Dynamic Deflection of Paper Emerging from a Channel

1992 ◽  
Vol 114 (2) ◽  
pp. 187-193 ◽  
Author(s):  
J. Stolte ◽  
R. C. Benson
Keyword(s):  
Dynamic Modeling ◽  
Nonlinear Theory ◽  
Feed Rate ◽  
Magnetic Tape ◽  
Constant Velocity ◽  
Open Space ◽  
Equations Of Motion ◽  
Nonlinear Static ◽  
Nonlinear Equations Of Motion ◽  
Magnetic Tape Drives

In many machines handling lightweight, flexible sheets, the sheet must transit an open space. Examples include magnetic tape drives, xerographic copiers, and sewing machines. The nonlinear theory of the elastica has often been used to model nonlinear, static deflections. Dynamic modeling is more difficult, and far less studied. Recently, however, L. Mansfield and J. G. Simmonds (1987) have considered the dynamic deflection of a sheet emerging from a horizontal channel at constant velocity and subjected to gravity loading. In this paper, we consider a generalization of that problem to include arbitrary exit angles and an accelerating “feed” rate. Gravity loading is retained. The resulting nonlinear equations of motion are tractable and are solved numerically.

Dynamic Deflection of Paper Emerging From a Channel

1991 ◽  
Author(s):  
James Stolte ◽  
Richard C. Benson
Keyword(s):  
Dynamic Modeling ◽  
Nonlinear Theory ◽  
Feed Rate ◽  
Magnetic Tape ◽  
Constant Velocity ◽  
Open Space ◽  
Equations Of Motion ◽  
Nonlinear Static ◽  
Nonlinear Equations Of Motion ◽  
Magnetic Tape Drives

Abstract For many machines handling lightweight, flexible sheets, it is necessary for the sheet to transit an open space. Examples include magnetic tape drives, xerographic copiers, and sewing machines. The nonlinear theory of the elastica has often been used to model nonlinear, static deflections. Dynamic modeling is more difficult, and far less studied. Recently, however, L. Mansfield and J.G. Simmonds (1987) have considered the dynamic deflection of a sheet emerging from a horizontal channel at constant velocity and subjected to gravity loading. In this paper, we consider a generalization of that problem to include arbitrary exit angles, and an accelerating “feed” rate. Gravity loading is retained. The resulting nonlinear equations of motion are tractable and are solved numerically.

The Reverse Spaghetti Problem: Drooping Motion of an Elastica Issuing from a Horizontal Guide

1987 ◽  
Vol 54 (1) ◽  
pp. 147-150 ◽  
Author(s):  
L. Mansfield ◽  
J. G. Simmonds
Keyword(s):  
Finite Element Method ◽  
Time Domain ◽  
Constant Velocity ◽  
Series Solution ◽  
Equations Of Motion ◽  
Space Time ◽  
Stiffness Ratio ◽  
The Finite Element Method ◽  
Dimensionless Velocity ◽  
Nonlinear Equations Of Motion

The nonlinear equations of motion of an elastica that moves out of a horizontal guide at a constant velocity are expressed in terms a dimensionless weight-to-stiffness ratio and a dimensionless velocity. The equations are written in horizontal-vertical directions rather than tangential-normal directions to minimize algebraic complexities. The introduction of deformation potentials allows each of the linear momentum equations to be integrated once. This simplifies the remaining equations. A series solution of the equations, useful for small motions—and perhaps useful for design—is given. To facilitate numerical solution, the triangular space-time domain of the problem is transformed into a square domain in pseudo space-time. Finally, some solutions based on the finite element method are presented for typical values of the dimensionless weight-to-stiffness and velocity parameters.

Coupled Torsional and Transverse Vibration of Unbalanced Rotor

1985 ◽  
Vol 52 (3) ◽  
pp. 701-705 ◽  
Author(s):  
R. Cohen ◽  
I. Porat
Keyword(s):  
Transverse Vibration ◽  
Constant Velocity ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Resonance Effect ◽  
Combination Resonance ◽  
Unbalanced Rotor ◽  
Direct Numerical Solution ◽  
Nonlinear Equations Of Motion ◽  
Good Agreement

A model of an unbalanced rotor, driven by a torsion-flexible shaft through a constant velocity joint, is used to investigate the combination-resonance effect in coupled torsional-transverse vibration. Analysis of the nonlinear equations of motion by an asymptotic method yields the instability zones of the system. Results are in very good agreement with those obtained by direct numerical solution of the equations of motion.

On the Parametric Excitation of Pendulum-Type Vibration Absorber

1961 ◽  
Vol 28 (3) ◽  
pp. 330-334 ◽  
Author(s):  
Eugene Sevin
Keyword(s):  
Energy Transfer ◽  
Numerical Solution ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Vibration Absorber ◽  
Single Cycle ◽  
Linearized System ◽  
Nonlinear Equations Of Motion ◽  
Beam Oscillation ◽  
Energy Interchange

The free motion of an undamped pendulum-type vibration absorber is studied on the basis of approximate nonlinear equations of motion. It is shown that this type of mechanical system exhibits the phenomenon of auto parametric excitation; a type of “instability” which cannot be accounted for on the basis of the linearized system. Complete energy transfer between modes is shown to occur when the beam frequency is twice the simple pendulum frequency. On the basis of a numerical solution, approximately 150 cycles of the beam oscillation take place during a single cycle of energy interchange.

Less=Moor: A Time-Efficient Computational Tool to Assess the Behavior of Moored Ships in Waves

2017 ◽  
Author(s):  
Yijun Wang ◽  
Alex van Deyzen ◽  
Benno Beimers
Keyword(s):  
Dynamic Response ◽  
Research Effort ◽  
Equations Of Motion ◽  
Line Tension ◽  
Mooring Line ◽  
Induced Response ◽  
Wave Forces ◽  
Computational Tool ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion

In the field of port design there is a need for a reliable but time-efficient method to assess the behavior of moored ships in order to determine if further detailed analysis of the behavior is required. The response of moored ships induced by gusting wind and/or waves is dynamic. Excessive motion response may cause interruption of the (un)loading operation. High line tension may cause lines to snap, introducing dangerous situations. A (detailed) Dynamic Mooring Analysis (DMA), however, is often a time-consuming and expensive exercise, especially when responses in many different environmental conditions need to be assessed. Royal HaskoningDHV has developed a time-efficient computational tool in-house to assess the wave (sea or swell) induced dynamic response of ships moored to exposed berths. The mooring line characteristics are linearized and the equations of motion are solved in the frequency domain with both the 1st and 2nd wave forces taken into account. This tool has been termed Less=Moor. The accuracy and reliability of the computational tool has been illustrated by comparing motions and mooring line forces to results obtained with software that solves the nonlinear equations of motion in the time domain (aNySIM). The calculated response of a Floating Storage and Regasification Unit (FSRU) moored to dolphins located offshore has been presented. The results show a good comparison. The computational tool can therefore be used to indicate whether the wave induced response of ships moored at exposed berths proves to be critical. The next step is to make this tool suitable to assess the dynamic response of moored ships with large wind areas, e.g. container ships, cruise vessels, RoRo or car carriers, to gusting wind. In addition, assessment of ship responses in a complicated wave field (e.g. with reflected infra-gravity waves) also requires more research effort.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

Consistent Tangent Stiffness of a Three-Dimensional Wheel–Rail Interaction Element

2021 ◽  
Author(s):  
Quan Gu ◽  
Jinghao Pan ◽  
Yongdou Liu
Keyword(s):  
Finite Element ◽  
Quadratic Convergence ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Light Rail ◽  
Software Framework ◽  
Tangent Stiffness ◽  
Rail Vehicle ◽  
Interaction Element ◽  
Nonlinear Equations Of Motion

Consistent tangent stiffness plays a crucial role in delivering a quadratic rate of convergence when using Newton’s method in solving nonlinear equations of motion. In this paper, consistent tangent stiffness is derived for a three-dimensional (3D) wheel–rail interaction element (WRI element for short) originally developed by the authors and co-workers. The algorithm has been implemented in finite element (FE) software framework (OpenSees in this paper) and proven to be effective. Application examples of wheelset and light rail vehicle are provided to validate the consistent tangent stiffness. The quadratic convergence rate is verified. The speeds of calculation are compared between the use of consistent tangent stiffness and the tangent by perturbation method. The results demonstrate the improved computational efficiency of WRI element when consistent tangent stiffness is used.

Nonlinear Analysis of a Rigid Rotor on Magnetic Bearings

1995 ◽  
Author(s):  
C. Nataraj
Keyword(s):  
Nonlinear Analysis ◽  
Equations Of Motion ◽  
Forced Response ◽  
Magnetic Bearings ◽  
Rigid Rotor ◽  
Stability Criteria ◽  
Safe Operation ◽  
Qualitative And Quantitative ◽  
Quantitative Results ◽  
Nonlinear Equations Of Motion

A simple model of a rigid rotor supported on magnetic bearings is considered. A proportional control architecture is assumed, the nonlinear equations of motion are derived and some essential nondimensional parameters are identified. The free and forced response of the system is analyzed using techniques of nonlinear analysis. Both qualitative and quantitative results are obtained and stability criteria are derived for safe operation of the system.

MULTIBODY DYNAMIC MODELING AND FLUTTER ANALYSIS OF A FLEXIBLE SLENDER VEHICLE

2012 ◽  
Vol 12 (06) ◽  
pp. 1250049 ◽  
Author(s):  
A. RASTI ◽  
S. A. FAZELZADEH
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
The Body ◽  
Elastic Deformations ◽  
Strip Theory ◽  
Multibody Dynamic ◽  
Flutter Analysis ◽  
Rigid Body Motions

In this paper, multibody dynamic modeling and flutter analysis of a flexible slender vehicle are investigated. The method is a comprehensive procedure based on the hybrid equations of motion in terms of quasi-coordinates. The equations consist of ordinary differential equations for the rigid body motions of the vehicle and partial differential equations for the elastic deformations of the flexible components of the vehicle. These equations are naturally nonlinear, but to avoid high nonlinearity of equations the elastic displacements are assumed to be small so that the equations of motion can be linearized. For the aeroelastic analysis a perturbation approach is used, by which the problem is divided into a nonlinear flight dynamics problem for quasi-rigid flight vehicle and a linear extended aeroelasticity problem for the elastic deformations and perturbations in the rigid body motions. In this manner, the trim values that are obtained from the first problem are used as an input to the second problem. The body of the vehicle is modeled with a uniform free–free beam and the aeroelastic forces are derived from the strip theory. The effect of some crucial geometric and physical parameters and the acting forces on the flutter speed and frequency of the vehicle are investigated.

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