On Quantifying Detectable Fatigue Crack Size in Aluminum Beams Using Vibration and Impedance-Based Methods

2009 ◽  
Author(s):  
Mana Afshari ◽  
Brad A. Butrym ◽  
Daniel J. Inman
Keyword(s):  
Fatigue Crack ◽  
Frequency Shift ◽  
Electrical Impedance ◽  
Fatigue Cracks ◽  
Beat Frequency ◽  
Crack Size ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Frequency Method ◽  
Euler Bernoulli Beam

This paper looks at the impedance-based and vibration methods used for the structural health monitoring (SHM) of aluminum beams and attempts to quantify the smallest fatigue crack size that is detectable by these two methods. The vibration-based method presented in this paper, uses the recent model of Aydin [1] which is based on a simple Euler-Bernoulli beam model. This method treats cracks as localized reduction in the beam’s stiffness and models them as massless rotational springs at the locations of the cracks. The beam is then considered to be of multiple sections connected by these springs. The beam studied in the present work is assumed to be an aluminum, uniform, Euler-Bernoulli beam having a single fatigue crack and being axially loaded. It is further assumed that frequencies can only be measured to within half a Hertz. This results in formulas that can be used to predict specific detectable sizes of fatigue cracks given specific geometry of the beam. For example for a beam of dimension 240×19.1×4.8 mm, it is found that the fatigue crack must be approximately 12.5% of the beam width in order to induce a frequency shift of 0.5 Hz. In the second part of this paper, different sets of experiments are conducted on aluminum beams. First, saw-cuts are made in the beams and the resultant shift in the beams’ natural frequency is examined to find the minimum detectable cut length. In order to improve this minimum detectable damage size, the beat frequency method is applied, which enhances the minimum detectable frequency shift. These results are then compared to those of the electrical impedance measurements through the HP 4194A Impedance analyzer. At the end, the aluminum beams are being fatigued and by measuring their electrical impedance at different numbers of fatigue cycling, their detectable fatigue crack size is investigated.

scholarly journals Numerical Solution of Bending of the Beam with Given Friction

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 898
Author(s):  
Michaela Bobková ◽  
Lukáš Pospíšil
Keyword(s):  
Sliding Friction ◽  
Quadratic Function ◽  
Building Construction ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Sustainable Building ◽  
Construction Design ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Fixed Beam

We are interested in a contact problem for a thin fixed beam with an internal point obstacle with possible rotation and shift depending on a given swivel and sliding friction. This problem belongs to the most basic practical problems in, for instance, the contact mechanics in the sustainable building construction design. The analysis and the practical solution plays a crucial role in the process and cannot be ignored. In this paper, we consider the classical Euler–Bernoulli beam model, which we formulate, analyze, and numerically solve. The objective function of the corresponding optimization problem for finding the coefficients in the finite element basis combines a quadratic function and an additional non-differentiable part with absolute values representing the influence of considered friction. We present two basic algorithms for the solution: the regularized primal solution, where the non-differentiable part is approximated, and the dual formulation. We discuss the disadvantages of the methods on the solution of the academic benchmarks.

Asymmetric Bifurcation of Initially Curved Nanobeam

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
X. Chen ◽  
S. A. Meguid
Keyword(s):  
Symmetry Breaking ◽  
Degrees Of Freedom ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Reduced Order ◽  
Euler Bernoulli Beam ◽  
Bifurcation Behavior

In this paper, we investigate the asymmetric bifurcation behavior of an initially curved nanobeam accounting for Lorentz and electrostatic forces. The beam model was developed in the framework of Euler–Bernoulli beam theory, and the surface effects at the nanoscale were taken into account in the model by including the surface elasticity and the residual surface tension. Based on the Galerkin decomposition method, the model was simplified as two degrees of freedom reduced order model, from which the symmetry breaking criterion was derived. The results of our work reveal the significant surface effects on the symmetry breaking criterion for the considered nanobeam.

Spectral analysis of Euler–Bernoulli beam model with distributed damping and fully non-conservative boundary feedback matrix

2021 ◽  
pp. 1-38
Author(s):  
Marianna A. Shubov
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Damping Coefficient ◽  
Control Input ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Boundary Feedback ◽  
Feedback Matrix ◽  
The Right ◽  
Euler Bernoulli Beam

The distribution of natural frequencies of the Euler–Bernoulli beam resting on elastic foundation and subject to an axial force in the presence of several damping mechanisms is investigated. The damping mechanisms are: ( i ) an external or viscous damping with damping coefficient ( − a 0 ( x )), ( ii ) a damping proportional to the bending rate with the damping coefficient a 1 ( x ). The beam is clamped at the left end and equipped with a four-parameter (α, β, κ 1 , κ 2 ) linear boundary feedback law at the right end. The 2 × 2 boundary feedback matrix relates the control input (a vector of velocity and its spacial derivative at the right end) to the output (a vector of shear and moment at the right end). The initial boundary value problem describing the dynamics of the beam has been reduced to the first order in time evolution equation in the state Hilbert space of the system. The dynamics generator has a purely discrete spectrum (the vibrational modes). Explicit asymptotic formula for the eigenvalues as the number of an eigenvalue tends to infinity have been obtained. It is shown that the boundary control parameters and the distributed damping play different roles in the asymptotical formulas for the eigenvalues of the dynamics generator. Namely, the damping coefficient a 1 and the boundary controls κ 1 and κ 2 enter the leading asymptotical term explicitly, while damping coefficient a 0 appears in the lower order terms.

scholarly journals Critical Velocity of High-Performance Yarn Transversely Impacted by Razor Blade

Fibers ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 95 ◽  
Author(s):  
Boon Lim ◽  
Jou-Mei Chu ◽  
Benjamin Claus ◽  
Yizhou Nie ◽  
Wayne Chen
Keyword(s):  
Critical Velocity ◽  
High Speed ◽  
High Performance ◽  
Hertzian Contact ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Razor Blade ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Hertzian Contact Model

A ballistic parameter that influences the ballistic performances of a high-performance yarn is the critical velocity. The critical velocity is defined as the projectile striking velocity that causes instantaneous rupture of the yarn upon impact. In this study, we performed ballistic experiments to determine the critical velocity of a Twaron® yarn transversely impacted by a razor blade. A high-speed camera was integrated into the experimental apparatus to capture the in-situ deformation of the yarn. The experimental critical velocity demonstrated a reduction compared to the critical velocity predicted by the classical theory. The high-speed images revealed the yarn specimen failed from the projectile side toward the free end when impacted by the razor blade. To improve the prediction capability, the Euler–Bernoulli beam and Hertzian contact models were used to predict the critical velocity. For the Euler–Bernoulli beam model, the critical velocity was obtained by assuming the specimen ruptured instantaneously when the maximum flexural strain reached the ultimate tensile strain of the yarn upon impact. On the other hand, for the Hertzian contact model, the yarn was assumed to fail when the indentation depth was equivalent to the diameter of the yarn. The errors between the average critical velocities determined from experiments and the predicted critical velocities were around 19% and 48% for the Euler–Bernoulli beam model and Hertzian contact model, respectively.

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