scholarly journals Direct, inverse and mirror wave modes of coupled displacements and microrotations monochromatic plane waves in hemitropic micropolar media

2021 ◽  
pp. 115-127
Author(s):  
Евгений Валерьевич Мурашкин ◽  
Юрий Николаевич Радаев
Keyword(s):  
Plane Waves ◽  
Elastic Solid ◽  
Mirror Reflection ◽  
Direct Wave ◽  
Micropolar Continuum ◽  
Reflected Wave ◽  
Simultaneous Existence ◽  
Micropolar Media ◽  
Space Inversion ◽  
Wave Modes

В статье обсуждаются вопросы распространения монохроматических волн в гемитропном микрополярном континууме. Сформулированы уравнения динамики гемитропного микрополярного упругого тела в терминах псевдотензоров с 9-ю определяющими псевдоскалярами. Рассмотрены преобразования указанных уравнений в случаях инверсии пространства и зеркального отражения относительно заданной плоскости. Показано наличие инверсных волновых мод (наряду с прямыми) в распространяющейся плоской волне. Получены формулы преобразования прямых волновых мод перемещений и микровращений в инверсные и зеркально отраженные моды. Приводятся соответствующие формулы. The paper deals with the propagation of monochromatic plane waves in a hemitropic micropolar continuum. The dynamics equations of a hemitropic micropolar elastic solid in terms of pseudotensors with 9 constitutive pseudoscalars are derived and discussed. Formulae for the cases of space inversion and mirror reflection relative to a given plane are obtained and considered. The simultaneous existence of the direct, inverse and mirror reflected wave modes in propagating plane waves is established. Formulae for direct wave modes of displacements and microrotations in inverse and mirror modes are given.

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.

scholarly journals Propagation of Plane Waves in a Thermally Conducting Mixture

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Baljeet Singh
Keyword(s):  
Free Surface ◽  
Longitudinal Wave ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Elastic Solid ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Thermally Conducting

The governing equations for generalized thermoelasticity of a mixture of an elastic solid and a Newtonian fluid are formulated in the context of Lord-Shulman and Green-Lindsay theories of generalized thermoelasticity. These equations are solved to show the existence of three coupled longitudinal waves and two coupled transverse waves, which are dispersive in nature. Reflection from a thermally insulated stress-free surface is considered for incidence of coupled longitudinal wave. The speeds and reflection coefficients of plane waves are computed numerically for a particular model.

scholarly journals PSEUDOTENSOR FORMULATION OF THE MECHANICS OF HEMITROPIC MICROPOLAR MEDIA

2020 ◽  
Vol 82 (4) ◽  
pp. 399-412
Author(s):  
Yu.N. Radayev ◽  
E.V. Murashkin
Keyword(s):  
Dimensional Space ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Elastic Potential ◽  
Micropolar Continuum ◽  
Micropolar Continua ◽  
Statics And Dynamics ◽  
Elasticity Tensors ◽  
Micropolar Media ◽  
Differential Properties

The possibility of applications of relative tensors concepts to the mechanics of micropolar continuum and, in particular, for the hemitropic micropolar continua is considered. The fundamental tensors and orienting relative scalars in three-dimensional space are introduced. Permutation symbols and absolute Levi-Civita tensors are investigated in further details. Algebraic and differential properties of the relative tensors are discussed. The weights of the fundamental kinematic tensors are determined. The wryness tensor and the asymmetric strain tensor are constructed in terms of the vectors of micro-rotation and displacements. Notions of force and couple traction vectors, associated force and associated couple stress vector, force and couple stresses tensors are discussed in the frameworks of relative tensors algebra. The weights of the basic micropolar elasticity tensors are determined and discussed. The constitutive form of the micropolar elastic potential is introduced as an absolute scalar in order to obtain micropolar constitutive equations. In the linear case, the elastic potential is a quadratic form whose coefficients are pseudoscalars. The weights of the constitutive pseudoscalars are calculated. The dimensionless constitutive micropolar constants and constitutive constants with physical dimensions are discriminated. Statics and dynamics of micropolar elastic continua are developed in terms of relative tensors. Dynamic equations involving displacements and microrotations in the case of semi-isotropic (hemitropic) symmetry are derived and represented by the pseudotensor technique. The paper can be considered as a script of fundamental formulas and concepts related to the algebra and differentiation of relative tensors of arbitrary rank.

scholarly journals Generalized Photo-Thermo-Microstretch Elastic Solid Semiconductor Medium Due To Excitation Process

2021 ◽  
Author(s):  
kh. lotfy ◽  
A. El-Bary
Keyword(s):  
Mechanical Load ◽  
Harmonic Wave ◽  
Plane Waves ◽  
Elastic Solid ◽  
Two Dimensions ◽  
Load Force ◽  
Normal Displacement ◽  
Physical Fields ◽  
Novel Model ◽  
Coupled Stress

Abstract A novel model in the theory of photo-thermoelasticity with microstretch properties is studied. The plasma-elastic-thermal plane waves are propagated in a linear isotropic generalized photo-thermo-microstretch elastic semiconductor solid medium. The photothermal excitation occurs in the context of the microinertia of microelement process during two dimensions (2D) deformation. The harmonic wave techniques are used to get the solutions for the basic variables. The analytical solution of the main physical fields; carrier intensity, normal displacement components, temperature, stress load force, microstress and tangential coupled stress can be obtained. Some graphics illustrated when using the plasma, thermal and mechanical load boundary conditions, which they apply at the outer free surface of the elastic medium. Some semiconductor materials as silicon (Si) and Germanium (Ge) are used to make the numerical simulation and some comparisons in different thermal memories are made. The main physical variables with new parameters are discussed theoretically and shown graphically.

Elastic Waves

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Elastic Waves ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Plane Waves ◽  
Elastic Solid ◽  
Stress And Strain ◽  
Field Equations ◽  
Strain Stress ◽  
Thermodynamic Variables ◽  
Dynamic Variables

This chapter focuses on the mathematics of elastic waves. In the case of a continuous medium, the field equations of physics (yielding the dynamic and thermodynamic variables) arise from three conservation equations: conservation of mass, momentum and energy. For an elastic medium, these equations of motion are known as Navier equations, which give rise to a rich variety of stress waves. There are two dynamic variables in an elastic solid: stress and strain. Stress and strain are linearly related in small-amplitude deformations; this relation is expressed by Hooke's law. The chapter first introduces the basic notation for elastic waves before discussing the solutions for plane waves. It also considers surface waves and Love waves.

Joint wave-equation traveltime inversion of diving/direct and reflected waves for the P- and S-wave velocity macromodel building

Geophysics ◽  
2021 ◽  
pp. 1-145
Author(s):  
Zhiming Ren ◽  
Qianzong Bao ◽  
Bingluo Gu
Keyword(s):  
Wave Velocity ◽  
Velocity Model ◽  
S Wave ◽  
Direct Wave ◽  
Reflected Waves ◽  
Traveltime Inversion ◽  
Long Wavelength ◽  
Velocity Models ◽  
Reflected Wave ◽  
Background Models

Full waveform inversion (FWI) suffers from the local minima problem and requires a sufficiently accurate starting model to converge to the correct solution. Wave-equation traveltime inversion (WETI) is an effective tool to retrieve the long-wavelength components of the velocity model. We develop a joint diving/direct and reflected wave WETI (JDRWETI) method to build the P- and S-wave velocity macromodels. We estimate the traveltime shifts of seismic events (diving/direct waves, PP and PS reflections) through the dynamic warping scheme and construct a misfit function using both the time shifts of diving/direct and reflected waves. We derive the adjoint wave equations and the gradients with respect to the background models based on the joint misfit function. We apply the kernel decomposition scheme to extract the kernel of the diving/direct wave and the tomography kernels of PP and PS reflections. For an explosive source, the kernels of diving/direct wave and PP reflections and the kernel of PS reflections are used to compute the P- and S-wave gradients of the background models, respectively. We implement JDRWETI by a two-stage inversion workflow: first invert the P- and S-wave velocity models using the P-wave gradients and then improve the S-wave velocity model using the S-wave gradients. Numerical tests on synthetic and field datasets reveal that the JDRWETI method successfully recovers the long-wavelength components of P- and S-wave velocity models, which can be used for an initial model for the subsequent elastic FWI. Moreover, the proposed JDRWETI method prevails over the existing reflection WETI method and the cascaded diving/direct and reflected wave WETI method, especially when large velocity errors are present in the shallow part of the starting models. The JDRWETI method with the two-stage inversion workflow can give rise to reasonable inversion results even for the model with different P- and S-wave velocity structures.

Research of the Influence of Geometric Parameters of Rooms for Sound Insulation of Lightweight Partitions

2021 ◽  
pp. 37-47
Author(s):  
Д. В. Монич ◽  
И. В. Матвеева ◽  
П. А. Гребнев ◽  
Д. С. Кузьмин
Keyword(s):  
Noise Source ◽  
Experimental Studies ◽  
Sound Field ◽  
Sound Insulation ◽  
Mirror Reflection ◽  
Sound Waves ◽  
Good Convergence ◽  
Boundary Frequency ◽  
Field Sound ◽  
Wave Modes

Состояние проблемы. Звукоизоляция легких перегородок значительно зависит от места их установки в здании. Необходимы исследования структуры звукового поля в несоразмерных помещениях и анализ его влияния на звукоизоляцию легких ограждений. Результаты. Проведены натурные и лабораторные экспериментальные исследования звукоизоляции каркасно-обшивной перегородки, установленной в коридоре. Для случая соразмерного помещения получена хорошая сходимость результатов. Теоретически исследована структура звукового поля при зеркальном отражении звука (с использованием метода прослеживания лучей). Выполнены расчеты с получением распределений долей осевых, касательных и косых лучей в помещениях, расчеты уровней интенсивности звуковых волн, падающих на боковые стены и потолок коридора. Учитывалось положение источника шума относительно перегородки и других ограждений. Выводы. Пропорции помещений влияют на звукоизоляцию легких ограждений. В диапазоне ниже граничной частоты диффузности несоразмерного помещения с источником шума структура звукового поля неоднородная, звуковые лучи падают на ограждение неравномерно с различных направлений. Это приводит к уменьшению совпадений мод колебаний в воздухе и в ограждающей конструкции, частотная характеристика звукоизоляции ограждения имеет пикообразный вид. Statement of the problem. Sound insulation of lightweight partitions depends significantly on the place of installation in the building. It is necessary to study the structure of the sound field in disproportionate rooms and analyze its effect on the sound insulation of light enclosures. Results. Natural and laboratory experimental studies of the sound insulation of the frame partitions installed in the corridor were carried out. For the case of a commensurate room, good convergence of the results was obtained. The structure of the sound field with mirror reflection of sound has been theoretically investigated using the method of tracing of sound rays. Calculations were performed to obtain the distributions of the proportions of axial sound rays, tangential sound rays, oblique sound rays in the premises, and the calculations of the intensity levels of sound waves incident on the lightweight partition and other enclosures of the corridor. The position of the noise source relative to the lightweight partition and other enclosures of the corridor was taken into account. Conclusions. The proportions of the rooms affect the sound insulation of lightweight enclosures. The structure of the sound field of a disproportionate room with a noise source is non-uniform in the range below the boundary frequency of diffuse sound field. Sound rays fall on the lightweight partition unevenly from different directions. This leads to a decrease in the coincidence of wave modes in the air and wave modes in the lightweight partition. The frequency characteristic of the sound insulation of the lightweight partition has a peak-like appearance.

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