Identification and severity estimation of a breathing crack in a plate via nonlinear dynamics

Aftab, H.; Baneen, Ummul; Israr, Asif

doi:10.1007/s11071-021-06275-9

Cited by 14 publications

(8 citation statements)

References 49 publications

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“…However, for symmetric BCs like simply supported on all sides(SSSS) and clampedclamped-free-free (CCFF) the difference does not exceed 1%. 45 Although the values of the frequency vary but when their respective IFR is taken, it is observed that both ratios have similar trends, as shown in Figure 6. The dotted lines show the drop in IFR for the direct method, that is, IFR between the plate with breathing crack and the intact plate (ω br /ω c ).…”

Section: Comparison Between Mathematical and Simulated Modelmentioning

confidence: 78%

“…The piecewise nonlinear equations representing the two states of the plate model were developed in the previous research using impulse excitation and the breathing crack frequencies were found from them. 45 In this paper, the mathematical and numerical model for the harmonic and random excitation has been presented.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Recently, the plate model for part-through breathing crack has been formulated mathematically with impulse loading. 45 The above review suggests that the detection of breathing crack in both beam and plate-like structures has been carried out under different excitations, that is, harmonic, impulse, and random along with different techniques. The crack location and severity in two-dimensional structures have been touched in some cases with respect to different parameters like natural frequencies and second-order harmonics but further research in this area is still required, especially for part-through cracks.…”

Section: Introductionmentioning

confidence: 99%

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Experimental investigation of a breathing crack in a plate under different excitations

Aftab

Baneen

Israr

2022

Structural Contr & Hlth

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Structures in real-life scenarios like industrial robots, spaceships, aircrafts, submarines, bridges, and pressure vessels undergo different loading conditions. These structures are prone to damage due to the risks related to fatigue and aging. Small cracks may appear in these complex structures and prove to be fatal. These cracks may open and close, hence termed as breathing cracks, exhibiting nonlinear behavior under load. Various nonlinear techniques exist

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Section: Comparison Between Mathematical and Simulated Modelmentioning

confidence: 78%

Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Experimental investigation of a breathing crack in a plate under different excitations

Aftab

Baneen

Israr

2022

Structural Contr & Hlth

Self Cite

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“…Mechanical systems with free-play gaps and piecewise constraints have aroused the interest of the scientific community in the past decades. They find practical engineering applications in the study of impacting capsule systems [1], impact drilling systems [2], cracked systems [3], mechanical oscillators [4][5][6][7] and aeroelastic systems with free-play gaps [8,9], buildings subjected to earthquakes [10], and impact oscillators with rigid walls [11][12][13]. These systems, generally referred to as non-smooth dynam-ical systems, incorporate discrete-events which guide the associated mathematical solution through regions of the domain where different characteristics are applied.…”

Section: Introductionmentioning

confidence: 99%

“…This is particularly clear in systems whose switching boundary is nonlinearly defined, e.g. when the border includes functions like sign(x) 3 . In these cases, the adoption of the Filippov regularisation [58] could prevent the generation of hidden attractors; this happens because the modelling assumptions could exclude hidden terms in the definition of the switching boundary [59].…”

Section: Introductionmentioning

confidence: 99%

Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

2023

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In the industry field, the increasingly stringent requirements of lightweight structures are exposing the ultimately nonlinear nature of mechanical systems. This is extremely true for systems with moving parts and loose fixtures which show piecewise stiffness behaviours. Nevertheless, the numerical solution of systems with ideal piecewise mathematical characteristics is associated with time-consuming procedures and a high computational burden. Smoothing functions can conveniently simplify the mathematical form of such systems, but little research has been carried out to evaluate their effect on the mechanical response of multi-degree-of-freedom systems. To investigate this problem, a slightly damped mechanical two-degree-of-freedom system with soft piecewise constraints is studied via numerical continuation and numerical integration procedures. Sigmoid functions are adopted to approximate the constraints, and the effect of such approximation is explored by comparing the results of the approximate system with the ones of the ideal piecewise counter-part. The numerical results show that the sigmoid functions can correctly catch the very complex dynamics of the proposed system when both the above-mentioned techniques are adopted. Moreover, a reduction in the computational burden, as well as an increase in numerical robustness, is observed in the approximate case.

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Exact periodic solution of the undamped Helmholtz oscillator subject to a constant force and arbitrary initial conditions

Big‐Alabo,

Alfred

2024

Math Methods in App Sciences

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The Helmholtz oscillator is a nonlinear mixed‐parity oscillator that models the asymmetric vibrations of many engineering and scientific systems. This paper investigated a general and completely integrable form of the Helmholtz oscillator and derived its exact periodic solution from the first integral of the governing differential equation. The considered Helmholtz oscillator has general linear and nonlinear stiffness constants, is subject to a constant force, and has arbitrary initial conditions. Its exact time period was derived in terms of the complete elliptic integral of the first kind, while the exact displacement was derived in terms of the Jacobi elliptic sine function. The validity of the exact solutions was verified for various combinations of the system parameters and initial conditions by comparing with numerical solutions. The exact solutions and numerical solutions were found to match perfectly. Furthermore, the exact solution was applied to analyze the vibration response of real‐world systems that could be modeled as Helmholtz oscillators. The present exact solutions provide benchmark solutions that could be used to determine the accuracy of new and existing approximate solutions for the Helmholtz oscillator.

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Identification and severity estimation of a breathing crack in a plate via nonlinear dynamics

Cited by 14 publications

References 49 publications

Experimental investigation of a breathing crack in a plate under different excitations

Experimental investigation of a breathing crack in a plate under different excitations

Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

Exact periodic solution of the undamped Helmholtz oscillator subject to a constant force and arbitrary initial conditions

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