scholarly journals Plane thermoelastic harmonic waves in hemitropic micropolar media

2020 ◽  
pp. 174-179
Author(s):  
Евгений Валерьевич Мурашкин ◽  
Юрий Николаевич Радаев
Keyword(s):  
Harmonic Wave ◽  
Dynamic Equations ◽  
Harmonic Waves ◽  
Micropolar Continuum ◽  
Coupled Thermoelasticity ◽  
Cubic Equation ◽  
Wave Solutions ◽  
Coupled Thermoelasticity Problems ◽  
Wave Numbers ◽  
Micropolar Media

В работе рассматривается решение задачи о распространении плоской термоупругой гармонической волны в гемитропной микрополярной среде. Приводятся два варианта динамических уравнений гемитропного микрополярного континуума. Определены пространственные поляризации волн перемещений и микровращений относительно волнового вектора плоской волны. Обсуждается качественный характер возможных волновых решений уравнений связанной термоупругости. Отдельно рассматривается случай атермической волны. Вычисление волновых чисел приводится к исследованию одного кубического уравнения с вещественными коэффициентами. The paper is devoted to the problem of a plane thermoelastic harmonic wave propagation in hemitropic micropolar media. Two versions of the dynamic equations of the hemitropic micropolar continuum are presented. The spatial polarizations of the displacements and microrotations waves relative to the wave vector of a plane wave are determined. The characterictic features of possible wave solutions of the coupled thermoelasticity problems are discussed. The case of athermal waves is separately considered. Computation of wave numbers is reduced to the analysis of a cubic equation with real coefficients.

scholarly journals On the theory of linear micropolar hemitropic media

2020 ◽  
pp. 16-24
Author(s):  
Евгений Валерьевич Мурашкин ◽  
Юрий Николаевич Радаев
Keyword(s):  
Differential Equations ◽  
Elastic Potential ◽  
Dynamic Equations ◽  
Crucial Importance ◽  
Micropolar Continuum ◽  
Micropolar Media ◽  
Basic Equations ◽  
Principle Of Virtual Displacements

В статье рассматриваются вопросы применения относительных тензоров при моделирвоании гемитропных микрополярных сред. Вводится определяющая форма микрополярного упругого потенциала. С помощью принципа виртуальной работы получаются определяющие уравнения для силовых и моментных характеристик микрополярного континуума в терминах относительных тензоров. Приводятся уравнения движения микрополярного континуума в терминах относительных тензоров. Выводится финальная форма динамических уравнений для перемещений и микровращений в случае полуизотропной (гемитропной) симметрии. The paper deals with the application of relative tensors to modeling hemitropic micropolar media. The latter is of crucial importance for biomechanics, mechanics of growing solids and mechanics of metamaterials. The constitutive form of the micropolar elastic potential is discussed. The basic equations of micropolar continuum are derived due to the principle of virtual displacements. Differential equations of the micropolar continuum are given in terms of relative tensors. The final form of dynamic equations for displacements and microrotations in the case of semi-isotropic (hemitropic) micropolar continuum is derived and discussed.

Discontinuous failure in micropolar elastic-degrading models

2017 ◽  
Vol 27 (10) ◽  
pp. 1482-1515 ◽  
Author(s):  
Lapo Gori ◽  
Samuel S Penna ◽  
Roque L da Silva Pitangueira
Keyword(s):  
Material Model ◽  
Element Model ◽  
Additional Material ◽  
Micropolar Continuum ◽  
Starting Point ◽  
Localization Analysis ◽  
Acceleration Waves ◽  
Micropolar Media ◽  
Waves Propagation ◽  
Bending Length

The present paper investigates the phenomenon of discontinuous failure (or localization) in elastic-degrading micropolar media. A recently proposed unified formulation for elastic degradation in micropolar media, defined in terms of secant tensors, loading functions and degradation rules, is used as a starting point for the localization analysis. Well-known concepts on acceleration waves propagation, such as the Maxwell compatibility condition and the Fresnel–Hadamard propagation condition, are derived for the considered material model in order to obtain a proper failure indicator. Peculiar problems are investigated analytically in details, in order to evaluate the effects on the onset of localization of two of the additional material parameters of the micropolar continuum, the Cosserat’s shear modulus and the internal bending length. Numerical simulations with a finite element model are also presented, in order to show the regularization behaviour of the micropolar formulation on the pathological effects due to the localization phenomenon.

Harmonic Wave Propagation in a Periodically Layered, Infinite Elastic Body: Plane Strain, Analytical Results

1979 ◽  
Vol 46 (1) ◽  
pp. 113-119 ◽  
Author(s):  
T. J. Delph ◽  
G. Herrmann ◽  
R. K. Kaul
Keyword(s):  
Wave Propagation ◽  
Asymptotic Behavior ◽  
Plane Strain ◽  
Elastic Body ◽  
Harmonic Wave ◽  
Wave Number ◽  
Periodic Medium ◽  
Frequency Wave ◽  
Wave Numbers ◽  
Band Characteristic

The problem of harmonic wave propagation in an unbounded, periodically layered elastic body in a state of plane strain is examined. The dispersion spectrum is shown to be governed by the roots of an 8 × 8 determinant, and represents a surface in frequency-wave number space. The spectrum exhibits the typical stopping band characteristic of wave propagation in a periodic medium. The dispersion equation is shown to uncouple along the ends of the Brillouin zones, and also in the case of wave propagation normal to the layering. The significance of this uncoupling is examined. Also, the asymptotic behavior of the spectrum for large values of the wave numbers is investigated.

Cancellation of Non-Harmonic Waves Using a Cycloidal Turbine

2011 ◽  
Author(s):  
John T. Imamura ◽  
Stefan G. Siegel ◽  
Casey Fagley ◽  
Tom McLaughlin
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Linear Time ◽  
Harmonic Wave ◽  
Point Vortex ◽  
Harmonic Waves ◽  
Incoming Wave ◽  
Response Characteristics ◽  
Depth Water ◽  
Multi Component System

We computationally investigate the ability of a cycloidal turbine to cancel two-dimensional non-harmonic waves in deep water. A cycloidal turbine employs the same geometry as the well established Cycloidal or Voith-Schneider Propeller. It consists of a shaft and one or more hydrofoils that are attached eccentrically to the main shaft and can be independently adjusted in pitch angle as the cycloidal turbine rotates. We simulate the cycloidal turbine interaction with incoming waves by viewing the turbine as a wave generator superimposed with the incoming flow. The generated waves ideally are 180° out of phase and cancel the incoming wave downstream of the turbine. The upstream wave is very small as generation of single-sided waves is a characteristic of the cycloidal turbine as has been shown in prior work. The superposition of the incoming wave and generated wave is investigated in the far-field and we model the hydrofoil as a point vortex. This model has previously been used to successfully terminate regular deep water waves as well as intermediate depth water waves. We explore the ability of this model to cancel non-harmonic waves. Near complete cancellation is possible for a non-harmonic wave with components designed to match those generated by the cycloidal turbine for specified parameters. Cancellation of a specific wave component of a multi-component system is also shown. Also, step changes in the device operating parameters of circulation strength, rotation rate, and submergence depth are explored to give insight to the cycloidal turbine response characteristics and adaptability to changes in incoming waves. Based on these studies a linear, time-invarient (LTI) model is developed which captures the steady state wave frequency response. Such a model can be used for control development in future efforts to efficiently cancel more complex incoming waves.

Analyzing Out-of-Plane Vibration of a Rotating Ring with Wave Propagation

2016 ◽  
Vol 693 ◽  
pp. 31-36
Author(s):  
Di Shan Huang ◽  
Hong He
Keyword(s):  
Wave Propagation ◽  
High Speed ◽  
Harmonic Wave ◽  
Roller Bearing ◽  
Torsional Motion ◽  
Plane Vibration ◽  
Coupled Equations ◽  
Wave Solutions ◽  
Thin Ring ◽  
Out Of Plane

Wave propagation is introduced to analyze out-of-plane vibration problem of a rotating ring. Harmonic wave solutions are found for the coupled equations of the axial and torsional motion. Wavenumber spectra and phase velocity map are obtained, and the ratio of axial displacement to torsional displacement and the cut-off frequencies are determined. Examples for the free vibration of the uniform rotating thin ring are given to illustrate the validity of the wave propagation. This research will be valuable in the application of a solid cage in high speed roller bearing.

RIEMANN THETA FUNCTIONS SOLUTIONS WITH RATIONAL CHARACTERISTICS FOR (2+1)-DIMENSIONAL SINH-GORDON EQUATION

2010 ◽  
Vol 24 (06) ◽  
pp. 575-584
Author(s):  
YANG FENG ◽  
HONG-QING ZHANG
Keyword(s):  
Gordon Equation ◽  
Theta Functions ◽  
Periodic Wave ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Wave Numbers ◽  
Riemann Theta Functions ◽  
The Waves ◽  
Hirota Bilinear

In this letter, we use the Riemann theta functions with rational characteristics and the Hirota bilinear method to construct quasi-periodic wave solutions for (2+1)-dimensional sinh-Gordon equation. This method not only conveniently obtains quasi-periodic solutions of nonlinear equations, but also directly gets the explicit expressions of frequencies, wave numbers, phase and amplitudes for the waves.

A Transformation in Coupled Thermoelasticity Problems

1966 ◽  
Vol 33 (1) ◽  
pp. 196-198 ◽  
Author(s):  
M. V. Mountfort
Keyword(s):  
Boundary Conditions ◽  
Large Class ◽  
Integral Equations ◽  
Field Equations ◽  
Coupled Thermoelasticity ◽  
Simple Transformation ◽  
Coupled Thermoelasticity Problems ◽  
Coupled Boundary Conditions ◽  
Thermoelastic Field ◽  
Thermoelastic Problems

It is shown that a simple transformation can uncouple the thermoelastic field equations but at the expense of coupled boundary conditions. A large class of coupled thermoelastic problems then becomes solvable using integral equations.

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