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.

Transverse Vibration Analysis of Euler-Bernoulli Beams Carrying Concentrated Masses with Rotatory Inertia at Both Ends

2010 ◽  
Vol 118-120 ◽  
pp. 925-929 ◽  
Author(s):  
Yu Zhang ◽  
Li Yang Xie ◽  
Xiao Jin Zhang
Keyword(s):  
Differential Equations ◽  
Transverse Vibration ◽  
Vibration Analysis ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Rotatory Inertia ◽  
Dimensional Parameters ◽  
Newton Raphson ◽  
Concentrated Masses ◽  
Raphson Algorithm

Transverse vibration analysis is presented for Euler-Bernoulli beams carrying concentrated masses and taking into account their rotatory inertia at both ends. The dimensionless eigenfunctions for the problems are first obtained using the differential equations of motion and considering translational and rotatory springs at both ends. A numerical technique, the Newton–Raphson algorithm, is then used to solve vibration eigenfunctions of the beams. Finally, the influences of different non-dimensional parameters on frequencies are discussed.

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.

Effect of the Transverse Shear Deformation on the Free Vibration of Rotating Blades Modeled as Thin-Walled Composite Beams

2015 ◽  
Vol 798 ◽  
pp. 119-124
Author(s):  
Serhat Yilmaz ◽  
Seher Eken ◽  
Metin Orhan Kaya
Keyword(s):  
Transverse Shear ◽  
Fiber Orientation ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Transverse Shear Deformation ◽  
Combined Effects ◽  
Shear Deformations ◽  
Thin Walled ◽  
Good Agreement

In this paper, vibration analysis of a blade modeled as an anisotropic composite thin-walled beam is carried out. The analytical formulation of the beam is derived for the flapwise bending, chordwise bending and transverse shear deformations. The equations of motion are solved by applying the extended Galerkin method (EGM) for anti-symmetric lay-up configuration that is also referred as Circumferentially Uniform Stiffness (CUS). Consequently, the natural frequencies are validated by making comparisons with the results in literature and it is observed that there is a good agreement between the results. Combined effects of transverse shear, fiber orientation, and rotational speed on the natural frequencies are further investigated.

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.

Analytical Approach to Vibration Analysis of a Pendulum Wrapping on a Cylinder

2011 ◽  
Author(s):  
H. Mazaheri ◽  
A. Hosseinzadeh ◽  
M. T. Ahmadian ◽  
Ahmad Barari
Keyword(s):  
Analytical Solution ◽  
Nonlinear Oscillation ◽  
Vibration Analysis ◽  
Analytical Approach ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Nonlinear Frequency ◽  
Initial Amplitude ◽  
System Frequency ◽  
Good Agreement

In this paper, nonlinear oscillation of a pendulum wrapping and unwrapping around two cylindrical bases is studied and an analytical solution is obtained using multiple scales method. Equations of motion are derived based on energy conservation technique. Applying perturbation method on the equations, nonlinear natural frequency of the system is calculated along with its time response. Analytical results are compared with numerical findings and good agreement is found. Effect of nonlinearity due to large amplitude and radius of cylinders on the system frequency is evaluated. Results indicate that as the radius of cylinder is increased, nonlinear frequency is enhanced. Initial amplitude plays a dual role on the frequency. As initial amplitude increases up to a certain point, frequency increases and decreases after wards.

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.

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.

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