scholarly journals Geometrically exact planar Euler-Bernoulli beam and time integration procedure for multibody dynamics

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Carlo Sansour ◽  
Tien Long Nguyen ◽  
Mohammed Hjiaj ◽  
Sophy Chhang
Keyword(s):  
Multibody Dynamics ◽  
Time Integration ◽  
Bernoulli Beam ◽  
Integration Procedure ◽  
Euler Bernoulli Beam

scholarly journals Multibody Dynamics of Nonsymmetric Planar 3PRR Parallel Manipulator with Fully Flexible Links

2020 ◽  
Vol 10 (14) ◽  
pp. 4816 ◽  
Author(s):  
Abdur Rosyid ◽  
Bashar El-Khasawneh
Keyword(s):  
Boundary Conditions ◽  
Multibody Dynamics ◽  
Parallel Manipulator ◽  
Flexible Multibody Dynamics ◽  
Elastic Displacement ◽  
Bernoulli Beam ◽  
Finite Element Approximations ◽  
Different Types ◽  
Floating Frame ◽  
Euler Bernoulli Beam

This paper presents the implementation of the floating frame of reference formulation to model the flexible multibody dynamics of a nonsymmetric planar 3PRR parallel manipulator. All of the links, including the moving platform, of the manipulator under study are assumed flexible whereas the joints are assumed rigid. Using the Euler-Bernoulli beam, the flexibility of the links is modeled by using the Rayleigh-Ritz and finite element approximations. In both approximations, fixed-free boundary conditions are applied to the elastic coordinates of the links. These boundary conditions enable the evaluation of the elastic displacement at a link tip coincident with the end-effector of the manipulator which is of interest in the high precision robotics application. Both the approximations were compared by applying two different types of loads to the manipulator. It is shown that the elastic displacements obtained by using both the approximations have an agreement with a slight difference in the magnitude. In addition, the sensitivity analysis shows that the rigidity of the manipulator is much affected by the in-plane depth of the manipulator links’ cross section.

Research on Dynamic Response of Bridge Subjected to Kinds of Load

2012 ◽  
Vol 256-259 ◽  
pp. 1601-1604
Author(s):  
Guang Cai Han ◽  
Yan Hong Wu ◽  
Fu Guo Bian ◽  
Chao Liu
Keyword(s):  
Integration Method ◽  
Moving Load ◽  
Time Integration ◽  
Bernoulli Beam ◽  
Harmonic Force ◽  
Lower Velocity ◽  
Time Integration Method ◽  
Precise Time Integration ◽  
Euler Bernoulli Beam ◽  
Precise Time

A vehicle-bridge system is simplified as a model of Euler-Bernoulli beam subjected to kinds of load. Dynamic behavior of the beam is researched in this paper. Several equations of the beam traversed by static or moving load and mass are given. Some of these equations are time-varying nonlinear. In order to avoid the problem of instability solving the equations, precise time integration method is used. Results show that the transversal deflection of the mid-span of the beam is greater when a harmonic force or a mass is traveling on the bridge at a lower velocity or by accelerating.

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.

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