Non-Linear ODEs Of First and Second Order

2007 ◽  
pp. 239-364
Author(s):  
Mircea V. Soare ◽  
Petre P. Teodorescu ◽  
Ileana Toma
Keyword(s):  
Second Order ◽  
Non Linear ◽  
Linear Odes

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

scholarly journals Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 285
Author(s):  
Saad Althobati ◽  
Jehad Alzabut ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Order Equation ◽  
Second Order ◽  
Riccati Technique ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Main Equation ◽  
Non Linear ◽  
Even Order

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

Bases for Second Order Linear ODEs

2020 ◽  
Vol 127 (9) ◽  
pp. 849-849
Author(s):  
Peter McGrath
Keyword(s):  
Second Order ◽  
Order Linear ◽  
Linear Odes

Synthesis, Electronic Characterisation and Significant Second-Order Non-Linear Optical Responses ofmeso-Tetraphenylporphyrins and Their ZnII Complexes Carrying a Push or Pull Group in the β Pyrrolic Position

2005 ◽  
Vol 2005 (19) ◽  
pp. 3857-3874 ◽  
Author(s):  
Elisabetta Annoni ◽  
Maddalena Pizzotti ◽  
Renato Ugo ◽  
Silvio Quici ◽  
Tamara Morotti ◽  
...  
Keyword(s):  
Second Order ◽  
Optical Responses ◽  
Non Linear ◽  
Linear Optical

scholarly journals Perturbations of nonlinear autonomous oscillators

1994 ◽  
Vol 35 (4) ◽  
pp. 445-468 ◽  
Author(s):  
P. B. Chapman
Keyword(s):  
General Theory ◽  
Fourier Coefficients ◽  
Multiple Scales ◽  
Second Order ◽  
Multiple Scales Method ◽  
Suitable Parameter ◽  
Non Linear

AbstractA general theory is given for autonomous perturbations of non-linear autonomous second order oscillators. It is found using a multiple scales method. A central part of it requires computation of Fourier coefficients for representation of the underlying oscillations, and these coefficients are found as convergent expansions in a suitable parameter.

High glass transition temperature syndioregic second-order non-linear optical polymer in Langmuir–Blodgett–Kuhn films

1998 ◽  
Vol 327-329 ◽  
pp. 5-8 ◽  
Author(s):  
M.J. Roberts ◽  
G.A. Lindsay ◽  
J.D. Stenger-Smith ◽  
R.A. Hollins ◽  
A.P. Chafin ◽  
...  
Keyword(s):  
Glass Transition ◽  
Transition Temperature ◽  
Glass Transition Temperature ◽  
Second Order ◽  
High Glass Transition Temperature ◽  
Langmuir Blodgett ◽  
Optical Polymer ◽  
Non Linear ◽  
Linear Optical

Second-order consensus of multiple non-identical agents with non-linear protocols

2012 ◽  
Vol 6 (9) ◽  
pp. 1319 ◽  
Author(s):  
S. Chen ◽  
J.C. Ji ◽  
J. Zhou
Keyword(s):  
Second Order ◽  
Non Linear
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