scholarly journals Track Model with Nonlinear Elastic Characteristic of the Rubber Rail Pad

2021 ◽  
Vol 58 (3) ◽  
pp. 84-98
Author(s):  
Traian Mazilu ◽  
Sorin Arsene ◽  
Ioan-Cristian Cruceanu
Keyword(s):  
Time Constant ◽  
Elastic Characteristic ◽  
Harmonic Component ◽  
Constant Component ◽  
Bernoulli Beam ◽  
Reflected Waves ◽  
Rail Deflection ◽  
Elastic Layers ◽  
Nonlinear Elastic ◽  
Euler Bernoulli Beam

This paper presents a new basic nonlinear track model consisting of an infinite Euler-Bernoulli beam (rail) resting on continuous foundation with two elastic layers (rail pad and ballast bed) and intermediate inertial layer (sleepers). The two elastic layers have bilinear elastic characteristic obtained from the load-displacement characteristic of the rail pad and ballast. A time-varying load with two components - time-constant one and harmonic other, representing the wheel/rail contact force is considered as the track model input. Rail deflection due to the time-constant component of the load is obtained solving the nonlinear equations of the balance position. Subsequently, the structure of the nonhomogeneous foundation is determined. Dynamic rail response in terms of receptance due to the harmonic component of the load is calculated using the linearised track model with nonhomogeneous elastic characteristic. Influence of the time-constant component and the reflected waves due to the nonhomogeneous foundation are presented.

Optimal Vibration Feedback Control of an Euler-Bernoulli Beam: Toward Realization of the Active Sink Method

1999 ◽  
Vol 121 (2) ◽  
pp. 174-182 ◽  
Author(s):  
N. Tanaka ◽  
Y. Kikushima
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Control Point ◽  
Control Law ◽  
Bernoulli Beam ◽  
Control Laws ◽  
Reflected Waves ◽  
Feedback Control Systems ◽  
Active Wave ◽  
Euler Bernoulli Beam

This paper discusses the optimal vibration feedback control of an Euler-Bernoulli beam from a viewpoint of active wave control making all structural modes inactive (more than suppressed). Using a transfer matrix method, the paper derives two kinds of optimal control laws termed “active sink” which inactivates all structural modes; one obtained by eliminating reflected waves and the other by transmitted waves at a control point. Moreover, the characteristic equation of the active sink system is derived, the fundamental properties being investigated. Towards the goal of implementing the optimal control law that is likely to be non-causal, a “classical” velocity feedback control law (Balas, 1979) widely used in a vibration control engineering is applied, revealing a substantial shortcoming. Introduction of a “classical” displacement feedback to the velocity is found to realize the optimal control law in a restricted frequency range. Finally, two kinds of stability verification for closed feedback control systems are presented for distributed parameter structures.

Tuning Stiffness Nonlinearity: Theory and Applications

2020 ◽  
Author(s):  
Mohamed Zanaty ◽  
Ilan Vardi ◽  
Simon Henein
Keyword(s):  
Compliant Mechanisms ◽  
Real Life ◽  
Beam Theory ◽  
Elastic Behavior ◽  
Bernoulli Beam ◽  
Stiffness Constant ◽  
Real Life Situation ◽  
Tuning Methods ◽  
Nonlinear Elastic ◽  
Euler Bernoulli Beam

Abstract Perfect elasticity is not achievable in real-life situation, so spring stiffness is not perfectly constant. In this paper, we study the effect of modifying non-linear stiffness terms while keeping the nominal stiffness constant. We introduce three methods to design and tune linear and nonlinear elastic behavior in the context of compliant mechanisms and we present mechanical realizations. These designs are modeled using Euler-Bernoulli beam theory. Numerical simulation and experimental measurement show a good match with the theoretical model. We then present applications of our stiffness tuning methods to mechanical meta-materials, mechanical resonators, and mechanical computation.

LMI-based hybrid temporal-spatial differential control design for a class of Euler-Bernoulli beam system

2021 ◽  
pp. 095440622110036
Author(s):  
Jiaqi Zhong ◽  
Xiaolei Chen ◽  
Yupeng Yuan ◽  
Jiajia Tan
Keyword(s):  
Vibration Suppression ◽  
Direct Method ◽  
Recursive Algorithm ◽  
Linear Matrix ◽  
Bernoulli Beam ◽  
Hybrid Controller ◽  
Beam System ◽  
Active Vibration ◽  
Differential Control ◽  
Euler Bernoulli Beam

This paper addresses the problem of active vibration suppression for a class of Euler-Bernoulli beam system. The objective of this paper is to design a hybrid temporal-spatial differential controller, which is involved with the in-domain and boundary actuators, such that the closed-loop system is stable. The Lyapunov’s direct method is employed to derive the sufficient condition, which not only can guarantee the stabilization of system, but also can improve the spatial cooperation of actuators. In the framework of the linear matrix inequalities (LMIs) technology, the gain matrices of hybrid controller can obtained by developing a recursive algorithm. Finally, the effectiveness of the proposed methodology is demonstrated by applying a numerical simulation.

Employing Surface Roughness for Bridge-Vehicle Interaction Based Damage Detection

2011 ◽  
Author(s):  
Vesna Jaksic ◽  
Vikram Pakrashi ◽  
Alan O’Connor
Keyword(s):  
Surface Roughness ◽  
Damage Detection ◽  
Flexural Rigidity ◽  
Single Point ◽  
Point Load ◽  
Ride Quality ◽  
Breathing Crack ◽  
Bernoulli Beam ◽  
Statistical Parameters ◽  
Euler Bernoulli Beam

Damage detection and Structural Health Monitoring (SHM) for bridges employing bridge-vehicle interaction has created considerable interest in recent times. In this regard, a significant amount of work is present on the bridge-vehicle interaction models and on damage models. Surface roughness on bridges is typically used for detailing models and analyses are present relating surface roughness to the dynamic amplification of response of the bridge, the vehicle or to the ride quality. This paper presents the potential of using surface roughness for damage detection of bridge structures through bridge-vehicle interaction. The concept is introduced by considering a single point observation of the interaction of an Euler-Bernoulli beam with a breathing crack traversed by a point load. The breathing crack is treated as a nonlinear system with bilinear stiffness characteristics related to the opening and closing of crack. A uniform degradation of flexural rigidity of an Euler-Bernoulli beam traversed by a point load is also considered in this regard. The surface roughness of the beam is essentially a spatial representation of some spectral definition and is treated as a broadband white noise in this paper. The mean removed residuals of beam response are analyzed to estimate damage extent. Uniform velocity and acceleration conditions of the traversing load are investigated for the appropriateness of use. The detection and calibration of damage is investigated through cumulant based statistical parameters computed on stochastic, normalized responses of the damaged beam due to passages of the load. Possibilities of damage detection and calibration under benchmarked and non-benchmarked cases are discussed. Practicalities behind implementing this concept are also considered.

Sign in / Sign up

Export Citation Format

Share Document