Stability of a Simply-Supported Beam Subjected to Randomly Spaced Moving Loads

1978 ◽  
Vol 100 (3) ◽  
pp. 507-513 ◽  
Author(s):  
M. Kurihara ◽  
T. Shimogo
Keyword(s):  
Elastic Beam ◽  
Inertia Force ◽  
Moving Loads ◽  
Simply Supported ◽  
Stability Chart ◽  
Vibration Problems ◽  
Load Sequence ◽  
Analytical Result ◽  
The Stability ◽  
Input Load

In this paper, vibration problems of a simply-supported elastic beam subjected to randomly spaced moving loads with a uniform speed are treated under the assumption that the input load sequence is a Poisson process. In the case in which the inertial effect of moving loads is taken into account, the stability problem relating to the speed and the mass of loads is dealt with, considering the inertia force, the centrifugal force, and the Coriolis force of the moving loads. As an analytical result a stability chart of the mean-squared deflection was obtained for the moving speed and the moving masses.

Vibration of an Elastic Beam Subjected to Discrete Moving Loads

1978 ◽  
Vol 100 (3) ◽  
pp. 514-519 ◽  
Author(s):  
M. Kurihara ◽  
T. Shimogo
Keyword(s):  
Spectral Density ◽  
Poisson Process ◽  
Time History ◽  
Elastic Beam ◽  
Moving Loads ◽  
Simply Supported ◽  
Power Spectral ◽  
Vibration Problems ◽  
Load Sequence ◽  
Input Load

In this paper, vibration problems of a simply-supported elastic beam subjected to randomly spaced moving loads with a uniform speed are treated under the assumption that the input load sequence is a Poisson process. In the case in which the inertial effect of moving loads is neglected, the time history, the power spectral density, and the various moments of the response are examined and the effects of the speed of moving loads upon the beam are made clear.

Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Classical Problem ◽  
Moment Of Inertia ◽  
Model Parameters ◽  
Stability Chart ◽  
The Stability ◽  
Transition Curves ◽  
Minimum Moment ◽  
Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

scholarly journals Driving Torque Model and Accuracy Test of Multilink High-Speed Punch

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Fuxing Li ◽  
Hao Liu ◽  
Menglei Li ◽  
Jun Guo ◽  
Xinjian Lu ◽  
...  
Keyword(s):  
High Speed ◽  
Calculation Model ◽  
Effective Control ◽  
Inertia Force ◽  
Conservation Of Energy ◽  
Accuracy Test ◽  
Operation Stability ◽  
Strategy Planning ◽  
The Stability ◽  
Driving Torque

Inertia force is an important factor for operation stability and stamping precision of high-speed punch; adjusting drive torque of high-speed punch can realize effective control of inertia force. In this paper, a kind of 600 KN multilink high-speed punch inertia force balancing mechanism was designed. The calculation model of ideal inertia force was proposed based on conservation of energy and numerical analysis method. In addition, the calculation model of ideal driving torque were analyzed, simplified, and corrected by using numerical calculation and simulation methods, which solved the problem of controlling inertia force from the perspective of driving torque and realized the stability strategy planning of high-speed multilink punch press. Finally, the proposed ideal driving torque calculation model was simulated and verified by ADAMAS and bottom-dead-point accuracy test was carried out.

scholarly journals Vibrations of an Elastic Beam Subjected by Two Kinds of Moving Loads and Positioned on a Foundation having Fractional Order Viscoelastic Physical Properties

2021 ◽  
Author(s):  
Lionel Merveil Anague Tabejieu ◽  
Blaise Roméo Nana Nbendjo ◽  
Giovanni Filatrella
Keyword(s):  
Physical Properties ◽  
Fractional Order ◽  
Elastic Beam ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Moderate Increase ◽  
Moving Loads ◽  
Resonant Amplitude ◽  
Wind Turbulence ◽  
And Shifts

The present chapter investigates both the effects of moving loads and of stochastic wind on the steady-state vibration of a first mode Rayleigh elastic beam. The beam is assumed to lay on foundations (bearings) that are characterized by fractional-order viscoelastic material. The viscoelastic property of the foundation is modeled using the constitutive equation of Kelvin-Voigt type, which contain fractional derivatives of real order. Based to the stochastic averaging method, an analytical explanation on the effects of the viscoelastic physical properties and number of the bearings, additive and parametric wind turbulence on the beam oscillations is provided. In particular, it is found that as the number of bearings increase, the resonant amplitude of the beam decreases and shifts towards larger frequency values. The results also indicate that as the order of the fractional derivative increases, the amplitude response decreases. We are also demonstrated that a moderate increase of the additive and parametric wind turbulence contributes to decrease the chance for the beam to reach the resonance. The remarkable agreement between the analytical and numerical results is also presented in this chapter.

Optimum Active Vehicle Suspensions With Actuator Time Delay

2000 ◽  
Vol 123 (1) ◽  
pp. 54-61 ◽  
Author(s):  
Nader Jalili ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Wide Band ◽  
Fixed Time ◽  
Realistic Model ◽  
Vertical Acceleration ◽  
Band Frequency ◽  
The Road ◽  
Stability Chart ◽  
The Stability

A new approach to optimal control of vehicle suspension systems, incorporating actuator time delay, is presented. The inclusion of time delay provides a more realistic model for the actuators, and the problem is viewed from a different perspective rather than the conventional optimal control techniques. The objective here is to select a set of feedback gains such that the maximum vertical acceleration of the sprung mass is minimized, over a wide band frequency range and when subjected to certain constraints. The constraints are dictated by the vehicle stability characteristics and the physical bounds placed on the feedback gains. Utilizing a Simple Quarter Car model, the constrained optimization is then carried out in the frequency domain with the road irregularities described as random processes. Due to the presence of the actuator time delay, the characteristic equation is found to be transcendental rather than algebraic, which makes the stability analysis relatively complex. A new scheme for the stability chart strategy with fixed time delay is introduced in order to address the stability issue. The stability characteristics are also verified utilizing other conventional methods such as the Michailov technique. Results demonstrate that the suspension system, when considering the effect of the actuator time delay, exhibits a completely different behavior.

Linear Dynamics of an Elastic Beam Under Moving Loads

2000 ◽  
Vol 122 (3) ◽  
pp. 281-289 ◽  
Author(s):  
G. Visweswara Rao
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Moving Load ◽  
Mass Parameter ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Mass Effect ◽  
Moving Loads ◽  
Parameter Ratio ◽  
Load Mass

The dynamic response of an Euler-Bernoulli beam under moving loads is studied by mode superposition. The inertial effects of the moving load are included in the analysis. The time-dependent equations of motion in modal space are solved by the method of multiple scales. Instability regions of parametric resonance are identified and the moving mass effect is shown to significantly affect the transient response of the beam. Importance of modal interaction arising out of the possible internal resonance is highlighted. While the external resonance is due to the gravity effects of the moving load, the parametric and internal resonance solely depends on the load mass parameter—ratio of the moving load mass to the beam mass. Numerical results show the influence of the load inertia terms on the beam response under either a single moving load or a series of moving loads. [S0739-3717(00)01703-7]

On the Natural Modes and Their Stability in Nonlinear Two-Degree-of-Freedom Systems

1959 ◽  
Vol 26 (3) ◽  
pp. 377-385
Author(s):  
R. M. Rosenberg ◽  
C. P. Atkinson
Keyword(s):  
Free Vibrations ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Natural Modes ◽  
Theoretical Predictions ◽  
Stability Chart ◽  
The Stability ◽  
Two Parameters ◽  
Two Degree Of Freedom

Abstract The natural modes of free vibrations of a symmetrical two-degree-of-freedom system are analyzed theoretically and experimentally. This system has two natural modes, one in-phase and the other out-of-phase. In contradistinction to the comparable single-degree-of-freedom system where the free vibrations are always orbitally stable, the natural modes of the symmetrical two-degree-of-freedom system are frequently unstable. The stability properties depend on two parameters and are easily deduced from a stability chart. For sufficiently small amplitudes both modes are, in general, stable. When the coupling spring is linear, both modes are always stable at all amplitudes. For other conditions, either mode may become unstable at certain amplitudes. In particular, if there is a single value of frequency and amplitude at which the system can vibrate in either mode, the out-of-phase mode experiences a change of stability. The experimental investigation has generally confirmed the theoretical predictions.

Vibration of Beam-Mass Systems With Time-Dependent Boundary Conditions

1959 ◽  
Vol 26 (3) ◽  
pp. 353-356
Author(s):  
T. C. Yen ◽  
S. Kao
Keyword(s):  
Boundary Conditions ◽  
Laplace Transforms ◽  
Time Dependent ◽  
Simply Supported ◽  
Vibration Problems ◽  
Fixed End

Abstract Vibration problems of beams with time-dependent boundary conditions are solved by the method of Laplace transforms. The problems treated include the simply supported, cantilevered, and fixed beams carrying a single arbitrarily placed mass; two equal masses symmetrically placed on a simply supported or fixed-end beam and a beam carrying a mass at the center and two equal masses at tips, striking a spring.

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