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.

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.

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.

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