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.

Pendulum as Vibration Absorber for Flexible Structures: Experiments and Theory

1996 ◽  
Vol 118 (4) ◽  
pp. 558-566 ◽  
Author(s):  
O. Cuvalci ◽  
A. Ertas
Keyword(s):  
Energy Transfer ◽  
Coupling Effect ◽  
Equations Of Motion ◽  
Flexible Structures ◽  
Experimental Results ◽  
Vibration Absorber ◽  
Pendulum System ◽  
Nonlinear Equations Of Motion ◽  
Tip Mass ◽  
Sinusoidal Excitation

The dynamic response of a beam-tip mass-pendulum system subjected to a sinusoidal excitation is investigated. A simple pendulum mounted to a tip mass of a beam is used as a vibration absorber. The nonlinear equations of motion are developed to investigate the autoparametric interaction between the first two modes of the system. The nonlinear terms appear due to the curvature of the beam and the coupling effect between the beam and pendulum. Complete energy transfer between modes is shown to occur when the beam frequency is twice the pendulum frequency. Experimental results are compared with a theoretical solution obtained using numerical integration. The experimental results are in qualitative agreement with the theory.

A Fluid Film Squeezed Between Two Rotating Parallel Plane Surfaces

1985 ◽  
Vol 107 (1) ◽  
pp. 110-115 ◽  
Author(s):  
E. A. Hamza
Keyword(s):  
Numerical Solution ◽  
Nonlinear Equations ◽  
Load Capacity ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
Parallel Plane ◽  
Fluid Film ◽  
Inertial Forces ◽  
Nonlinear Equations Of Motion ◽  
Radial Outflow

This paper is concerned with the motion of a fluid film squeezed between two rotating parallel plane surfaces. Attention is given to the case of impulsive squeezing and impulsive rotation. Approximate analytic solutions are obtained and a numerical solution to the full nonlinear equations of motion is presented. The results show that the centrifugal inertial forces increase the radial outflow and reduce considerably the load capacity while the noncentrifugal inertial forces increase the torque.

Nonlinear Bending-Torsion Flutter of a Cantilever Wing Subjected to Parametric Excitation

2005 ◽  
Author(s):  
R. A. Ibrahim ◽  
S. C. Castravete
Keyword(s):  
Parametric Excitation ◽  
Multiple Scales ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Air Flow ◽  
Parametric Instability ◽  
Flow Speed ◽  
Nonlinear Bending ◽  
Nonlinear Flutter ◽  
Nonlinear Equations Of Motion

This study deals with the nonlinear flutter of a cantilever wing in the absence and presence of parametric excitation that acts in the plane of highest rigidity. The nonlinear equations of motion in the presence of an incompressible fluid flow are derived using Hamilton’s principle. The regions of parametric instability are obtained for different values of flow speed. In the neighborhood of combination parametric resonance, the nonlinear response is determined using the multiple scales method for different values of flow speed. In the absence of parametric excitations, numerical simulation is performed for flow speeds at the critical flutter speed. It is found that the nonlinear flutter of the two modes depends on initial conditions, and exhibits symmetric periodic oscillations. Under parametric excitation and in the absence of air flow, each mode oscillates at its own natural frequency. In the presence of air flow, the two modes possess the same frequency response. Depending on the flow speed the response could be periodic, quasi-periodic, or chaotic.

Vibration Control of the Flexible Robotic Arm through Modal Interaction

2014 ◽  
Vol 490-491 ◽  
pp. 1142-1145
Author(s):  
Zhi Hui Gao ◽  
Bing Dong Liu ◽  
Bo Shan
Keyword(s):  
Vibration Control ◽  
Control Method ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Rigid Motion ◽  
Robotic Arm ◽  
Vibration Absorber ◽  
Modal Interaction ◽  
Flexible Arm ◽  
Nonlinear Equations Of Motion

A vibration control method is proposed to suppress nonlinear large vibration of the flexible robotic arm undergoing rigid motion. The method takes advantage of modal interaction and is implemented based on internal resonance. To attenuate vibration of the flexible arm, another vibrating system, consisting of a rigid link, a flexible joint and a damper, is introduced as a vibration absorber. Perturbation technique is used to study the transient response of the nonlinear equations of motion. Numerical simulation results preliminarily verify that the proposed control strategy is able to effectively reduce vibration of the flexible robotic arm.

Design of a slender turning cutting tool via a vibration absorber equipped with piezoelectric ceramic

2021 ◽  
pp. 107754632110144
Author(s):  
Yiqing Yang ◽  
Haoyang Gao ◽  
Qiang Liu
Keyword(s):  
Piezoelectric Ceramic ◽  
Cutting Tool ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Electrical Energy ◽  
Diameter Ratio ◽  
Vibration Absorber ◽  
Machined Surface ◽  
Structural Part ◽  
Machined Surface Roughness

Turning cutting tool with large length–diameter ratio has been essential when machining structural part with deep cavity and in-depth hole features. However, chatter vibration is apt to occur with the increase of tool overhang. A slender turning cutting tool with a length–diameter ratio of 7 is developed by using a vibration absorber equipped with piezoelectric ceramic. The vibration absorber has dual functions of vibration transfer to the absorber mass and vibration conversion to the electrical energy via the piezoelectric effect. Equations of motion are established considering the dual damping from the piezoelectric ceramic and rubber gasket. The equivalent damping of piezoelectric ceramic is derived, and the geometries are optimized to achieve optimal vibration suppression. The modal analysis demonstrates that the cutting tool with the vibration absorber can reach 80.1% magnitude reduction. Machining tests are carried out in the end. The machining acceleration and machined surface roughness validate the vibration suppression of the VA, and the output voltage by the piezoelectric ceramic demonstrates the ability of vibration sensing.

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.

Rolling Bearing Parametric Excitation of a Jeffcott Rotor System

2020 ◽  
Author(s):  
Ghasem Ghannad Tehrani ◽  
Chiara Gastaldi ◽  
Teresa Maria Berruti
Keyword(s):  
Parametric Excitation ◽  
Rotational Speed ◽  
Input Parameter ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Mean Value ◽  
Hertzian Contact ◽  
Rolling Bearings ◽  
Jeffcott Rotor

Abstract Rolling bearings are still widely used in aeroengines. Whenever rotors are modeled, rolling bearing components are typically modeled using springs. In simpler models, this spring is considered to have a constant mean value. However, the rolling bearing stiffness changes with time due to the positions of the balls with respect to the load on the bearing, thus giving rise to an internal excitation known as Parametric Excitation. Due to this parametric excitation, the rotor-bearings system may become unstable for specific combinations of boundary conditions (e.g. rotational speed) and system characteristics (rotor flexibility etc.). Being able to identify these instability regions at a glance is an important tool for the designer, as it allows to discard since the early design stages those configurations which may lead to catastrophic failures. In this paper, a Jeffcott rotor supported and excited by such rolling bearings is used as a demonstrator. In the first step, the expression for the time–varying stiffness of the bearings is analytically derived by applying the Hertzian Contact Theory. Then, the equations of motion of the complete system are provided. In this study, the Harmonic Balance Method (HBM) is used to as an approximate procedure to draw a stability map, thus dividing the input parameter space, i.e. rotational speed and rotor physical characteristics, into stable and unstable regions.

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.

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