STABILITY CHART FOR UNSUPPORTED SQUARE TUNNELS IN HOMOGENEOUS UNDRAINED CLAY

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.

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Distribution of Sub and Super Harmonic Solution of Mathieu Equation Within Stable Zones

Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ◽

10.1115/detc2005-85391 ◽

2005 ◽

Author(s):

G. Nakhaie Jazar ◽

M. Mahinfalah ◽

M. Rastgaar Aagaah ◽

N. Mahmoudian

Keyword(s):

Spectral Density ◽

Periodic Solutions ◽

Mathieu Equation ◽

Stable Region ◽

Transition Curve ◽

Harmonic Solution ◽

The Third ◽

Power Spectral ◽

Stability Chart ◽

Spectral Density Method

The third stable region of the Mathieu stability chart, surrounded by one π-transition and one 2π-transition curve is investigated. It is known that the solution of Mathieu equation is either periodic or quasi-periodic when its parameters are within stable regions. Periodic responses occur when they are on a “splitting curve”. Splitting curves are within stable regions and are corresponding to coexisting of periodic curves where an instability tongue closes. Distributions of sub and super-harmonics, as well as quasi-periodic solutions are analyzed using power spectral density method.

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Developing coal pillar stability chart using logistic regression

International Journal of Rock Mechanics and Mining Sciences ◽

10.1016/j.ijrmms.2012.09.004 ◽

2013 ◽

Vol 58 ◽

pp. 55-60 ◽

Cited By ~ 38

Author(s):

R.K. Wattimena ◽

S. Kramadibrata ◽

I.D. Sidi ◽

M.A. Azizi

Keyword(s):

Logistic Regression ◽

Coal Pillar ◽

Pillar Stability ◽

Stability Chart

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Optimum Active Vehicle Suspensions With Actuator Time Delay

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1345530 ◽

2000 ◽

Vol 123 (1) ◽

pp. 54-61 ◽

Cited By ~ 35

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.

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

Journal of Applied Mechanics ◽

10.1115/1.4012049 ◽

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.

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A Theoretical Investigation of the Effect of the Stochasticity in the Material Properties on the Chatter Detection During Turning

Volume 8: 29th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2017-67900 ◽

2017 ◽

Cited By ~ 6

Author(s):

Henrik T. Sykora ◽

Daniel Bachrathy ◽

Gabor Stepan

Keyword(s):

White Noise ◽

Time Evolution ◽

Material Properties ◽

Discretization Method ◽

Chatter Detection ◽

Turning Process ◽

Stochastic Parameters ◽

Stability Chart ◽

The Moment ◽

Moment Stability

In this work the effect of the inhomogeneous material properties are investigated in regenerative turning processes by introducing white noise in the cutting coefficient. The model is a one degree of freedom linear delayed oscillator with stochastic parameters. A full discretization method is used to calculate the time evolution of the second moment to determine the moment stability of the turning process. The resultant stability chart is compared with the deterministic turning model.

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Stable islands in the stability chart of milling processes due to unequal tooth pitch

International Journal of Machine Tools and Manufacture ◽

10.1016/j.ijmachtools.2010.09.007 ◽

2011 ◽

Vol 51 (2) ◽

pp. 152-164 ◽

Cited By ~ 55

Author(s):

V. Sellmeier ◽

B. Denkena

Keyword(s):

Stability Chart ◽

The Stability

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

Journal of Mechanical Design ◽

10.1115/1.3453959 ◽

1978 ◽

Vol 100 (3) ◽

pp. 507-513 ◽

Cited By ~ 13

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.

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Stability chart of parametric vibrating systems using energy-rate method

International Journal of Non-Linear Mechanics ◽

10.1016/j.ijnonlinmec.2003.08.009 ◽

2004 ◽

Vol 39 (8) ◽

pp. 1319-1331 ◽

Cited By ~ 20

Author(s):

G.Nakhaie Jazar

Keyword(s):

Energy Rate ◽

Stability Chart ◽

Rate Method ◽

Vibrating Systems

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Surface Error and Stability Chart of Beam-Type Workpiece in Milling Processes

Volume 8: 28th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2016-59940 ◽

2016 ◽

Cited By ~ 1

Author(s):

Adam K. Kiss ◽

Daniel Bachrathy ◽

Gabor Stepan

Keyword(s):

Forced Vibration ◽

Tool Path ◽

High Surface ◽

Element Analysis ◽

Surface Location Error ◽

Excited Vibration ◽

Stability Chart ◽

Beam Type ◽

Regeneration Effect ◽

The Stability

In milling processes, the intermittent cutting force may lead to harmful vibrations. These vibrations are classified into two groups. One of them is the self excited vibration which comes from the loss of stability due to the regeneration effect and these vibrations lead to unacceptable chatter marks. The other one is the forced vibration which can lead to high Surface Location Error (SLE) in case of resonant spindle speeds. In this paper, the dynamics of the beam-type workpiece is considered which is modelled by means of Finite Element Analysis (FEA). Both the forced vibration and the stability properties are predicted along the tool path. The surface properties are computed on the stable regions of the stability chart which presents the chatter-free (stable) parameter domain as a function of the spindle speed and the tool path. The theoretical results are compared to the measured SLE and surface roughness.

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