modeled with linear springs that transmit torque from the driving pulley to the accessory pulley. The one-way clutch is modeled as a piecewise linear spring with discontinuous stiffness that separates the driven pulley into two degrees of freedom (DOF). The harmonic balance method (HBM) combined with arc-length continuation is employed to illustrate the nonlinear dynamic behavior of the one-way clutch. HBM with arc-length continuation yields the stable and unstable periodic solutions for given parameters. These solutions are examined across a range of excitation frequencies. The results are confirmed by numerical integration and the widely used bifurcation software AUTO. At the first primary resonance, most of the responses are aperiodic, including quasiperiodic and chaotic solutions. At the second primary resonance, the peak bends to the left with classical softening nonlinearity because clutch disengagement decouples the pulley and the accessory over portions of the response period. The dependence on system parameters such as clutch stiffness, excitation amplitude, and inertia ratio between the pulley and accessory is studied to characterize the nonlinear dynamics across a range of conditions.

Numerical Investigation of the Influence of Friction Coefficient on Brake Groan

2010 ◽  
Vol 44-47 ◽  
pp. 1923-1927 ◽  
Author(s):  
Xian Jie Meng
Keyword(s):  
Nonlinear Dynamics ◽  
Friction Coefficient ◽  
Degrees Of Freedom ◽  
Equilibrium Points ◽  
Static Friction ◽  
Kinetic Friction ◽  
Dynamics Model ◽  
Excited Vibration ◽  
Nonlinear Dynamics Model ◽  
The Stability

A two degrees of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction of brake disk and pads is built firstly, the stability of vibration system at the equilibrium points is analyzed using the nonlinear dynamics theory. Finally the numerical method is taken to study the impacts of friction coefficient on brake groan. The calculation result shows that with the increase of kinetic friction coefficient /or the decrease of difference value between static friction coefficient and kinetic friction coefficient can prevent or restrain self-excited vibration from happening.

Parametric Resonance of a Two Degrees-of-Freedom System Induced by Bounded Noise

2009 ◽  
Vol 76 (4) ◽  
Author(s):  
Jinyu Zhu ◽  
W.-C. Xie ◽  
Ronald M. C. So ◽  
X. Q. Wang
Keyword(s):  
Lyapunov Exponents ◽  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Singular Perturbation Method ◽  
Bounded Noise ◽  
Two Degrees Of Freedom ◽  
Moment Lyapunov Exponent ◽  
The Moment ◽  
Combined Resonance ◽  
Moment Lyapunov Exponents

The dynamic stability of a two degrees-of-freedom system under bounded noise excitation with a narrowband characteristic is studied through the determination of moment Lyapunov exponents. The partial differential eigenvalue problem governing the moment Lyapunov exponent is established. For weak noise excitations, a singular perturbation method is employed to obtain second-order expansions of the moment Lyapunov exponents and Lyapunov exponents, which are shown to be in good agreement with those obtained using Monte Carlo simulation. The different cases when the system is in subharmonic resonance, combination additive resonance, and combined resonance in the absence of noise, respectively, are considered. The effects of noise and frequency detuning on the parametric resonance are investigated.

scholarly journals Kinematic Modelling of FES Induced Sit-to-stand Movement in Paraplegia

2017 ◽  
Vol 7 (6) ◽  
pp. 3060
Author(s):  
Mohammed Ahmed ◽  
M. S. Huq ◽  
B. S. K. K. Ibrahim
Keyword(s):  
Dynamic Model ◽  
Initial Phase ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Future Research ◽  
Upper Limbs ◽  
Body System ◽  
Segmental Dynamics ◽  
Sit To Stand ◽  
Kinematic Modelling

FES induced movements from indication is promising due to encouraging results being obtained by scholars. The kinematic model usually constitute the initial phase towards achieving the segmental dynamics of any rigid body system. It can be used to ascertain that the model is capable of achieving the desired goal. The dynamic model builds on the kinematic model and is usually mathematically cumbersome depending on the number of degrees-of-freedom. This paper presents a kinematic model applicable for human sit-to-stand movement scenario that will be used to obtain the dynamic model the FES induced movement in a later study. The study shows that the 6 DOF conceptualized sit-to-stand movement can be achieved conveniently using 4 DOF. The 4 DOF has an additional joint compared to similar earlier works which makes more it accurate and flexible. It is more accurate in the sense that it accommodates additional joint i.e. the neck joint whose dynamics could be captured. And more flexible in the sense that if future research uncover more contributions by the segments it can be easily incorporated including that of other segments e.g. the trunk, neck and upper limbs.

scholarly journals Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

2021 ◽  
pp. 66-70
Author(s):  
S. Homeniuk ◽  
S. Grebenyuk ◽  
D. Gristchak
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Hybrid Approach ◽  
Time Dependent ◽  
Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

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