scholarly journals Stability of a suspension bridge with a localized structural damping

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zayd Hajjej ◽  
Mohammad Al-Gharabli ◽  
Salim Messaoudi
Keyword(s):  
Evolution Equation ◽  
Decay Rate ◽  
Suspension Bridge ◽  
Resonance Phenomenon ◽  
Structural Damping ◽  
Exponential Decay Rate ◽  
Nonlocal Evolution Equation ◽  
Bridge Collapse ◽  
Sudden Transition ◽  
Tacoma Narrows Bridge

<p style='text-indent:20px;'>Strong vibrations can cause lots of damage to structures and break materials apart. The main reason for the Tacoma Narrows Bridge collapse was the sudden transition from longitudinal to torsional oscillations caused by a resonance phenomenon. There exist evidences that several other bridges collapsed for the same reason. To overcome unwanted vibrations and prevent structures from resonating during earthquakes, winds, ..., features and modifications such as dampers are used to stabilize these bridges. In this work, we use a minimum amount of dissipation to establish exponential decay- rate estimates to the following nonlocal evolution equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_{tt}(x,y,t)+\Delta^2 u(x,y,t) - \phi(u) u_{xx}- \left(\alpha(x, y) u_{xt}(x,y,t)\right)_x = 0, $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>which models the deformation of the deck of either a footbridge or a suspension bridge.</p>

scholarly journals Stability of suspension bridge I: Aerodynamic and structural damping

1998 ◽  
Vol 4 (1) ◽  
pp. 73-98 ◽  
Author(s):  
N. U. Ahmed ◽  
H. Harbi
Keyword(s):  
Numerical Simulation ◽  
Decay Rate ◽  
Dynamic Models ◽  
Relative Effectiveness ◽  
Suspension Bridge ◽  
Viscous Damping ◽  
Structural Damping ◽  
High Wind ◽  
Linear And Nonlinear ◽  
The Stability

In this paper we consider a few dynamic models of suspension bridge described by partial differential equations with linear and nonlinear couplings. We study analytically the stability properties of these models and the relative effectiveness of aerodynamic and structural damping. Increasing aerodynamic or structural damping indefinitely does not necessarily increase the decay rate indefinitely. In view of possible disastrous effects of high wind, structural damping is preferable to aerodynamic (viscous) damping. These results are illustrated by numerical simulation.

scholarly journals Decision Theory and large deviations for dynamical hypotheses tests: The Neyman-Pearson Lemma, Min-Max and Bayesian tests

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hermes H. Ferreira ◽  
Artur O. Lopes ◽  
Silvia R. C. Lopes
Keyword(s):  
Decision Theory ◽  
Large Deviations ◽  
Sample Size ◽  
Decay Rate ◽  
Thermodynamic Formalism ◽  
Exponential Decay Rate ◽  
Log Likelihood ◽  
Two Measures ◽  
Classical Hypothesis ◽  
The Ideal

<p style='text-indent:20px;'>We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different Hölder Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is that here the two measures are singular with respect to each other. Among other objectives, we are interested in the decay rate of the wrong decisions probability, when the sample size <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> goes to infinity. We show a dynamical version of the Neyman-Pearson Lemma displaying the ideal test within a certain class of similar tests. This test becomes exponentially better, compared to other alternative tests, when the sample size goes to infinity. We are able to present the explicit exponential decay rate. We also consider both, the Min-Max and a certain type of Bayesian hypotheses tests. We shall consider these tests in the log likelihood framework by using several tools of Thermodynamic Formalism. Versions of the Stein's Lemma and Chernoff's information are also presented.</p>

scholarly journals Nonlinear Observer Design of the Generalized Rössler Hyperchaotic Systems via DIL Methodology

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Yeong-Jeu Sun
Keyword(s):  
Exponential Stability ◽  
Decay Rate ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Observer Design ◽  
Nonlinear Observer ◽  
State Observation ◽  
Exponential Decay Rate ◽  
Error System ◽  
Hyperchaotic Systems

The generalized Rössler hyperchaotic systems are presented, and the state observation problem of such systems is investigated. Based on the differential inequality with Lyapunov methodology (DIL methodology), a nonlinear observer design for the generalized Rössler hyperchaotic systems is developed to guarantee the global exponential stability of the resulting error system. Meanwhile, the guaranteed exponential decay rate can be accurately estimated. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of proposed approach.

Characterization of Contact Damping and Frequency in Elastic-Plastic Contact

2008 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Decay Rate ◽  
Closed Form ◽  
Natural Frequency ◽  
Compressive Load ◽  
Vibration Response ◽  
Elastic Plastic ◽  
Exponential Decay Rate ◽  
Damping Rate ◽  
Nonlinear Normal

Elastic-plastic interaction of a block of rough surface with a smooth plane is considered in this paper. The nonlinear normal vibration response of the block is examined when subject to an external compressive load. Free vibration response of the block is studied. The vibration response corresponds to the application of a constant compressive external load and the study yields closed-form equations for the contact damping rate and contact natural frequency. It is shown that vibration decay rate is constant as opposed to the exponential decay rate for the linear vibrating systems. Closed form equations relating contact damping rate and contact natural frequency to the surface parameters are given.

scholarly journals Assessment of Patellar Tendon Reflex Responses Using Second-Order System Characteristics

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
Brett D. Steineman ◽  
Pavan Karra ◽  
Kiwon Park
Keyword(s):  
Decay Rate ◽  
Natural Frequency ◽  
Patellar Tendon ◽  
Exponential Decay ◽  
Second Order ◽  
Order System ◽  
Sample Population ◽  
Exponential Decay Rate ◽  
Tendon Reflex ◽  
Patellar Tendon Reflex

Deep tendon reflex tests, such as the patellar tendon reflex (PTR), are widely accepted as simple examinations for detecting neurological disorders. Despite common acceptance, the grading scales remain subjective, creating an opportunity for quantitative measures to improve the reliability and efficacy of these tests. Previous studies have demonstrated the usefulness of quantified measurement variables; however, little work has been done to correlate experimental data with theoretical models using entire PTR responses. In the present study, it is hypothesized that PTR responses may be described by the exponential decay rate and damped natural frequency of a theoretical second-order system. Kinematic data was recorded from both knees of 45 subjects using a motion capture system and correlation analysis found that the meanR2value was 0.99. Exponential decay rate and damped natural frequency ranges determined from the sample population were −5.61 to −1.42 and 11.73 rad/s to 14.96 rad/s, respectively. This study confirmed that PTR responses strongly correlate to a second-order system and that exponential decay rate and undamped natural frequency are novel measurement variables to accurately measure PTR responses. Therefore, further investigation of these measurement variables and their usefulness in grading PTR responses is warranted.

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