The Forced Oscillation of the Centrifugal Pendulum With Wide Angles

1953 ◽  
Vol 20 (1) ◽  
pp. 41-47
Author(s):  
F. R. E. Crossley
Keyword(s):  
Forced Oscillation ◽  
Torsional Oscillation ◽  
Equations Of Motion ◽  
Harmonic Excitation ◽  
Harmonic Order ◽  
Pendulum Motion ◽  
Type Curves ◽  
Effective Dynamic ◽  
Nonlinear Equations Of Motion ◽  
Effective Resonance

Abstract The simple pendulum mounted to a rotor suffering torsional oscillation is used as an effective dynamic damper which may be tuned to any one harmonic order of vibration. The nonlinear equations of motion are here developed to investigate whether wider angles of swing, or whether larger or smaller sizes of pendulum relative to its carrier, are more effective. Resonance-type curves are drawn by assuming a single harmonic excitation and hyperelliptic pendulum motion without damping; it is shown that theoretically oscillations up to 90 deg may be used which are predictable, and that in all cases the tuning must be higher than that indicated by small-angle theory.

Periodic Response of Front End Accessory Drives With Dry Friction

1997 ◽  
Author(s):  
Michael J. Leamy ◽  
Noel C. Perkins
Keyword(s):  
Dry Friction ◽  
Equations Of Motion ◽  
Harmonic Excitation ◽  
Stick Slip ◽  
Automotive Engine ◽  
Belt Drives ◽  
Wide Range ◽  
Serpentine Belt ◽  
Incremental Harmonic Balance ◽  
Nonlinear Equations Of Motion

Abstract Belt drives have long been utilized in engine applications to power accessories such as alternators, pumps, compressors and fans. Drives employing a single, flat, ‘serpentine belt’ tensioned by an ‘automatic tensioner’ are now common in automotive engine applications. The automatic tensioner helps maintain constant belt tension and to dissipate unwanted belt drive vibration through dry friction. The objective of this study is to predict the periodic rotational response of the entire drive to harmonic excitation from the crankshaft. To this end, a multi-degree of freedom incremental harmonic balance (IHB) method is utilized to compute periodic solutions to the nonlinear equations of motion over a wide range of engine speeds. Computed results illustrate primary and secondary resonances of accessories and tensioner stick-slip motions.

Nonlinear Periodic Response of Engine Accessory Drives With Dry Friction Tensioners

1998 ◽  
Vol 120 (4) ◽  
pp. 909-916 ◽  
Author(s):  
M. J. Leamy ◽  
N. C. Perkins
Keyword(s):  
Dry Friction ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Incremental Harmonic Balance Method ◽  
Stick Slip ◽  
Automotive Engine ◽  
Wide Range ◽  
Serpentine Belt ◽  
Nonlinear Equations Of Motion

Belt drives have long been utilized in engine applications to power accessories such as alternators, pumps, compressors and fans. Drives employing a single, flat, “serpentine belt” tensioned by an “automatic tensioner” are now common in automotive engine applications. The automatic tensioner helps maintain constant belt tension and to dissipate unwanted belt drive vibration through dry friction. The objective of this study is to predict the periodic rotational response of the entire drive to harmonic excitation from the crankshaft. To this end, a multi-degree of freedom incremental harmonic balance method (IHB) is utilized to compute periodic solutions to the nonlinear equations of motion over a wide range of engine speeds. Computed results illustrate primary and secondary resonances of the accessory drive and tensioner stick-slip motions.

Large Amplitude Forced Vibrations of Simply Supported Thin Cylindrical Shells

1973 ◽  
Vol 40 (2) ◽  
pp. 471-477 ◽  
Author(s):  
J. H. Ginsberg
Keyword(s):  
Nonlinear Response ◽  
Nonlinear Boundary ◽  
Circular Cylindrical Shell ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Harmonic Excitation ◽  
Inertia Effects ◽  
Modal Expansion ◽  
Wide Range ◽  
Nonlinear Equations Of Motion

The response of a thin circular cylindrical shell to resonant harmonic excitation is examined by a modal expansion approach. The nonlinear strain-displacement relations lead to a nonlinear boundary condition, as well as nonlinear equations of motion. The solution, which retains tangential inertia effects, is obtained by a perturbation technique that yields a consistent first approximation of the nonlinear response. The results are applicable for a wide range of parameters and to cases of excitation near any of the three lowest natural frequencies corresponding to given axial and circumferential wavelengths. For situations where shallow shell theory is valid, the results of previous studies, which were based upon such a theory, are in close agreement.

Nonlinear Vibrations of Circular Cylindrical Panels: Theory and Experiments

2003 ◽  
Author(s):  
M. Amabili ◽  
M. Pellegrini
Keyword(s):  
Nonlinear Vibrations ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Elastic Strain Energy ◽  
Laminated Composite ◽  
Harmonic Excitation ◽  
Cylindrical Panels ◽  
Radial And Axial Displacements ◽  
Nonlinear Equations Of Motion ◽  
Spectral Neighborhood

Large-amplitude (geometrically nonlinear) vibrations of circular cylindrical panels subjected to radial harmonic excitation in the spectral neighborhood of the lowest resonances are investigated. The Donnell’s nonlinear thin-shell theory is used to calculate the elastic strain energy. The formulations is also valid for orthotropic and symmetric cross-ply laminated composite shells; geometric imperfections are taken into account. Comparison of calculations to numerical results available in the literature is also performed. The nonlinear equations of motion are studied by using a code based on arclength continuation method that allows bifurcation analysis. Vibration response of three thin circular cylindrical panels of different materials (stainless steel, copper and composite) to harmonic excitation in the neighborhood of the first three natural frequencies has been measured for different force levels. The experimental boundary conditions approximate (i) on the curved edges: zero radial, axial and circumferential displacements; all rotations were allowed; (ii) on the straight edges: zero radial and axial displacements; all rotations and circumferential displacements were allowed. The different levels of excitation permitted to reconstruct the relatively strong, softening type nonlinearity of the panels.

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.

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