Local solvability and blowup of the solution of the Rosenau-Bürgers equation with different boundary conditions

2013 ◽  
Vol 177 (1) ◽  
pp. 1361-1376 ◽  
Author(s):  
A. A. Panin
Keyword(s):  
Boundary Conditions ◽  
Burgers Equation ◽  
Local Solvability ◽  
Different Boundary Conditions

scholarly journals Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

2021 ◽  
Author(s):  
Jacopo Quaglierini ◽  
Alessandro Lucantonio ◽  
Antonio DeSimone
Keyword(s):  
Boundary Conditions ◽  
Elastic Properties ◽  
Central Region ◽  
Mechanical Response ◽  
Different Boundary Conditions ◽  
Kirchhoff Rods ◽  
Model Versus ◽  
The Individual ◽  
Opposite Chirality

Abstract Nature and technology often adopt structures that can be described as tubular helical assemblies. However, the role and mechanisms of these structures remain elusive. In this paper, we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchhoff rods, arranged in pairs with opposite chirality and connected by pin joints, both analytically and numerically. We first focus on compression and find that, whereas a single helical rod would buckle, the rods of the assembly deform coherently as stable helical shapes wound around a common axis. Moreover, we investigate the response of the assembly under different boundary conditions, highlighting the emergence of a central region where rods remain circular helices. Secondly, we study the effects of different hypotheses on the elastic properties of rods, i.e., stress-free rods when straight versus when circular helices, Kirchhoff’s rod model versus Sadowsky’s ribbon model. Summing up, our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods, as well as some interesting features, and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology. Graphic Abstract We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

Thermal phase transition behaviours of the blue phase of bent-core nematogen and chiral dopant mixtures under different boundary conditions

Soft Matter ◽  
2014 ◽  
Vol 10 (41) ◽  
pp. 8224-8228 ◽  
Author(s):  
Min-Jun Gim ◽  
Gohyun Han ◽  
Suk-Won Choi ◽  
Dong Ki Yoon
Keyword(s):  
Phase Transition ◽  
Boundary Conditions ◽  
Liquid Crystalline ◽  
Isotropic Phase ◽  
Different Boundary Conditions ◽  
Various Boundary Conditions ◽  
Thermal Phase Transition ◽  
Thermal Phase ◽  
Blue Phase ◽  
Chiral Dopants

We have investigated dramatic changes in the thermal phase transition of a liquid-crystalline (LC) blue phase (BP) consisting of bent-core nematogen and chiral dopants under various boundary conditions during cooling from the isotropic phase.

Experimental Validation and Numerical Simulation of Shape Memory Flat Wire Actuators

2014 ◽  
Author(s):  
Alexander Czechowicz ◽  
Sven Langbein
Keyword(s):  
Shape Memory Alloy ◽  
Boundary Conditions ◽  
Shape Memory ◽  
Smart Materials ◽  
Empirical Data ◽  
Dynamic Properties ◽  
Fatigue Behavior ◽  
Different Boundary Conditions ◽  
Heating And Cooling ◽  
Actual Shape

Shape memory alloys (SMA) are thermally activated smart materials. Due to their ability to change into a previously imprinted actual shape through the means of thermal activation, they are suitable as actuators for mechatronical systems. Despite of the advantages shape memory alloy actuators provide, these elements are only seldom integrated by engineers into mechatronical systems. Reasons are the complex characteristics, especially at different boundary conditions and the missing simulation- and design tools. Also the lack of knowledge and empirical data are a reason why development projects with shape memory actuators often lead to failures. This paper deals with the dynamic properties of SMA-actuators (Shape Memory Alloy) — characterized by their rate of heating and cooling procedures — that today can only be described insufficiently for different boundary conditions. Based on an analysis of energy fluxes into and out of the actuator, a numerical model of flat-wire used in a bow-like structure, implemented in MATLAB/SIMULINK, is presented. Different actuation parameters, depending on the actuator-geometry and temperature are considered in the simulation in real time. Additionally this publication sums up the needed empirical data (e.g. fatigue behavior) in order to validate the numerical two dimensional model and presents empirical data on SMA flat wire material.

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1991 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Abstract Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

scholarly journals Structural Health Monitoring of Steel Pipes under Different Boundary Conditions and Choice of Signal Processing Techniques

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Rais Ahmad ◽  
Tribikram Kundu
Keyword(s):  
Signal Processing ◽  
Boundary Conditions ◽  
Fourier Transforms ◽  
Guided Wave ◽  
Continuous Wavelet ◽  
Mother Wavelet ◽  
Different Boundary Conditions ◽  
Steel Pipes ◽  
Processing Techniques ◽  
Signal Processing Techniques

Guided wave technique is an efficient method for monitoring structural integrity by detecting and forecasting possible damages in distributed pipe networks. Efficient detection depends on appropriate selection of guided wave modes as well as signal processing techniques. Fourier analysis and wavelet analysis are two popular signal processing techniques that provide a flexible set of tools for solving various fundamental problems in science and engineering. In this paper, effective ways of using Fourier and Wavelet analyses on guided wave signals for detecting defects in steel pipes are discussed for different boundary conditions. This research investigates the effectiveness of Fourier transforms and Wavelet analysis in detecting defects in steel pipes. Cylindrical Guided waves are generated by piezo-electric transducers and propagated through the pipe wall boundaries in a pitch-catch system. Fourier transforms of received signals give information regarding the propagating guided wave modes which helps in detecting defects by selecting appropriate modes that are affected by the presence of defects. Continuous wavelet coefficients are found to be sensitive to defects. Several types of mother wavelet functions such as Daubechies, Symlet, and Meyer have been used for the continuous wavelet transform to investigate the most suitable wavelet function for defect detection. This research also investigates the effect of different boundary conditions on wavelet transforms for different mother wavelet functions.

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