Dynamic Stability of Nonlinear Antisymmetrically-Laminated Cross-Ply Rectangular Plates

1989 ◽  
Vol 56 (2) ◽  
pp. 375-381 ◽  
Author(s):  
Andrzej Tylikowski
Keyword(s):  
Asymptotic Stability ◽  
Dynamic Stability ◽  
Material Properties ◽  
Stability Problem ◽  
Large Deflection ◽  
Direct Method ◽  
Rectangular Plates ◽  
Stability Criteria ◽  
The Stability ◽  
Liapunov's Direct Method

The dynamic stability problem is solved for rectangular plates that are laminated antisymmetrically about their middle plane and compressed by time-dependent deterministic or stochastic membrane forces. Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov’s direct method. A relation between the stability of nonlinear equations and linearized ones is analyzed. An influence on the number of orthotropic layers, material properties for different classes of parametric excitation on stability domains is shown.

Dynamic Stability of Elastic Rotor-Bearing Systems via Liapunov’s Direct Method

1991 ◽  
Vol 58 (4) ◽  
pp. 1056-1063 ◽  
Author(s):  
Abd Alla El-Marhomy ◽  
A. L. Schlack
Keyword(s):  
Dynamic Stability ◽  
Direct Method ◽  
Stability Criteria ◽  
Rotor Bearing ◽  
Coupling Stiffness ◽  
Direct Stiffness ◽  
Instability Regions ◽  
Stiffness And Damping ◽  
General Method ◽  
Liapunov's Direct Method

A general method of analysis based on Liapunov’s direct method is presented for studying the dynamic stability of elastic rotor-bearing systems. A model comprised of a continuous elastic shaft mounted on two 8-coefficient bearings is used to develop closed-form (series) stability criteria involving system stiffness and damping parameters. It is quantitatively shown by means of graphs how the instability regions are reduced by (a) increasing the shaft dimensionless stiffness parameters, (b) increasing the bearing direct stiffness and damping parameters, and (c) decreasing the bearing cross-coupling stiffness and damping parameters.

scholarly journals Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao
Keyword(s):  
Asymptotic Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Stability Criteria ◽  
Differential Systems ◽  
Discrete Delays ◽  
Transcendental Equations ◽  
The Stability ◽  
Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

Dynamic Stability of Unidirectional Fiber-Reinforced Viscoelastic Composite Plates

1989 ◽  
Vol 42 (11S) ◽  
pp. S39-S47 ◽  
Author(s):  
N. K. Chandiramani ◽  
L. Librescu
Keyword(s):  
Shear Deformation ◽  
Dynamic Stability ◽  
Stability Problem ◽  
Micromechanical Model ◽  
Shear Deformation Theory ◽  
Constitutive Law ◽  
Fiber Reinforced ◽  
Viscoelastic Composite ◽  
Unidirectional Fiber ◽  
The Stability

This paper deals with a dynamic stability analysis of unidirectional fiber-reinforced composite viscoelastic plates subjected to compressive edge loads. The integrodifferential equations governing the stability problem are obtained by using, in conjunction with a Boltzmann hereditary constitutive law for a 3-D viscoelastic medium, a higher-order shear deformation theory of orthotropic plates. Such a theory incorporates transverse shear deformation, transverse normal stress, and rotatory inertia effects. The solution of the stability problem as considered within this paper concerns the determination of the critical in-plane edge loads yielding the asymptotic instability. Numerical applications, based on material properties derived within the framework of Aboudi’s micromechanical model, are presented and pertinent conclusions concerning the nature of the loss of stability and the influence of various parameters are outlined.

Asymptotic stability criteria for delay-differential equations

1988 ◽  
Vol 110 (1-2) ◽  
pp. 31-44
Author(s):  
L.C. Becker ◽  
T.A. Burton
Keyword(s):  
Differential Equations ◽  
Direct Method ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
State Variables ◽  
Stability Criteria ◽  
Bounded State ◽  
Functional Differential ◽  
Delay Differential ◽  
Liapunov's Direct Method

SynopsisThis paper is concerned with the problem of showing uniform stability and equiasymptotic stability of thezero solution of functional differential equations with either finite or infinite delay. The investigations are based on Liapunov's direct method and attention is focused on those equations whose right-hand sides are unbounded for bounded state variables.

Development of a Dynamic Stability Simulator for Articulated and Conventionaltractors Useful for Real-Time Safety Devices

2013 ◽  
Vol 394 ◽  
pp. 546-553 ◽  
Author(s):  
Fabrizio Mazzetto ◽  
Marco Bietresato ◽  
Renato Vidoni
Keyword(s):  
Real Time ◽  
Dynamic Stability ◽  
Stability Problem ◽  
Stability Index ◽  
Real Field ◽  
Circular Trajectory ◽  
Safety Devices ◽  
Test Platform ◽  
Agricultural Tractors ◽  
The Stability

The safety of agricultural tractors drivers is a very actual topic, especially when tractors operate on side slopes, such as in terraced vineyards. This work approaches the stability problem of articulated tractors by modelling, simulating and quantifying the safety of the driver with respect to both roll and pitch overturns. First of all, an articulated tractor has been modelled and simplified, after that a stability index has been defined and calculatedin several simulated slope conditions when the tractor travels along a circular trajectory; then, the obtained results have beencompared with respect to a conventional tractor. This work is a preliminary studyfor a tilting test platform for real vehicles, capable to reproduce real field conditions (slope, obstacles, roughness). Finally, some directives on how exploiting the obtained results for real-time safety devices have been formulated.

scholarly journals Boundary Criteria for the Stability of Delay Differential-Algebraic Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Leping Sun ◽  
Yuhao Cong
Keyword(s):  
Asymptotic Stability ◽  
Differential Algebraic Equations ◽  
Analytical Function ◽  
Algebraic Equations ◽  
Stability Criteria ◽  
Stability Regions ◽  
The Stability ◽  
Delay Differential

This paper is concerned with the asymptotic stability of delay differential-algebraic equations. Two stability criteria described by evaluating a corresponding harmonic analytical function on the boundary of a certain region are presented. Stability regions are also presented so as to show the method geometrically. Our results are not reported.

scholarly journals Obtaining approximate region of asymptotic stability by computer algebra: A case study

2002 ◽  
Vol 20 (1) ◽  
pp. 56 ◽  
Author(s):  
S Prakash ◽  
J Vanualailai ◽  
T Soma
Keyword(s):  
Asymptotic Stability ◽  
Computer Algebra ◽  
System Analysis ◽  
Direct Method ◽  
Quantifier Elimination ◽  
Optimization Method ◽  
Analysis And Design ◽  
The Stability ◽  
Computer Algebra Software

One of the classical problems in nonlinear control system analysis and design is to find a region of asymptotic stability by the Direct Method of Lyapunov. This paper tentatively shows, via a numercial example, that this problem can be easily solved using Quantifier Elimination (QE). In particular, if the governing equations are described by differential equations containing only polynomials, then the problem can be conveniently solved by a computer algebra software packages such as Qepcad or Redlog. In our case study, we use a simple Lyapunov function and Qepcad to estimate the stability region, and the results are verified by an optimization method based on Lagrange's method.

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