Gyroscopic Drifts Associated With Rotational Vehicle Vibrations

1968 ◽  
Vol 35 (3) ◽  
pp. 553-559 ◽  
Author(s):  
R. A. Wenglarz ◽  
T. R. Kane
Keyword(s):  
Digital Computer ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Arbitrary Orientation ◽  
Moving Vehicle ◽  
System Parameters ◽  
Drift Theory ◽  
Two Degree Of Freedom

Exact dynamical and kinematical equations governing motions of a two-degree-of-freedom gyroscope mounted on a moving vehicle are formulated. From these equations, a set of simpler ones is derived by taking advantage of a number of experimentally verifiable facts, and this set is solved for a vehicle performing oscillations of small amplitude about an axis having an arbitrary orientation. The validity of the resulting drift theory is established by comparing its predictions with those of digital computer solutions of the exact equations of motion, and formulas relating drift rates to system parameters are presented.

Nonlinear Dynamic of Cantilever Functionally Graded Plates Under the Thermalmechanical Loads

2009 ◽  
Author(s):  
Yu-xin Hao ◽  
Wei Zhang ◽  
Jian-hua Wang
Keyword(s):  
Nonlinear System ◽  
Functionally Graded Materials ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Governing Equations ◽  
Graded Materials ◽  
Two Degree Of Freedom

An analysis on nonlinear dynamic of a cantilevered functionally graded materials (FGM) plate which subjected to the transverse excitation in the uniform thermal environment is presented for the first time. Materials properties of the constituents are graded in the thickness direction according to a power-law distribution and assumed to be temperature dependent. In the framework of the Third-order shear deformation plate theory, the nonlinear governing equations of motion for the functionally graded materials plate are derived by using the Hamilton’s principle. For cantilever rectangular plate, the first two vibration mode shapes that satisfy the boundary conditions is given. The Galerkin’s method is utilized to discretize the governing equations of motion to a two-degree-of-freedom nonlinear system under combined thermal and external excitations. By using the numerical method, the two-degree-of-freedom nonlinear system is analyzed to find the nonlinear responses of the cantilever FGMs plate. The influences of the thermal environments on the nonlinear dynamic response of the cantilevered FGM plate are discussed in detail through a parametric study.

Determination of Gyroscopic Drifts Associated With Angular Support Motions

1970 ◽  
Vol 37 (2) ◽  
pp. 279-286
Author(s):  
R. A. Wenglarz
Keyword(s):  
Differential Equations ◽  
Digital Computer ◽  
Systematic Approach ◽  
Equations Of Motion ◽  
System Parameters ◽  
Constant Rate ◽  
Wide Range ◽  
Fixed Line

A previously proposed systematic approach for the analysis of gyroscopic drifts associated with angular support motions is further developed. For a wide range of support motions, the problem of determination of drifts is reduced to the evaluation of four integrals. The validity of the theory is tested by applying it to a gyroscope experiencing a constant rate about a fixed line and comparing the resulting predictions with those of digital computer solutions of the exact differential equations of motion, and formulas relating steady drifts to system parameters are presented.

Basic Study on the Seismic Response of the High-Speed-Moving Vehicle Considering Passengers' Dynamics

2012 ◽  
Vol 452-453 ◽  
pp. 1200-1204
Author(s):  
Atsuhiko Shintani ◽  
Tomohiro Ito ◽  
Yudai Iwasaki
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Seismic Excitations ◽  
Lagrangian Equation ◽  
Basic Study ◽  
Moving Vehicle ◽  
Seismic Input ◽  
The Stability ◽  
Risk Rate ◽  
Two Degree Of Freedom

The stability of the high-speed running vehicle subjected to seismic excitations considering passengers' dynamics are considered. A vehicle consists of one body, two trucks and four wheel sets. A passenger is modeled by simple two degree of freedom vibration system. The equations of motion of the vehicle and passengers are calculated by Lagrangian equation of motion. Combining two models, the behavior of the vehicle subjected to actual seismic input considering passengers' dynamics are calculated by numerical simulation. The stability of the vehicle is evaluated by using the risk rate of rollover. We investigate the possibility of the rollover of the vehicle. We focus on the effect of the dynamic characteristics of the human and the number of the passengers when the vehicle is subjected to the seismic excitation.

Flow-Induced Vibration of Long-Span Gates

2017 ◽  
pp. 294-386
Keyword(s):  
Vortex Shedding ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Full Scale ◽  
Degree Of Freedom ◽  
Theoretical Development ◽  
Flow Induced Vibration ◽  
Long Span ◽  
Free Discharge ◽  
Two Degree Of Freedom

In this chapter the theoretical equations for fluctuating pressures due to vertical and streamwise gate motions developed in Chapters 4 and 5 are used to derive equations of motion for long-span gates with underflow, overflow and simultaneous over- and underflow. Theoretical development of analysis methods is supported by laboratory and full-scale measurements. Specifically, this chapter considers long-span gate instabilities including one degree-of-freedom vibration of gates with underflow and free discharge, one degree-of-freedom vibration of a gate with submerged discharge and vortex shedding excitation, a two degree-of-freedom vibration of long-span gates with only underflow, and two degrees-of-freedom vibration of long-span gates with simultaneous over and underflow. A method is developed to predict pressure loading on the crest of the gate with overflow.

Dynamic Behavior of Vehicles Travelling on Bridges

1993 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Mehrdaad Ghorashi
Keyword(s):  
Boundary Conditions ◽  
Dynamic Behavior ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Parameter System ◽  
Moving Vehicle ◽  
Lumped Parameter ◽  
Euler Bernoulli Beam ◽  
Two Degree Of Freedom

Abstract An investigation into the dynamic behavior of a bridge with simply supported boundary conditions, carrying a moving vehicle, is performed. The vehicle has been modelled as a two degree of freedom lumped-parameter system travelling at a uniform speed. Furthermore, the bridge is assumed to obey the Euler-Bernoulli beam theory of vibration. This analysis may well be applied to a beam with different boundary conditions, but the computer simulation results given in this paper are set for only the case of freely hinged ends. Numerical solutions for the derived differential equations of motion are obtained and their close agreement, in some extreme cases, with those reported earlier by the authors are observed. Finally, the effect of speed on the maximum dynamic deflection of bridge is shown to be of much importance and hence an estimation for the critical speed of the vehicle is presented.

Coupled Nonlinear Barge Motions, Part I: Deterministic Models Development, Identification and Calibration

2005 ◽  
Vol 127 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Solomon C. S. Yim ◽  
Tongchate Nakhata ◽  
Warren A. Bartel ◽  
Erick T. Huang
Keyword(s):  
Guideline Development ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Body Motion ◽  
Physical Model Test ◽  
Random Wave ◽  
Deterministic Models ◽  
System Parameters ◽  
Hydrostatic Force ◽  
Force Moment

This paper focuses on the development of optimal deterministic, nonlinearly coupled barge motion models, identification of their system parameters, and calibration of their prediction capability using experimental results. The ultimate objective is to develop accurate yet sufficiently low degree-of-freedom stochastic models suitable for efficient probabilistic stability and reliability analyses of US Naval barges for preliminary design and operation guideline development (see Part II). First a three-degree-of-freedom (3DOF) fully coupled roll-heave-sway model, which features realistic and practical high-degree polynomial approximations of rigid body motion relations, hydrostatic and hydrodynamic force-moment specifically suitable for barges, is examined. The hydrostatic force-moment relationship includes effects of the barge’s sharp edge and combined roll-heave states, and the hydrodynamic terms are in a “Morison” type quadratic form. System parameters of the 3DOF model are identified using physical model test results from several regular wave cases. The predictive capability of the model is then calibrated using results from a random wave test case. Recognizing the negligible sway influence on coupled roll and heave motions and overall barge stability, and in an attempt to reduce anticipated stochastic computational efforts in stability analysis, a two-degree-of-freedom (2DOF) roll-heave model is derived by uncoupling sway from the roll-heave governing equations of motion. Time domain simulations are conducted using the 3DOF roll-heave-sway and the 2DOF roll-heave models for regular and random wave cases to validate the model assumptions and to assess their (numerical) prediction capabilities.

Vibration Control of Two-Degree-of-Freedom Structures Utilizing Sloshing in Nearly Square Tanks

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Shota Ninomiya
Keyword(s):  
Vibration Control ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Response Curves ◽  
Chaotic Motions ◽  
Installation Angle ◽  
Two Degree Of Freedom ◽  
Theoretical Results

This paper investigates the vibration control of a towerlike structure with degrees of freedom utilizing a square or nearly square tuned liquid damper (TLD) when the structure is subjected to horizontal, harmonic excitation. In the theoretical analysis, when the two natural frequencies of the two-degree-of-freedom (2DOF) structure nearly equal those of the two predominant sloshing modes, the tuning condition, 1:1:1:1, is nearly satisfied. Galerkin's method is used to derive the modal equations of motion for sloshing. The nonlinearity of the hydrodynamic force due to sloshing is considered in the equations of motion for the 2DOF structure. Linear viscous damping terms are incorporated into the modal equations to consider the damping effect of sloshing. Van der Pol's method is employed to determine the expressions for the frequency response curves. The influences of the excitation frequency, the tank installation angle, and the aspect ratio of the tank cross section on the response curves are examined. The theoretical results show that whirling motions and amplitude-modulated motions (AMMs), including chaotic motions, may occur in the structure because swirl motions and Hopf bifurcations, followed by AMMs, appear in the tank. It is also found that a square TLD works more effectively than a conventional rectangular TLD, and its performance is further improved when the tank width is slightly increased and the installation angle is equal to zero. Experiments were conducted in order to confirm the validity of the theoretical results.

CHAOS AND HYPERCHAOS IN SHAPE MEMORY SYSTEMS

2002 ◽  
Vol 12 (03) ◽  
pp. 645-657 ◽  
Author(s):  
M. A. SAVI ◽  
P. M. C. L. PACHECO
Keyword(s):  
Shape Memory ◽  
Intelligent Systems ◽  
Equations Of Motion ◽  
Memory Systems ◽  
Degree Of Freedom ◽  
Dynamical Analysis ◽  
Dimensional System ◽  
Shape Memory Actuators ◽  
Martensitic Phase Transformations ◽  
Two Degree Of Freedom

Shape memory and pseudoelastic effects are thermomechanical phenomena associated with martensitic phase transformations, presented by shape memory alloys. The dynamical analysis of intelligent systems that use shape memory actuators involves a multi-degree of freedom system. This contribution concerns with the chaotic response of shape memory systems. Two different systems are considered: a single and a two-degree of freedom oscillator. Equations of motion are formulated assuming a polynomial constitutive model to describe the restitution force of oscillators. Since equations of motion of the two-degree of freedom oscillator are associated with a five-dimensional system, the analysis is performed considering two oscillators, both with single-degree of freedom, connected by a spring-dashpot system. With this assumption, it is possible to analyze the transmissibility of motion between two oscillators. Results show some relation between the transmissibility of order, chaos and hyperchaos with temperature.

Vibrations of Dynamical Systems With Quadratic Nonlinearities

1965 ◽  
Vol 32 (3) ◽  
pp. 576-582 ◽  
Author(s):  
P. R. Sethna
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Method ◽  
Degree Of Freedom ◽  
System Parameters ◽  
Quadratic Nonlinearities ◽  
The Stability ◽  
Physical Phenomena ◽  
Two Degree Of Freedom

General two-degree-of-freedom dynamical systems with weak quadratic nonlinearities are studied. With the aid of an asymptotic method of analysis a classification of these systems is made and the more interesting subclasses are studied in detail. The study includes an examination of the stability of the solutions. Depending on the values of the system parameters, several different physical phenomena are shown to occur. Among these is the phenomenon of amplitude-modulated motions with modulation periods that are much larger than the periods of the excitation forces.

Gain-scheduled flight control via two-degree-of-freedom H∞ optimization

1997 ◽  
Vol 211 (4) ◽  
pp. 263-268 ◽  
Author(s):  
D J Walker
Keyword(s):  
Flight Control ◽  
Equations Of Motion ◽  
Linear Interpolation ◽  
Gain Scheduling ◽  
Degree Of Freedom ◽  
Nonlinear Simulation ◽  
On Line ◽  
Air Speed ◽  
Gain Scheduled ◽  
Two Degree Of Freedom

The gain scheduling of a multivariable controller designed using H∞ optimization is presented. The design uses a two-degree-of-freedom H∞ optimization based on five linearizations taken from the non-linear rigid body equations of motion of a helicopter over the range 0–80 knots. The scheduled controller's parameters were computed on-line by linear interpolation with air speed of the design parameter sets. The resulting controller schedule was tested using a sophisticated and representative nonlinear simulation.

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