scholarly journals Spherical Pendulum Small Oscillations for Slewing Crane Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Alexander V. Perig ◽  
Alexander N. Stadnik ◽  
Alexander I. Deriglazov
Keyword(s):  
Reference Frame ◽  
Natural Frequencies ◽  
Computational Results ◽  
Numerical Estimation ◽  
Spherical Pendulum ◽  
Lagrange Equations ◽  
Uniform Rotation ◽  
Small Oscillations ◽  
Mechanical Interpretation ◽  
Lagrange Mechanics

The present paper focuses on the Lagrange mechanics-based description of small oscillations of a spherical pendulum with a uniformly rotating suspension center. The analytical solution of the natural frequencies’ problem has been derived for the case of uniform rotation of a crane boom. The payload paths have been found in the inertial reference frame fixed on earth and in the noninertial reference frame, which is connected with the rotating crane boom. The numerical amplitude-frequency characteristics of the relative payload motion have been found. The mechanical interpretation of the terms in Lagrange equations has been outlined. The analytical expression and numerical estimation for cable tension force have been proposed. The numerical computational results, which correlate very accurately with the experimental observations, have been shown.

Feasibility of Two-Dimensional Control for Ship-Mounted Cranes

2001 ◽  
Author(s):  
Eihab M. Abdel-Rahman ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
Major Axis ◽  
Double Pendulum ◽  
Spherical Pendulum ◽  
Safe Operation ◽  
Control Effort ◽  
Pendulum System ◽  
Out Of Plane ◽  
The One

Abstract We test the feasibility of employing an exclusively planar control effort to suppress unsafe ship-mounted crane pendulations induced by sea motions. The new crane configuration, designed to apply the control effort, is modeled and the proposed control effort, employing Coulomb friction and viscous damping, is applied. The three-dimensional nonlinear dynamics of the crane is then investigated. The new crane configuration, dubbed Maryland Rigging, transforms a crane from a single spherical pendulum to a double pendulum system. The upper pendulum, a pulley riding on a cable suspended from the boom, is constrained to move over an ellipsoid. The major axis of the ellipsoid is the boom and the foci are the two points at which the riding cable attaches to it. The lower pendulum, the payload suspended by a cable from the pulley, continues to act as a spherical pendulum. Due to the geometry of the ellipsoid, the natural frequencies of the crane in the plane of the boom (in-plane) are almost equal to the out-of-plane natural frequencies. The model is used to examine the response of a Maryland rigged crane to direct, in-plane, harmonic forcing. The frequency of the excitation is set almost equal to the crane’s lowest natural frequency. It is found that under this excitation and due to the one-to-one internal resonance between the lowest in-plane and out-of-plane natural frequencies, significant out-of-plane motions are induced by applying a purely in-plane forcing. Thus an in-plane control mechanism is not adequate for safe operation of the crane. To guarantee safe operation of a ship-mounted crane, one must apply both in-plane and out-of-plane control efforts.

Two-Dimensional Control for Ship-Mounted Cranes: A Feasibility Study

2003 ◽  
Vol 9 (12) ◽  
pp. 1327-1342 ◽  
Author(s):  
Eihab Abdel-Rahman ◽  
Ali H Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
Major Axis ◽  
Double Pendulum ◽  
Spherical Pendulum ◽  
Safe Operation ◽  
Control Effort ◽  
Pendulum System ◽  
Out Of Plane ◽  
The One

We test the feasibility of employing an exclusively planar control effort to suppress unsafe ship-mounted crane pendulations induced by sea motions. The new crane configuration, designed to apply the control effort, is modeled and the proposed control effort, employing Coulomb friction and viscous damping, is applied. The three-dimensional nonlinear dynamics of the crane is then investigated. The new crane configuration, dubbed Maryland rigging, transforms a crane from a single spherical pendulum to a double pendulum system. The upper pendulum, a pulley riding on a cable suspended from the boom, is constrained to move over an ellipsoid. The major axis of the ellipsoid is the boom and the foci are the two points at which the riding cable attaches to it. The lower pendulum, the payload suspended by a cable from the pulley, continues to act as a spherical pendulum. Due to the geometry of the ellipsoid, the natural frequencies of the crane in the plane of the boom (in-plane) are almost equal to the out-of-plane natural frequencies. The model is used to examine the response of a Maryland rigged crane to direct, in-plane, harmonic forcing. The frequency of the excitation is set almost equal to the crane's lowest natural frequency. It is found that under this excitation and due to the one-to-one internal resonance between the lowest in-plane and out-of-plane natural frequencies, significant out-of-plane motions are induced by applying a purely in-plane forcing. Thus, an in-plane control mechanism is not adequate for safe operation of the crane. To guarantee safe operation of a ship-mounted crane, both in-plane and out-of-plane control efforts must be applied.

Free Vibration of Beams With Two Sections of Distributed Mass

1998 ◽  
Vol 120 (4) ◽  
pp. 944-948 ◽  
Author(s):  
Kwok-Tung Chan ◽  
Xiao-Quan Wang ◽  
Tin-Pui Leung
Keyword(s):  
Experimental Data ◽  
Exact Solution ◽  
Free Vibration ◽  
Cantilever Beam ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Computational Results ◽  
Free Transverse Vibration

The equation of free transverse vibration of beams with two sections of partially distributed mass is derived and its exact solution has been obtained. Experimental data for a cantilever beam are given to verify the computational results. Using a cantilever beam as an example, some interesting features of changes of natural frequencies with mass length and position are described. The method is finally generalized for the case of beams with multiple spans of distributed mass.

scholarly journals Motions of a Constrained Spherical Pendulum in an Arbitrarily Moving Reference Frame: The Automobile Seatbelt Inertial Sensor

1995 ◽  
Vol 2 (3) ◽  
pp. 227-236 ◽  
Author(s):  
A. Peter Allan ◽  
Miles A. Townsend
Keyword(s):  
Numerical Simulation ◽  
Reference Frame ◽  
Inertial Sensor ◽  
Equations Of Motion ◽  
Sensor Design ◽  
Spherical Pendulum ◽  
Crash Data ◽  
Kane’S Method ◽  
Kane's Method ◽  
Automobile Crash

A common automatic seatbelt inertial sensor design, comprised of a constrained spherical pendulum, is modeled to study its motions and possible unintentional release during vehicle emergency maneuvers. The kinematics are derived for the system with the most general inputs: arbitrary pivot motions. The influence of forces due to gravity and constraint torque functions is developed. The equations of motion are then derived using Kane's method. The equations of motion are used in a numerical simulation with both actual and hypothetical automobile crash data.

scholarly journals Small oscillations of an ideal liquid contained in a vessel closed by an elastic circular plate, in uniform rotation

2017 ◽  
Vol 44 (1) ◽  
pp. 35-49
Author(s):  
Hilal Essaouini ◽  
Bakkali El ◽  
Pierre Capodanno
Keyword(s):  
Circular Plate ◽  
Small Amplitude ◽  
Variational Equation ◽  
Equations Of Motion ◽  
Coupled System ◽  
Ideal Liquid ◽  
Existence And Uniqueness Theorem ◽  
Uniform Rotation ◽  
Small Oscillations ◽  
Elastic Circular Plate

The problem of the small oscillations of an ideal liquid contained in a vessel in uniform rotation has been studied by Kopachevskii and Krein in the case of an entirely rigid vessel [3]. We propose here, a generalization of this model by considering the case of a vessel closed by an elastic circular plate. In this context, the linearized equations of motion of the system plateliquid are derived. Functional analysis is used to obtain a variational equation of the small amplitude vibrations of the coupled system around its equilibrium position, and then two operatorial equations in a suitable Hilbert space are presented and analyzed. We show that the spectrum of the system is real and consists of a countable set of eigenvalues and an essential continuous spectrum filling an interval. Finally the existence and uniqueness theorem for the solution of the associated evolution problem is proved by means the semigroups theory.

scholarly journals Invariant-Based Inverse Engineering for Fast and Robust Load Transport in a Double Pendulum Bridge Crane

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 350
Author(s):  
Ion Lizuain ◽  
Ander Tobalina ◽  
Alvaro Rodriguez-Prieto ◽  
Juan Gonzalo Muga
Keyword(s):  
Natural Frequencies ◽  
Initial Conditions ◽  
Boundary Effects ◽  
Double Pendulum ◽  
Bridge Crane ◽  
Small Oscillations ◽  
Load Transport

We set a shortcut-to-adiabaticity strategy to design the trolley motion in a double-pendulum bridge crane. The trajectories found guarantee payload transport without residual excitation regardless of the initial conditions within the small oscillations regime. The results are compared with exact dynamics to set the working domain of the approach. The method is free from instabilities due to boundary effects or to resonances with the two natural frequencies.

The Study of the Pendulum with Heavy Neo-Hookean Rod

2013 ◽  
Vol 430 ◽  
pp. 45-52
Author(s):  
Nicolae Doru Stanescu ◽  
Dinel Popa
Keyword(s):  
Numerical Simulation ◽  
Stable Equilibrium ◽  
Equations Of Motion ◽  
Second Order ◽  
Variable Length ◽  
Lagrange Equations ◽  
Small Oscillations ◽  
Theoretical Results

The present paper is a generalization of the problem of a rubber spring pendulum discussed by Bhattacharyya in 2000 and Stănescu in 2011, which studied the case of the neo-Hookean rod without mass. In our paper we consider that the mass of the neo-Hookean rod is not negligible and its deformation is realized such that at any moment of time the rod can be treated as a homogeneous rigid bar of variable length. Using the second order Lagrange equations we obtained the equations of motion in the most general case and we identified as particular cases the situations presented in the bibliography. We also performed a study of the equilibrium positions and their stability. A study of the small oscillations about the stable equilibrium positions is realized too. The theoretical results are finally compared to those obtained by numerical simulation.

Natural Frequency Analysis of a Jeffcott Rotor Having Stepped Shaft

2021 ◽  
Vol 6 (3) ◽  
pp. 170-172
Author(s):  
Ahmed A. Alahmadi ◽  
Khalid A. Alnefaie ◽  
Hamza Diken
Keyword(s):  
Natural Frequencies ◽  
Lagrange Equations ◽  
Shaft Length ◽  
Variable Diameter ◽  
Stepped Shaft ◽  
Disc Position ◽  
Jeffcott Rotor ◽  
Mechanical Elements ◽  
Natural Frequency Analysis ◽  
Rotor Model

The Rotating shafts are mechanical elements used to transmit power or motion. A shaft with a step or steps is widely used instead of a shaft with a fixed (non-variable) diameter when operating at high speeds. The aim of this research is to study the effect of the step amount and its location in the shaft on the natural frequencies of the Jeffcott rotor model. Analytical methods are used to find an approximate formulation to obtain the natural frequencies of the Jeffcott rotor model neglecting the shaft mass. Lagrange equations are used to develop dynamic equations assuming elastic shaft with steps carrying a disk. The finite element method by using ANSYS is used to validate and compare the results obtained in the analytical method. The results obtained analytically and numerically were compatible and in good agreement. In addition, some parameters such as the step amount and the stepped shaft length are changed to check its effects on the natural frequencies. the results showed that the natural frequencies increase with an increase in the amount and length of the stepped part, while they decrease the closer the disc position to the center.

The Influence of Axial-Torsional Coupling on the Natural Frequencies of an Aerial Cable

1993 ◽  
Vol 115 (3) ◽  
pp. 271-276
Author(s):  
S. H. Venkatasubramanian ◽  
W. N. White
Keyword(s):  
Close Agreement ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Element Analysis ◽  
Small Oscillations ◽  
Overhead Transmission Line ◽  
Coupling Case ◽  
Aerial Cable ◽  
Torsional Coupling ◽  
Zero Coupling

The equations of motion for the small oscillations of a stranded, overhead transmission line are derived and linearized about the static equilibrium position. The influence of axial-torsional coupling on the natural frequencies is studied analytically and an expression is presented for the coupled natural frequency in torsion. In order to verify the analytical results, a finite element analysis of the linearized coupled differential equations is carried out. The results of each analysis are compared and show close agreement. The results of the zero coupling case also closely agree with previous work.

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