scholarly journals Error propagation dynamics of velocimetry-based pressure field calculations (2): on the error profile

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Matthew Faiella ◽  
Corwin G. J. MacMillan ◽  
Jared Whitehead ◽  
Zhao Pan
Keyword(s):  
Error Propagation ◽  
Solid Mechanics ◽  
Pressure Field ◽  
Neumann Boundary ◽  
Significant Error ◽  
Bernoulli Beam ◽  
Error Profile ◽  
Data Field ◽  
The Difference ◽  
Euler Bernoulli Beam

This work investigates the propagation of error in a Velocimetry-based Pressure field reconstruction (VPressure) problem to determine and explain the effects of error profile of the data on the error propagation. The results discussed are an extension to those found in Pan et al. (2016). We first show how to determine the upper bound of the error in the pressure field, and that this worst scenario for error in the data field is unique and depends on the characteristics of the domain. We then show that the error propagation for a V-Pressure problem is analogous to elastic deformation in, for example, a Euler-Bernoulli beam or Kirchhoff-Love plate for one- and two-dimensional problems, respectively. Finally, we discuss the difference in error propagation near Dirichlet and Neumann boundary conditions, and explain the behavior using Green’s function and the solid mechanics analogy. The methods discussed in this paper will benefit the community in two ways: i) to give experimentalists intuitive and quantitative insights to design tests that minimize error propagation for a V-pressure problem, and ii) to create tests with significant error propagation for the benchmarking of V-Pressure solvers or algorithms. This paper is intended as a summary of recent research conducted by the authors, whereas the full work has been recently published (Faiella et al., 2021).

On the Curvature of an Euler–Bernoulli Beam

2003 ◽  
Vol 31 (2) ◽  
pp. 132-142 ◽  
Author(s):  
Osman Kopmaz ◽  
Ömer Gündoğdu
Keyword(s):  
Nonlinear Theory ◽  
Quantitative Assessment ◽  
Bending Moment ◽  
Point Of View ◽  
Bernoulli Beam ◽  
Cantilevered Beam ◽  
Single Moment ◽  
The Difference ◽  
Euler Bernoulli Beam ◽  
The Relationship

This paper deals with different approaches to describing the relationship between the bending moment and curvature of a Euler—Bernoulli beam undergoing a large deformation, from a tutorial point of view. First, the concepts of the mathematical and physical curvature are presented in detail. Then, in the case of a cantilevered beam subjected to a single moment at its free end, the difference between the linear theory and the nonlinear theory based on both the mathematical curvature and the physical curvature is shown. It is emphasized that a careless use of the nonlinear mathematical curvature and moment relationship given in most standard textbooks may lead to erroneous results. Furthermore, a numerical example is given for the reader to make a quantitative assessment.

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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