scholarly journals Scour monitoring of a bridge pier through eigenfrequencies analysis

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Mohamed Belmokhtar ◽  
Franziska Schmidt ◽  
Alireza Ture Savadkoohi ◽  
Christophe Chevalier
Keyword(s):  
Soil Structure ◽  
Dynamic Behaviour ◽  
Dynamical Behaviour ◽  
Bridge Pier ◽  
Bernoulli Beam ◽  
Scour Monitoring ◽  
Innovative Method ◽  
Equivalent Length ◽  
Cantilevered Beam ◽  
Euler Bernoulli Beam

AbstractThis paper presents an innovative method for scour monitoring, based on the analysis of the dynamic response of a bridge pier embedded in the riverbed. Apart from the mechanical and physical characteristics of the pier itself, soil-structure interaction (SSI) has an impact on the dynamical behaviour of the system. This is particularly the case for eigenfrequencies of the pier which decrease when the free length increases. In this paper, analytical developments are carried out for an Euler–Bernoulli beam, modelling the pier which is embedded in the soil with Winkler springs for SSI. By using Hamilton’s principle and endowing the specific boundary conditions, the system frequencies are assessed by looking for roots of the characteristic equation of the system. These eigenfrequencies are then compared with those of an equivalent cantilevered beam, which can be expressed analytically. Moreover, experiments are carried out to validate the concept of equivalent length as a parameter of the inverse problem, linking the dynamic behaviour of the system and the embedded length.

Dynamic Behavior of Sandwich Beams with Different Cores

2012 ◽  
Vol 468-471 ◽  
pp. 1344-1348
Author(s):  
Ying Wu ◽  
Han Bin Jia ◽  
Dong Xu Zhang ◽  
Lei Tian ◽  
Yan Jun Lü
Keyword(s):  
Dynamic Behaviour ◽  
Metal Foam ◽  
Lattice Structure ◽  
Beam Theory ◽  
Porous Metal ◽  
Nonlinear Ordinary Differential Equation ◽  
Sandwich Beams ◽  
Bernoulli Beam ◽  
Metal Fiber ◽  
Euler Bernoulli Beam

The nonlinear dynamic behaviour of sandwich beams with different cores under transverse cycling loads is investigated in this paper. Based on Euler-Bernoulli beam theory, the second-order nonlinear ordinary differential equation of the sandwich beams with different cores is established by applying Hamilton’s principle and Galerkin method. The effects of the cores of metal foam and lightweight wood and porous metal fiber as well as pyramid lattice structure on the dynamic behaviour are studied through numerical simulations. It is shown that the dynamic behaviour of sandwich beams is not solely determined by and

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.

Vibration Analysis of a Cantilevered Beam with Spring Loading at the Tip as a Generic Elastic Structure

2014 ◽  
Vol 629 ◽  
pp. 407-413 ◽  
Author(s):  
Mohammad Jafari ◽  
Harijono Djojodihardjo ◽  
Kamarul Arifin Ahmad
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Vibration Analysis ◽  
Equation Of Motion ◽  
Bernoulli Beam ◽  
Fundamental Vibration ◽  
Finite Element Approach ◽  
Cantilevered Beam ◽  
Element Approach ◽  
Euler Bernoulli Beam

Although fundamental, vibration of a cantilevered Euler-Bernoulli beam with spring attached at the tip is not found in literatures and is here solved analytically and numerically using finite element approach. The equation of motion of the beam is obtained by using Hamilton’s principle. Finite element method is utilized to write in-house program for the free vibration of the beam. Results show plausible agreements.

The Usefulness of Elementary Theory for the Linear Vibrations of Layered, Orthotropic Elastic Beams and Corrections Due to Two-Dimensional End Effects

1991 ◽  
Vol 58 (1) ◽  
pp. 175-180 ◽  
Author(s):  
J. M. Duva ◽  
J. G. Simmonds
Keyword(s):  
Natural Frequencies ◽  
Elementary Theory ◽  
Beam Theory ◽  
Relative Order ◽  
Bernoulli Beam ◽  
End Effects ◽  
Cantilevered Beam ◽  
Linear Vibrations ◽  
Order Of Magnitude ◽  
Euler Bernoulli Beam

With the aid of formal asymptotic expansions, we conclude not only that elementary (Euler-Bernoulli) beam theory can be applied successfully to layered, orthotropic beams, possibly weak in shear, but also that, in computing the lower natural frequencies of a cantilevered beam, the most important correction to the elementary theory—of the relative order of magnitude of the ratio of depth to length—comes from effects in a neighborhood of the built-in end. We compute this correction using the fundamental work on semi-infinite elastic strips of Gregory and Gladwell (1982) and Gregory and Wan (1984). We also show that, except in unusual cases (e.g., a zero Poisson’s ratio in a homogeneous, elastically isotropic beam), Timoshenko beam theory produces an erroneous correction to the frequencies of elementary theory of the relative order of magnitude of the square of the ratio of depth to length.

Bond Thickness Effects upon Dynamic Behaviour in Adhesive Joints

2010 ◽  
Vol 97-101 ◽  
pp. 3920-3923 ◽  
Author(s):  
Xiao Cong He
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Behaviour ◽  
Adhesive Layer ◽  
Adhesive Joints ◽  
Response Functions ◽  
Frequency Range ◽  
Element Analysis ◽  
Cantilevered Beam ◽  
Different Thickness

The influence of adhesive layer thickness on the dynamic behaviour of the single-lap adhesive joints is investigated in this paper. The ABAQUS finite element analysis (FEA) software was used to predict the frequency response functions (FRFs) of the single-lap adhesive joints of different thickness of the adhesive layer. As a reference, the FRFs of a cantilevered beam without joint were investigated as well. It is clear that the FRFs of the four beams are close to each other within the frequency range 0~1000 Hz. It is also found that the composite damping of the single-lap adhesive joint increases as the thickness of the adhesive layer increases.

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.

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