A non-reflecting wave equation through directional wave-field suppression and its finite difference implementation

The acoustic wave equation describes wave propagation directly from basic physical laws, even in heterogeneous acoustic media. When numerically simulating waves with the wave equation, contrasts in the medium parameters automatically generate all scattering effects. For some applications - such as propagation analysis or certain wave-equation based imaging techniques - it is desirable to suppress these reflections, as we are only interested in the transmitted wave-field. To achieve this, a modification to the constitutive relations is proposed, yielding an extra term that suppresses waves with reference to a preferred direction. The scale-factor $$\alpha$$ α of this extra term can either be interpreted as a penetration depth or as a typical decay time. This modified theory is implemented using a staggered-grid, time-domain finite difference scheme, where the acoustic Poynting-vector is used to estimate the local propagation direction of the wave-field. The method was successfully used to suppress reflections in media with bone tissue (medical ultrasound) and geophysical subsurface structures, while introducing only minor perturbations to the transmitted wave-field and a small increase in computation time.

Behavior of thermo-mechanically treated rebar exposed to elevated temperatures

PurposeThe purpose of the paper is to mathematically model and predict the characteristics of thermo-mechanically treated (TMT) rebar when subjected to elevated temperatures.Design/methodology/approachData were collected from a few selected studies for developing the constitutive relations. Using the exposed temperature and the duration of heating as independent variables, the empirical relations were developed for determining the changes in mechanical properties of TMT rebars at elevated temperatures.FindingsRecrystallization of TMT rebar crystals took place around 500 °C, which led to a decrease in the dislocation density along with the increase of large-sized grains, resulting in the degradation of strength. Up to a temperature range of 500 °C, the normalized fracture strength was higher, while the normalized fracture strain is not so high. This indicated a failure of brittle nature.Originality/valueThis is an original work done by others as a study to theoretically predict the mechanical behavior of TMT rebars when exposed to elevated temperature.HighlightsThe TMT bars showed brittleness characteristics up to 500 °C and showed ductility characteristics after that on account of its recrystallization and extensive tempering of the outer martensitic rim around that temperature.The comparison between the super ductile (SD) TMT and the regular TMT exhibit shows that the SD-TMT bars were about 1.5 times more ductile than the normal ones.

NUMERICAL MODELLING OF BIRD STRIKE ON A ROTATING ENGINE BLADES BASED ON VARIATIONS OF POROSITY DENSITY

A numerical investigation is conducted on a rotating engine blade subjected to a bird strike impact. The bird strike is numerically modelled as a cylindrical gelatine with hemispherical ends to simulate impact on a rotating engine blade. Numerical modelling of a rotating engine blade has shown that bird strikes can severely damage an engine blade, especially as the engine blade rotates, as the rotation causes initial stresses on the root of the engine blade. This paper presents a numerical modelling of the engine blades subjected to bird strike with porosity implemented on the engine blades to investigate further damage assessment due to this porosity effect. As porosity influences the decibel levels on a propeller blade or engine blade, the damage due to bird strikes can investigate the compromise this effect has on the structural integrity of the engine blades. This paper utilizes a bird strike simulation through an LS-Dyna Pre-post software. The numerical constitutive relations are keyed into the keyword manager where the bird’s SPH density, a 10 ms simulation time, and bird velocity of 100 m/s are all set. The blade rotates counter-clockwise at 200 rad/s with a tetrahedron mesh. The porous regions or voids along the blade are featured as 5 mm diameter voids, each spaced 5 mm apart. The bird is modelled as an Elastic-Plastic-Hydrodynamic material model to analyze the bird’s fluid behavior through a polynomial equation of state. To simulate the fluid structure interaction, the blade is modelled with Johnson-Cook Material model parameters of aluminium where the damage of the impact can be observed. The observations presented are compared to previous study of a bird strike impact on non-porous engine blades. ABSTRAK: Penyelidikan berangka telah dijalankan ke atas bilah enjin berputar tertakluk kepada impak pelanggaran burung. Pelanggaran burung tersebut telah dimodelkan secara berangka sebagai silinder gelatin dengan hujungnya berbentuk hemisfera demi mensimulasikan impaknya ke atas bilah enjin yang berputar. Pemodelan berangka bilah-bilah enjin yang berputar tersebut menunjukkan bahawa pelanggaran burung mampu menyebabkan kerosakan teruk terhadap bilah enjin terutamanya apabila bilah enjin sedang berputar oleh sebab putaran menghasilkan tekanan asal di pangkal bilah enjin. Kajian ini mengetengahkan pemodelan berangka ke atas bilah-bilah enjin tertakluk kepada pelanggaran burung terhadap bilah-bilah enjin yg mempunyai keliangan demi menyelidik dan menilai kerosakan kesan daripada keliangan tersebut. Keliangan juga mempengaruhi tahap-tahap desibel ke atas bilah kipas ataupun bilah enjin, kerosakan hasil serangan burung boleh menterjemah tahap ketahanan struktur integriti bagi bilah-bilah enjin tersebut. Penyelidikan ini mengguna pakai perisian “LS-Dyna Pre-post” untuk simulasi pelanggaran burung. Hubungan konstitutif berangka telah dimasukkan sebagai kata kunci di mana ketumpatan SPH burung, masa simulasi 10ms, dan halaju burung ditetapkan kepada 100 m/s. Bilah tersebut berputar pada 200 rad/s arah lawan jam dengan jejaring tetrahedron. Kawasan berliang atau kosong di sepanjang bilah ditetapkan diameternya kepada 5 mm, dan dijarakkan 5 mm di antara satu sama lain. Burung pula dimodelkan sebagai material “Elastic-Plastic-Hydrodynamic” untuk mengkaji sifat bendalir burung melalui persamaan polinomial. Demi mensimulasi interaksi struktur bendalir, bilah tersebut dimodelkan sebagai parameter aluminium material “Johnson Cook” di mana kerosakan daripada impak tersebut dapat diteliti. Penelitian-penelitian tersebut dibandingkan dengan kajian terdahulu ke atas serangan burung terhadap bilah-bilah enjin tidak berliang.

Non-Abelian anomalous constitutive relations of a chiral hadronic fluid

We study the constitutive relations of a chiral hadronic fluid in presence of non-Abelian’t Hooft anomalies. Analytical expressions for the covariant currents are obtained at first order in derivatives in the chiral symmetric phase, for both two and three quark flavors in the presence of chiral imbalance. We also investigate the constitutive relations after chiral symmetry breaking at the leading order.

Exact Three-Dimensional Stability Analysis of Plate Using an Direct Variational Energy Method

In this paper, direct variational calculus was put into practical use to analyses the three dimensional (3D) stability of rectangular thick plate which was simply supported at all the four edges (SSSS) under uniformly distributed compressive load. In the analysis, both trigonometric and polynomial displacement functions were used. This was done by formulating the equation of total potential energy for a thick plate using the 3D constitutive relations, from then on, the equation of compatibility was obtained to determine the relationship between the rotations and deflection. In the same way, governing equation was obtained through minimization of the total potential energy functional with respect to deflection. The solution of the governing equation is the function for deflection. Functions for rotations were obtained from deflection function using the solution of compatibility equations. These functions, deflection and rotations were substituted back into the energy functional, from where, through minimizations with respect to displacement coefficients, formulas for analysis were obtained. In the result, the critical buckling loads from the present study are higher than those of refined plate theories with 7.70%, signifying the coarseness of the refined plate theories. This amount of difference cannot be overlooked. However, it is shown that, all the recorded average percentage differences between trigonometric and polynomial approaches used in this work and those of 3D exact elasticity theory is lower than 1.0%, confirming the exactness of the present theory. Thus, the exact 3D plate theory obtained, provides a good solution for the stability analysis of plate and, can be recommended for analysis of any type of rectangular plates under the same loading and boundary condition. Doi: 10.28991/CEJ-2022-08-01-05 Full Text: PDF

On the statements of boundary conditions in models of the woven materials production

В статье обсуждаются проблемы постановка краевых задач при моделировании процессов аддитивного производства 3D материала, при учете наличия в нем дополнительных выделенных направлений (выкладки волокон в тканых материалах, арматуры в бетонных конструкциях, биоволокон в мышечной ткани и т.д.). Выводится общая форма тензорного соотношения на поверхности наращивания, при учете дополнительного выделенного направления. Определяется необходимая система независимых аргументов определяющей тензорной функции на поверхности наращивания в рассматриваемом случае. Определяется полный набор совместных рациональных инвариантов тензора напряжений и характерных директоров. Дается инвариантно-полная формулировка определяющих соотношений на поверхности наращивания. Предложены постановки краевых задач, моделирующих процессы синтеза тканых 3D материалов. Полученные дифференциальные ограничения конкретизируются для ортогональных систем координат, учитывающих геометрию процесса наращивания. The article discusses the problem of boundary value problems in models of the additive production processes of a 3D material, taking into account the presence of additional selected directions in it (laying out fibers in woven materials, reinforcement in concrete structures, biofibers in muscle tissue, etc.). The general form of the tensor relation on the growing surface is shown, taking into account the additional selected direction. The necessary system of independent arguments of the constitutive tensor function on the growing surface in the considered case is determined. A complete set of joint rational invariants of the stress tensor and characteristic directors is determined. An invariant-complete formulation of the constitutive relations on the growing surface is given. The formulation of boundary value problems that simulate the processes of synthesis of woven 3D materials are proposed. The resulting differential constraints are specified for orthogonal coordinate systems taking account of the geometry of the growing process.

Analysis of the Vibration Behaviors of Rotating Composite Nano-Annular Plates Based on Nonlocal Theory and Different Plate Theories

Rotating machinery has significant applications in the fields of micro and nano meters, such as nano-turbines, nano-motors, and biomolecular motors, etc. This paper takes rotating nano-annular plates as the research object to analyze their free vibration behaviors. Firstly, based on Kirchhoff plate theory, Mindlin plate theory, and Reddy plate theory, combined with nonlocal constitutive relations, the differential motion equations of rotating functionally graded nano-annular plates in a thermal environment are derived. Subsequently, the numerical method is used to discretize and solve the motion equations. The effects of nonlocal parameter, temperature change, inner and outer radius ratio, and rotational velocity on the vibration frequencies of the nano-annular plates are analyzed through numerical examples. Finally, the relationship between the fundamental frequencies and the thickness-to-radius ratio of the nano-annular plates of clamped inner and outer rings is discussed, and the differences in the calculation results among the three plate theories are compared.

Change Seen Through the Lens of Social Psychology in Europe and the United States

In this chapter, the authors consider the theme both by browsing through seminal reference books and scholars’ contributions and by using digital methods, probing all the abstracts published in two key journals: the US Journal of Personality and Social Psychology and the European Journal of Social Psychology. The keyword change is explored in its frequency, concordances, and usage contexts and trends over time in the two journals. The results empirically support Marková’s claim that change has mostly been studied in social psychology as perturbation of patterns of stability and has focused on individuals as surrounded and affected by social contexts. To better understand and foster societal changes, a “more social” social psychology would be helpful, particularly adopting study designs and projects oriented by perspectives that can emphasize the mutual and constitutive relations between the individual and the social.

Evaluation of Corrosion, Mechanical Properties and Hydrogen Embrittlement of Casing Pipe Steels with Different Microstructure

In the research, the corrosion and mechanical properties, as well as susceptibility to hydrogen embrittlement, of two casing pipe steels were investigated in order to assess their serviceability in corrosive and hydrogenating environments under operation in oil and gas wells. Two carbon steels with different microstructures were tested: the medium carbon steel (MCS) with bainitic microstructure and the medium-high carbon steel (MHCS) with ferrite–pearlite microstructure. The results showed that the corrosion resistance of the MHCS in CO2-containing acid chloride solution, simulating formation water, was significantly lower than that of the MCS, which was associated with microstructure features. The higher strength MCS with the dispersed microstructure was less susceptible to hydrogen embrittlement under preliminary electrolytic hydrogenation than the lower strength MHCS with the coarse-grained microstructure. To estimate the embrittlement of steels, the method of the FEM load simulation of the specimens with cracks was used. The constitutive relations of the true stress–strain of the tested steels were defined. The stress and strain dependences in the crack tip were calculated. It was found that the MHCS was characterized by the lower plasticity on the stage of the neck formation of the specimen and the lower fracture toughness than the other one. The obtained results demonstrating the limitations of the usage of casing pipes made of the MHCS with the coarse-grained ferrite/pearlite microstructure in corrosive and hydrogenating environments were discussed.