Dynamic Analysis of Coupled Vehicle-Bridge System with Uniformly Variable Speed

2016 ◽  
Vol 5 (3) ◽  
Author(s):  
Li Wei-zhen ◽  
Chen Chang-ping ◽  
Mao Yi-qi ◽  
Qian Chang-zhao
Keyword(s):  
Degrees Of Freedom ◽  
Inertia Force ◽  
Variable Speed ◽  
Vehicle Model ◽  
Response Curves ◽  
Mass System ◽  
Moving Vehicle ◽  
Dynamical Characteristics ◽  
Runge Kutta Method ◽  
Bridge System

AbstractIn this paper, a planar biaxial vehicle model with four degrees of freedom is presented based on spring-damping-mass system theory. By using Runge-Kutta method, the dynamic characteristics of a simply support bridge acting by moving vehicle with uniform variable speed are analyzed, and the effects of inertia force, relative acceleration and initial velocity are taken into consideration in the present research. The time-deflection response curves of the bridge under the variation of initial speed and acceleration are analyzed. Some valuable results are found which can provide a theoretical direction for the consideration of dynamical characteristics in design of bridge system.

Theoretical and Experimental Study of the Nonlinearly Coupled Heave, Pitch, and Roll Motions of a Ship in Longitudinal Waves

1993 ◽  
Author(s):  
I. G. Oh ◽  
A. H. Nayfeh ◽  
D. T. Mook
Keyword(s):  
Large Amplitude ◽  
Degrees Of Freedom ◽  
Excitation Frequency ◽  
Force Response ◽  
Governing Equations ◽  
Response Curves ◽  
Varying Coefficients ◽  
Jump Phenomena ◽  
Time Varying Coefficients ◽  
Three Degrees Of Freedom

Abstract The loss of dynamic stability and the resulting large-amplitude roll of a vessel in a head or following sea were studied theoretically and experimentally. A ship model with three degrees of freedom (roll, pitch, heave) was considered. The governing equations for the heave and pitch modes were linearized and their harmonic solutions were coupled with the nonlinear equation governing roll. The resulting equation, which has time-varying coefficients, was used to predict the response in roll. The principal parametric resonance was considered in which the excitation frequency is twice the natural frequency in roll. Force-response curves were obtained. The existence of jump phenomena and multiple stable solutions for the case of subcritical instability was observed in the experiments and found to be in good qualitative agreement with the results predicted by the theory. The experiments also revealed that the large-amplitude roll is dependent on the location of the model in the standing waves.

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

Vertical vibration modelling and vibration response analysis of Chinese high-speed train passengers at different locations of a high-speed train

2020 ◽  
Vol 235 (1) ◽  
pp. 35-46 ◽  
Author(s):  
Chun-jun Chen ◽  
Chao Fang ◽  
Guo-qing Qu ◽  
Zhi-ying He
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Vibration Signal ◽  
Vertical Vibration ◽  
Response Analysis ◽  
High Speed Train ◽  
Vehicle Model ◽  
Internal Organs ◽  
Damping Coefficients ◽  
Track Irregularity

To study the vibration of a passenger's head and internal organs at different locations of a high-speed train, a 9-degrees-of-freedom (DOF) model of seated passengers is proposed in this paper, and its parameters of the damping coefficients and stiffnesses are identified. Next, the response of the head and internal organs is simulated by applying the vibrational stimulation generated by a 27-DOF vehicle model under track irregularity. Moreover, by applying the measured vibration signal, the following conclusions can be drawn: (1) the weakest response is detected at the centre of the compartment of the wagon, and a stronger response is detected at the centre of the bogie, with the rolling motion having a greater effect 1 m away from the centre of the bogie; (2) the response of the human internal organs is stronger than that of the head under stimulation with a lower frequency of less than 3 Hz, and a similar conclusion can be drawn in the range of 5 to 8 Hz. However, if the frequency is in the range between 8 and 15 Hz, the situation is entirely different. The responses of both the head and internal organs are reduced at frequencies over 20 Hz; (3) from the real application, it can be inferred that the greatest response can be detected at approximately 3 Hz for internal organs and at 8 Hz or higher for the head.

Nonlinear Vibrations of a Beam-Spring-Large Mass System

2017 ◽  
Author(s):  
Mohammad A. Bukhari ◽  
Oumar R. Barry
Keyword(s):  
Natural Frequencies ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Large Mass ◽  
Mode Shapes ◽  
Resonance Excitation ◽  
Response Curves ◽  
Mass System ◽  
Spring System

This paper presents the nonlinear vibration of a simply supported Euler-Bernoulli beam with a mass-spring system subjected to a primary resonance excitation. The nonlinearity is due to the mid-plane stretching and cubic spring stiffness. The equations of motion and the boundary conditions are derived using Hamiltons principle. The nonlinear system of equations are solved using the method of multiple scales. Explicit expressions are obtained for the mode shapes, natural frequencies, nonlinear frequencies, and frequency response curves. The validity of the results is demonstrated via comparison with results in the literature. Exact natural frequencies are obtained for different locations, rotational inertias, and masses.

Stability and Bifurcation of Nonlinear Bearing-Flexible Rotor System with a Single Disk

2010 ◽  
Vol 148-149 ◽  
pp. 141-146
Author(s):  
Di Hei ◽  
Yong Fang Zhang ◽  
Mei Ru Zheng ◽  
Liang Jia ◽  
Yan Jun Lu
Keyword(s):  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Rotor System ◽  
Dynamic Responses ◽  
Flexible Rotor ◽  
Runge Kutta Method ◽  
Stability And Bifurcation ◽  
Single Disk ◽  
The Stability ◽  
Predictor Corrector

Dynamic model and equation of a nonlinear flexible rotor-bearing system are established based on rotor dynamics. A local iteration method consisting of improved Wilson-θ method, predictor-corrector mechanism and Newton-Raphson method is proposed to calculate nonlinear dynamic responses. By the proposed method, the iterations are only executed on nonlinear degrees of freedom. The proposed method has higher efficiency than Runge-Kutta method, so the proposed method improves calculation efficiency and saves computing cost greatly. Taking the system parameter ‘s’ of flexible rotor as the control parameter, nonlinear dynamic responses of rotor system are obtained by the proposed method. The stability and bifurcation type of periodic responses are determined by Floquet theory and a Poincaré map. The numerical results reveal periodic, quasi-periodic, period-5, jump solutions of rich and complex nonlinear behaviors of the system.

Full-State Feedback Control of a Variable-Speed Wind Turbine: A Comparison of Periodic and Constant Gains

2001 ◽  
Vol 123 (4) ◽  
pp. 319-326 ◽  
Author(s):  
Karl Stol ◽  
Mark Balas
Keyword(s):  
Wind Turbine ◽  
Degrees Of Freedom ◽  
State Feedback ◽  
State Feedback Control ◽  
Variable Speed ◽  
Horizontal Axis Wind Turbine ◽  
Speed Regulation ◽  
Significant Difference ◽  
Full State ◽  
Full State Feedback

An investigation of the performance of a model-based periodic gain controller is presented for a two-bladed, variable-speed, horizontal-axis wind turbine. Performance is based on speed regulation using full-span collective blade pitch. The turbine is modeled with five degrees-of-freedom; tower fore-aft bending, nacelle yaw, rotor position, and flapwise bending of each blade. An attempt is made to quantify what model degrees-of-freedom make the system most periodic, using Floquet modal properties. This justifies the inclusion of yaw motion in the model. Optimal control ideas are adopted in the design of both periodic and constant gain full-state feedback controllers, based on a linearized periodic model. Upon comparison, no significant difference in performance is observed between the two types of control in speed regulation.

Methods of Using a Vibratory System to Measure Small Rates of Turn

1969 ◽  
Vol 11 (5) ◽  
pp. 526-533 ◽  
Author(s):  
J. A. Linnett
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Exciting Force ◽  
Velocity Curve ◽  
Alternative Methods ◽  
Vibratory System ◽  
Mass System ◽  
The One ◽  
Good Agreement

The equations of motion for a vibratory two-degrees-of-freedom spring mass system subjected to rotation about an axis perpendicular to its plane of vibration are considered, taking into account the various couplings that may be present. The rate of turn can be measured by three alternative methods, two of which involve an exciting force in the sensing direction in addition to the one vibrating the system. The shape of the phase angle against angular velocity curve is shown to be independent of damping, enabling the transient performance to be improved without affecting the sensitivity of the device. Experimental work shows good agreement with the developed theory.

Sign in / Sign up

Export Citation Format

Share Document