Dynamic Bending of Plastic Polymetallic Plates with Piecewise-Smooth Elliptic Contours

2021 ◽  
Vol 258 (4) ◽  
pp. 568-575
Author(s):  
Yu. V. Nemirovskii
Keyword(s):  
Piecewise Smooth ◽  
Dynamic Bending

Modified split Hopkinson pressure bars for dynamic bending and shear tests

2006 ◽  
Vol 134 ◽  
pp. 725-730 ◽  
Author(s):  
A. Pignon ◽  
G. Mathieu ◽  
S. Richomme ◽  
J. M. Margot ◽  
F. Delvare
Keyword(s):  
Shear Tests ◽  
Split Hopkinson ◽  
Split Hopkinson Pressure Bars ◽  
Dynamic Bending

scholarly journals Singularly Perturbed Oscillators with Exponential Nonlinearities

2021 ◽  
Author(s):  
S. Jelbart ◽  
K. U. Kristiansen ◽  
P. Szmolyan ◽  
M. Wechselberger
Keyword(s):  
Limit Cycles ◽  
Space Dimension ◽  
Blow Up ◽  
Exponential Convergence ◽  
Model System ◽  
Piecewise Smooth ◽  
Singularly Perturbed ◽  
Model Systems ◽  
Smooth System ◽  
Unique Limit

AbstractSingular exponential nonlinearities of the form $$e^{h(x)\epsilon ^{-1}}$$ e h ( x ) ϵ - 1 with $$\epsilon >0$$ ϵ > 0 small occur in many different applications. These terms have essential singularities for $$\epsilon =0$$ ϵ = 0 leading to very different behaviour depending on the sign of h. In this paper, we consider two prototypical singularly perturbed oscillators with such exponential nonlinearities. We apply a suitable normalization for both systems such that the $$\epsilon \rightarrow 0$$ ϵ → 0 limit is a piecewise smooth system. The convergence to this nonsmooth system is exponential due to the nonlinearities we study. By working on the two model systems we use a blow-up approach to demonstrate that this exponential convergence can be harmless in some cases while in other scenarios it can lead to further degeneracies. For our second model system, we deal with such degeneracies due to exponentially small terms by extending the space dimension, following the approach in Kristiansen (Nonlinearity 30(5): 2138–2184, 2017), and prove—for both systems—existence of (unique) limit cycles by perturbing away from singular cycles having desirable hyperbolicity properties.

scholarly journals Bending Setups for Reliability Investigation of Flexible Electronics

Micromachines ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 78
Author(s):  
Rafat Saleh ◽  
Maximilian Barth ◽  
Wolfgang Eberhardt ◽  
André Zimmermann
Keyword(s):  
Flexible Electronics ◽  
Test Methods ◽  
Bending Test ◽  
Flexible Systems ◽  
Flexible Displays ◽  
Dynamic Bending

Flexible electronics is a rapidly growing technology for a multitude of applications. Wearables and flexible displays are some application examples. Various technologies and processes are used to produce flexible electronics. An important aspect to be considered when developing these systems is their reliability, especially with regard to repeated bending. In this paper, the frequently used methods for investigating the bending reliability of flexible electronics are presented. This is done to provide an overview of the types of tests that can be performed to investigate the bending reliability. Furthermore, it is shown which devices are developed and optimized to gain more knowledge about the behavior of flexible systems under bending. Both static and dynamic bending test methods are presented.

scholarly journals The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification

Meccanica ◽  
2020 ◽  
Vol 55 (10) ◽  
pp. 1885-1902
Author(s):  
Yang Liu ◽  
Joseph Páez Chávez ◽  
Jiajia Zhang ◽  
Jiyuan Tian ◽  
Bingyong Guo ◽  
...  
Keyword(s):  
Dynamical System ◽  
Mathematical Formulation ◽  
Path Following ◽  
Piecewise Smooth ◽  
Experimental Results ◽  
Scale Down ◽  
Speed Up ◽  
Small Bowel Endoscopy ◽  
Numerical Optimisation ◽  
Smooth Dynamical System

Abstract The vibro-impact capsule system has been studied extensively in the past decade because of its research challenges as a piecewise-smooth dynamical system and broad applications in engineering and healthcare technologies. This paper reports our team’s first attempt to scale down the prototype of the vibro-impact capsule to millimetre size, which is 26 mm in length and 11 mm in diameter, aiming for small-bowel endoscopy. Firstly, an existing mathematical model of the prototype and its mathematical formulation as a piecewise-smooth dynamical system are reviewed in order to carry out numerical optimisation for the prototype by means of path-following techniques. Our numerical analysis shows that the prototype can achieve a high progression speed up to 14.4 mm/s while avoiding the collision between the inner mass and the capsule which could lead to less propulsive force on the capsule so causing less discomfort on the patient. Secondly, the experimental rig and procedure for testing the prototype are introduced, and some preliminary experimental results are presented. Finally, experimental results are compared with the numerical results to validate the optimisation as well as the feasibility of the vibro-impact technique for the potential of a controllable endoscopic procedure.

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