On stability loss delay for a periodic trajectory

Author(s):  
A. I. Neishtadt ◽  
C. Simó ◽  
D. V. Treschev
2021 ◽  
Vol 249 ◽  
pp. 113264
Author(s):  
Xing-Ping Shu ◽  
Huai-Bing Wang ◽  
Yi Li ◽  
Zhi-Shen Yuan ◽  
Ke Li

2021 ◽  
Vol 13 (7) ◽  
pp. 324-328
Author(s):  
Pavel Grigoriev ◽  
Sergey Bespalco ◽  
Vladimir Goncharov

Author(s):  
J. Awrejcewicz ◽  
A. V. Krysko ◽  
S. P. Pavlov ◽  
M. V. Zhigalov ◽  
V. A. Krysko

The size-dependent model is studied based on the modified couple stress theory for the geometrically nonlinear curvilinear Timoshenko beam made from a functionally graded material having its properties changed along the beam thickness. The influence of the size-dependent coefficient and the material grading on the stability of the curvilinear beams is investigated with the use of the setup method. The second-order accuracy finite difference method is used to solve the problem of nonlinear partial differential equations (PDEs) by reducing it to the Cauchy problem. The obtained set of nonlinear ordinary differential equations (ODEs) is then solved by the fourth-order Runge–Kutta method. The relaxation method is employed to solve numerous static problems based on the dynamic approach. Eight different combinations of size-dependent coefficients and the functionally graded material coefficient are used to study the stress-strain responses of Timoshenko beams. Stability loss of the curvilinear Timoshenko beams is investigated using the Lyapunov criterion based on the estimation of the Lyapunov exponents. Beams with/without the size-dependent behavior, homogeneous beams, and functionally graded beams having the same stiffness are investigated. It is shown that in straight-line beams, the size-dependent effect decreases the beam deflection. The same is observed if the most rigid layer is located on the top of the beam. In the curvilinear Timoshenko beam, such a location of the most rigid layer essentially improves the beam strength against stability loss. The observed transition of the largest Lyapunov exponent from a negative to positive value corresponds to the transition from a precritical to postcritical beam state.


2016 ◽  
Author(s):  
P. A. Lyukshin ◽  
S. A. Bochkareva ◽  
N. Yu. Grishaeva ◽  
B. A. Lyukshin ◽  
N. Yu. Matolygina ◽  
...  

Author(s):  
A. P. S. Selvadurai ◽  
A. P. Suvorov

The paper investigates the development of instability in an internally pressurized annulus of a poro-hyperelastic material. The theory of poro-hyperelasticity is proposed as an approach for modelling the mechanical behaviour of highly deformable elastic materials, the pore space of which is saturated with a fluid. The consideration of coupling between the mechanical response of the hyperelastic porous skeleton and the pore fluid is important when applying the developments to soft tissues encountered in biomechanical applications. The paper examines the development of an instability in a poro-hyperelastic annulus subjected to internal pressure. Using a computational approach, numerical solutions are obtained for the internal pressures that promote either short-term or long-term instability in a poro-hyperelastic annulus and a poro-hyperelastic shell. In addition, time-dependent effects of stability loss are examined. The analytical solutions are used to benchmark the accuracy of the computational approach.


2020 ◽  
Vol 10 (3) ◽  
pp. 245-255
Author(s):  
Mahsa Hasanzadeh ◽  
Zahra Hasanzadeh ◽  
Sakineh Alizadeh ◽  
Mehran Sayadi ◽  
Mojtaba Nasiri Nezhad ◽  
...  

CuxO-NiO nanocomposite film for the non-enzymatic determination of glucose was prepared by the novel modifying method. At first, anodized Cu electrode was kept in a mixture solution of CuSO4, NiSO4 and H2SO4 for 15 minutes. Then, a cathodization process with a step potential of -6 V in a mixture solution of CuSO4 and NiSO4 was initiated, generating formation of porous Cu-Ni film on the bare Cu electrode by electrodeposition assisted by the release of hydrogen bubbles acting as soft templates. Optimized conditions were determined by the experimental design software for electrodeposition process. Afterward, Cu-Ni modified electrode was scanned by cyclic voltammetry (CV) method in NaOH solution to convert Cu and Ni nanoparticles to the nano-scaled CuxO-NiO film. The electrocatalytic behavior of the novel CuxO-NiO film toward glucose oxidation was studied by CV and chronoamperometry (CHA) techniques. The calibration curve of glucose was found linear in a wide range of 0.04–5.76 mM, with a low limit of detection (LOD) of 7.3 µM (S/N = 3) and high sensitivity (1.38 mA mM-1 cm-2). The sensor showed high selectivity against some usual interfering species and high stability (loss of only 6.3 % of its performance over one month). The prepared CuxO-NiO nanofilm based sensor was successfully applied for monitoring glucose in human blood serum and urine samples.


Author(s):  
Oleksandr Shkurupiy ◽  
Pavlo Mytrofanov ◽  
Yuriy Davydenko ◽  
Muhlis Hajiyev

One of the most powerful modern methods of calculating complex building structures is the finite element method in theform of a displacement method for discrete systems, which involves the creation of a finite element model, that is, splittingthe structure into separate elements within each of which the functions of displacements and stresses are known. On the basisof the displacement method and the methods of iterations and half-division, an algorithm for stability calculation of the firstkind equilibrium form of compressed reinforced concrete columns with hinged fixing at the ends, considering the stiffnesschanging has been developed. The use of the above methods enables to determine the minimum critical load or stress at thefirst bifurcation and their stability loss corresponding form. The use of matrix forms contributes to simplification of high order stability loss equation. This approach enables to obtain the form of stability loss that corresponds to the critical load.


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