Stability Analysis of a Class of Interconnected Systems

1993 ◽  
Vol 115 (3) ◽  
pp. 546-551 ◽  
Author(s):  
E. Barbieri
Keyword(s):  
Decentralized Control ◽  
Cellular Structure ◽  
Interconnected Systems ◽  
Simple Test ◽  
Bernoulli Beam ◽  
The Stability ◽  
Mass Spring ◽  
Countably Infinite ◽  
Euler Bernoulli Beam ◽  
Infinite String

There exists a class of systems that is characterized by having a so called regular cellular structure or homogeneous interconnection. In this note, the bilateral Z-Transform is used to obtain a mathematical model parametrized by z and it is shown that the stability properties of the system can be more easily investigated by a simple test applied to the parametrized model. The analysis is illustrated via three examples: the heat equation, the Euler-Bernoulli beam, and decentralized control of a countably infinite string of interconnected mass-spring-damper systems.

Application of HOHWM in the stability analysis of nonlocal Euler-Bernoulli beam

2020 ◽  
Author(s):  
Subrat Kumar Jena ◽  
Snehashish Chakraverty ◽  
Mart Ratas ◽  
Maarjus Kirs
Keyword(s):  
Stability Analysis ◽  
Bernoulli Beam ◽  
The Stability ◽  
Euler Bernoulli Beam

Lyapunov-Based Vibration Control of Translational Euler-Bernoulli Beams Using the Stabilizing Effect of Beam Damping Mechanisms

2004 ◽  
Vol 10 (7) ◽  
pp. 933-961 ◽  
Author(s):  
Mohsen Dadfarnia ◽  
Nader Jalili ◽  
Bin Xian ◽  
Darren M. Dawson
Keyword(s):  
Equation Model ◽  
Bernoulli Beam ◽  
Differential Equation Model ◽  
Partial Differential Equation Model ◽  
Dissipation Mechanism ◽  
Beam Displacement ◽  
The Stability ◽  
Tip Mass ◽  
Euler Bernoulli Beam ◽  
Stability Results

A translational cantilevered Euler-Bernoulli beam with tip mass dynamics at its free end is used to study the effect of several damping mechanisms on the stabilization of the beam displacement. Specifically, a Lyapunov-based controller utilizing a partial differential equation model of the translational beam is developed to exponentially stabilize the beam displacement while the beam support is regulated to a desired set-point position. Depending on the composition of the tip mass dynamics assumption (i.e. body-mass, point-mass, or massless). it is shown that proper combination of different damping mechanisms (i.e. strain-rate, structural, or viscous damping) guarantees exponential stability of the beam displacement. This novel Lyapunov-based approach. which is based on the energy dissipation mechanism in the beam, brings new dimensions to the stabilization problem of translational beams with tip mass dynamics. The stability analysis utilizes relatively simple mathematical tools to illustrate the exponential and asymptotic stability results. The numerical results are presented to show the effectiveness of the controller.

An Investigation of Damping Mechanisms in Translational Euler-Bernoulli Beams Using a Lyapunov-Based Stability Approach

2003 ◽  
Author(s):  
Mohsen Dadfarnia ◽  
Nader Jalili ◽  
Darren M. Dawson
Keyword(s):  
Equation Model ◽  
Bernoulli Beam ◽  
Differential Equation Model ◽  
Partial Differential Equation Model ◽  
Dissipation Mechanism ◽  
Beam Displacement ◽  
The Stability ◽  
Tip Mass ◽  
Euler Bernoulli Beam ◽  
Stability Results

A translational cantilevered Euler-Bernoulli beam with tip mass dynamics at its free end is used to study the effect of several damping mechanisms on the stabilization of the beam displacement. Specifically, a Lyapunov-based controller utilizing a partial differential equation model of the translational beam is developed to exponentially stabilize the beam displacement while the beam support is regulated to a desired set-point position. Depending on the composition of the tip mass dynamics assumption (i.e. body-mass, point-mass, or massless), it is shown that proper combination of different damping mechanisms (i.e., strain-rate, structural, or viscous damping) guarantees exponential stability of the beam displacement. This novel Lyapunov-based approach, which is based on the energy dissipation mechanism in the beam, brings new dimensions to the stabilization problem of translational beams with tip mass dynamics. The stability analysis utilizes relatively simple mathematical tools to illustrate the exponential and asymptotic stability results. The numerical results are presented to show the effectiveness of the controller.

scholarly journals Dynamic analysis of railway bridges exposed to high-speed trains considering the vehicle–track–bridge–soil interaction

2021 ◽  
Author(s):  
Paul König ◽  
Patrick Salcher ◽  
Christoph Adam ◽  
Benjamin Hirzinger
Keyword(s):  
Dynamic Response ◽  
High Speed ◽  
Element Model ◽  
Bernoulli Beam ◽  
Railway Bridges ◽  
Modal Expansion ◽  
High Speed Trains ◽  
Mass Spring ◽  
Track Bridge ◽  
Euler Bernoulli Beam

AbstractA new semi-analytical approach to analyze the dynamic response of railway bridges subjected to high-speed trains is presented. The bridge is modeled as an Euler–Bernoulli beam on viscoelastic supports that account for the flexibility and damping of the underlying soil. The track is represented by an Euler–Bernoulli beam on viscoelastic bedding. Complex modal expansion of the bridge and track models is performed considering non-classical damping, and coupling of the two subsystems is achieved by component mode synthesis (CMS). The resulting system of equations is coupled with a moving mass–spring–damper (MSD) system of the passing train using a discrete substructuring technique (DST). To validate the presented modeling approach, its results are compared with those of a finite element model. In an application, the influence of the soil–structure interaction, the track subsystem, and geometric imperfections due to track irregularities on the dynamic response of an example bridge is demonstrated.

Hermite Reproducing Kernel Meshfree Thermal Buckling Analysis of Euler-Bernoulli Beams with Elastic Foundation

2014 ◽  
Vol 574 ◽  
pp. 85-88
Author(s):  
Chao Song ◽  
Ming Sun ◽  
Bo Ya Dong
Keyword(s):  
Elastic Foundation ◽  
Reproducing Kernel ◽  
Meshfree Method ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Bernoulli Beam ◽  
Meshfree Approximation ◽  
The Stability ◽  
Solution Accuracy ◽  
Euler Bernoulli Beam

The Hermite reproducing kernel meshfree method is employed for the stability analysis of Euler-Bernoulli beams with particular reference to the thermal buckling problem. This meshfree approximation employs both the nodal deflectional and rotational variables to construct the deflectional approximant according to the reproducing kernel conditions. In this paper, we apply this HRK meshfree method to the thermal buckling analysis of Euler-Bernoulli beam on elastic foundation. By comparison to the Gauss Integration method, HRK meshfree method shows much better solution accuracy.

Magnetoelastic Instability of a Long Graphene Nano-Ribbon Carrying Electric Current

2014 ◽  
Vol 6 (3) ◽  
pp. 299-306
Author(s):  
R. D. Firouz-Abadi ◽  
H. Mohammadkhani
Keyword(s):  
Electric Current ◽  
Governing Equation ◽  
Equation Of Motion ◽  
Current Strength ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Resonance Frequencies ◽  
The Stability ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

AbstractThis paper aims at investigating the resonance frequencies and stability of a long Graphene Nano-Ribbon (GNR) carrying electric current. The governing equation of motion is obtained based on the Euler-Bernoulli beam model along with Hamilton’s principle. The transverse force distribution on the GNR due to the interaction of the electric current with its own magnetic field is determined by the Biot-Savart and Lorentz force laws. Using Galerkin’s method, the governing equation is solved and the effect of current strength and dimensions of the GNR on the stability and resonance frequencies are investigated.

scholarly journals Dynamics and Stability of Stepped Gun-Barrels with Moving Bullets

2008 ◽  
Vol 2008 ◽  
pp. 1-6 ◽  
Author(s):  
Mohammad Tawfik
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Stability Region ◽  
Element Model ◽  
Simple Eigenvalue ◽  
Bernoulli Beam ◽  
Stability Boundaries ◽  
The Stability ◽  
Euler Bernoulli Beam ◽  
Lowest Eigenvalue

The stability of an Euler-Bernoulli beam under the effect of a moving projectile will be reintroduced using simple eigenvalue analysis of a finite element model. The eigenvalues of the beam change with the mass, speed, and position of the projectile, thus, the eigenvalues are evaluated for the system with different speeds and masses at different positions until the lowest eigenvalue reaches zero indicating the instability occurrence. Then a map for the stability region may be obtained for different boundary conditions. Then the dynamics of the beam will be investigated using the Newmark algorithm at different values of speed and mass ratios. Finally, the effect of using stepped barrels on the stability and the dynamics is going to be investigated. It is concluded that the technique used to predict the stability boundaries is simple, accurate, and reliable, the mass of the barrel on the dynamics of the problem cannot be ignored, and that using the stepped barrels, with small increase in the diameter, enhances the stability and the dynamics of the barrel.

Flow Induced Vibration and Critical Velocities

2011 ◽  
Author(s):  
Akindeji Ojetola ◽  
Noel Jordan Jameson ◽  
Hamid R. Hamidzadeh
Keyword(s):  
Nuclear Reactor ◽  
Aerospace Industry ◽  
Design Guidelines ◽  
Flow Density ◽  
Bernoulli Beam ◽  
Unstable Condition ◽  
Flow Induced Vibration ◽  
Critical Velocities ◽  
The Stability ◽  
Euler Bernoulli Beam

Flow induced instability has been observed in numerous fields, including the aerospace industry, nuclear reactor components and power generation/transmission. This paper considers the stability analysis of a cantilever pipe excited by the flow of fluid. The developed mathematical model can be used to determine a number of critical flow velocities where the instability may occur. The pipe is modeled as an Euler-Bernoulli beam by considering the effect of fluid mass and the Coriolis acceleration caused by the flow. The required mathematical procedure is presented and it is accompanied by a set of design guidelines for determining the stable and unstable condition for these structures. Parameters to be considered are velocity of the flow, density of the flow, and properties of the pipe as well as its geometry.

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