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1

Shantarin, V. D., und M. Yu Zemenkova. „WATER STRUCTURES IN MECHANICAL FIELDS“. Oil and Gas Studies, Nr. 3 (30.06.2015): 126–33. http://dx.doi.org/10.31660/0445-0108-2015-3-126-133.

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This article is devoted to studying the properties of water and its model. It is shown that the existing models are not able to explain the entire set of properties of water, considering water as a non-equilibrium system and possessing the properties of self-organization and sensitive to weak field effects. The results of the authors’ research confirm a cluster-fractal model which considers water as a mixture of free molecules and fragments with the ordered hexagonal structure. It is shown that pure water electric conductivity depends on concentration of ions and the water capability of a relay way of transfer of these ions, which depends on its structural- information state.
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2

Kruch, S. „Homogenized and relocalized mechanical fields“. Journal of Strain Analysis for Engineering Design 42, Nr. 4 (Mai 2007): 215–26. http://dx.doi.org/10.1243/03093247jsa229.

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3

Shao, Yihan, Andrew Simmonett, Frank Pickard, Gerhard Koenig und Bernard Brooks. „Quantum Mechanical Molecular Mechanical Calculations using AMOEBA Force Fields“. Biophysical Journal 108, Nr. 2 (Januar 2015): 158a. http://dx.doi.org/10.1016/j.bpj.2014.11.871.

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4

Palomaki, T. A., J. D. Teufel, R. W. Simmonds und K. W. Lehnert. „Entangling Mechanical Motion with Microwave Fields“. Science 342, Nr. 6159 (03.10.2013): 710–13. http://dx.doi.org/10.1126/science.1244563.

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5

Stevens Jr., Herbert H. „Evolution of Minds and Quantum Mechanical Fields.“ Physics Essays 3, Nr. 2 (01.06.1990): 126–32. http://dx.doi.org/10.4006/1.3033430.

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6

Ai, Shu-Tao, Jin-Song Wang und Wei-Tao Lu. „Internal, Thermo-Electro-Mechanical Fields of Ferroelectrics“. Ferroelectrics Letters Section 40, Nr. 1-3 (Januar 2013): 11–16. http://dx.doi.org/10.1080/07315171.2013.813822.

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7

Cieplak, Piotr, François-Yves Dupradeau, Yong Duan und Junmei Wang. „Polarization effects in molecular mechanical force fields“. Journal of Physics: Condensed Matter 21, Nr. 33 (24.07.2009): 333102. http://dx.doi.org/10.1088/0953-8984/21/33/333102.

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8

Brooke, Matthew, und Bernard Richardson. „Mechanical vibrations and radiation fields of guitars“. Journal of the Acoustical Society of America 94, Nr. 3 (September 1993): 1806. http://dx.doi.org/10.1121/1.407873.

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9

Panchenko, Yu N. „Scaling of quantum-mechanical molecular force fields“. Russian Chemical Bulletin 45, Nr. 4 (April 1996): 753–60. http://dx.doi.org/10.1007/bf01431292.

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10

Bengtsson, A. K. H. „Mechanical models for higher spin gauge fields“. Fortschritte der Physik 57, Nr. 5-7 (06.04.2009): 499–504. http://dx.doi.org/10.1002/prop.200900032.

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11

Hemmingsen, Lars, Daniel E. Madsen, Anders L. Esbensen, Lars Olsen und Søren B. Engelsen. „Evaluation of carbohydrate molecular mechanical force fields by quantum mechanical calculations“. Carbohydrate Research 339, Nr. 5 (April 2004): 937–48. http://dx.doi.org/10.1016/j.carres.2003.11.024.

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12

Suh, N. P. „Axiomatic Design of Mechanical Systems“. Journal of Mechanical Design 117, B (01.06.1995): 2–10. http://dx.doi.org/10.1115/1.2836467.

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Design is done in many fields. Although the design practices in different fields appear to be distinct from each other, all fields use a common thought process and design principles. Consequently, the true differences between these fields are minor, often consisting of the definitions of words, the specific data, and knowledge. In comparison, larger differences can exist within a given field between simple systems and large systems due to the size and the time dependent nature of functional requirements. The axiomatic approach to design provides a general theoretical framework for all these design fields, including mechanical design. The key concepts of axiomatic design are: the existence of domains, the characteristic vectors within the domains that can be decomposed into hierarchies through zigzagging between the domains, and the design axioms (i.e., the Independence Axiom and the Information Axiom). Based on the two design axioms, corollaries and theorems can be stated or derived for simple systems, large systems, and organizations. These theorems and corollaries can be used as design rules or guidelines for designers. The basic concepts are illustrated using simple mechanical design examples. When design is viewed axiomatically, not only product design but all other designs, including design of process, systems, software, organizations, and materials, are amenable to systematic treatment.
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13

Suh, N. P. „Axiomatic Design of Mechanical Systems“. Journal of Vibration and Acoustics 117, B (01.06.1995): 2–10. http://dx.doi.org/10.1115/1.2838673.

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Design is done in many fields. Although the design practices in different fields appear to be distinct from each other, all fields use a common thought process and design principles. Consequently, the true differences between these fields are minor, often consisting of the definitions of words, the specific data, and knowledge. In comparison, larger differences can exist within a given field between simple systems and large systems due to the size and the time dependent nature of functional requirements. The axiomatic approach to design provides a general theoretical framework for all these design fields, including mechanical design. The key concepts of axiomatic design are: the existence of domains, the characteristic vectors within the domains that can be decomposed into hierarchies through zigzagging between the domains, and the design axioms (i.e., the Independence Axiom and the Information Axiom). Based on the two design axioms, corollaries and theorems can be stated or derived for simple systems, large systems, and organizations. These theorems and corollaries can be used as design rules or guidelines for designers. The basic concepts are illustrated using simple mechanical design examples. When design is viewed axiomatically, not only product design but all other designs, including design of process, systems, software, organizations, and materials, are amenable to systematic treatment.
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14

Tonica, Oleg Vladimirovych. „METHODS OF STOCHASTIC MODELING OF PHYSICAL-MECHANICAL FIELDS“. Bulletin of National Technical University "KhPI". Series: System Analysis, Control and Information Technologies, Nr. 2 (13.11.2019): 34–39. http://dx.doi.org/10.20998/2079-0023.2019.02.06.

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15

Galea, Russell, Krzysztof K. Dudek, Pierre-Sandre Farrugia, Louis Zammit Mangion, Joseph N. Grima und Ruben Gatt. „Reconfigurable magneto-mechanical metamaterials guided by magnetic fields“. Composite Structures 280 (Januar 2022): 114921. http://dx.doi.org/10.1016/j.compstruct.2021.114921.

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16

Panchenko, Yurii N. „Methods of scaling quantum mechanical molecular force fields“. Journal of Molecular Structure 410-411 (Juni 1997): 327–29. http://dx.doi.org/10.1016/s0022-2860(96)09472-0.

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17

Franklin, J., und K. Cole Newton. „Classical and quantum mechanical motion in magnetic fields“. American Journal of Physics 84, Nr. 4 (April 2016): 263–69. http://dx.doi.org/10.1119/1.4941571.

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18

Panchenko, Yu N., G. R. De Maré und N. F. Stepanov. „Advantages of scaled quantum mechanical molecular force fields“. Journal of Molecular Structure 348 (März 1995): 413–16. http://dx.doi.org/10.1016/0022-2860(95)08676-m.

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19

Qin, Fei, und Dong-mei Yan. „The perturbed magnetic fields caused by mechanical stress“. Frontiers of Mechanical Engineering in China 1, Nr. 2 (Juni 2006): 151–56. http://dx.doi.org/10.1007/s11465-006-0015-1.

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20

Shindo, Yasuhide, Kotaro Mori und Fumio Narita. „Electromagneto-mechanical fields of giant magnetostrictive/piezoelectric laminates“. Acta Mechanica 212, Nr. 3-4 (11.12.2009): 253–61. http://dx.doi.org/10.1007/s00707-009-0259-z.

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21

Meyer, A. Y., und F. R. F. Forrest. „Towards the convergence of molecular-mechanical force fields“. Journal of Computational Chemistry 6, Nr. 1 (Februar 1985): 1–4. http://dx.doi.org/10.1002/jcc.540060102.

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22

Hart, Francis X. „The mechanical transduction of physiological strength electric fields“. Bioelectromagnetics 29, Nr. 6 (September 2008): 447–55. http://dx.doi.org/10.1002/bem.20411.

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23

Cariñena, José F., und Miguel-C. Muñoz-Lecanda. „Geodesic and Newtonian Vector Fields and Symmetries of Mechanical Systems“. Symmetry 15, Nr. 1 (07.01.2023): 181. http://dx.doi.org/10.3390/sym15010181.

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Geodesic vector fields and other distinguished vector fields on a Riemann manifold were used in the study of free motions on such a manifold, and we applied the geometric Hamilton–Jacobi theory for the search of geodesic vector fields from Hamilton–Jacobi vector fields and the same for closed vector fields. These properties were appropriately extended to the framework of Newtonian and generalised Newtonian systems, in particular systems defined by Lagrangians of the mechanical type and velocity-dependent forces. Conserved quantities and a generalised concept of symmetry were developed, particularly for Killing vector fields. Nonholonomic constrained Newtonian systems were also analysed from this perspective, as well as the relation among Newtonian vector fields and Hamilton–Jacobi equations for conformally related metrics.
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24

Greated, C. A. „Measurement of acoustic velocity fields“. Strain 22, Nr. 1 (Februar 1986): 21–24. http://dx.doi.org/10.1111/j.1475-1305.1986.tb00016.x.

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25

Lorenzo, Guillermo, Thomas J. R. Hughes, Pablo Dominguez-Frojan, Alessandro Reali und Hector Gomez. „Computer simulations suggest that prostate enlargement due to benign prostatic hyperplasia mechanically impedes prostate cancer growth“. Proceedings of the National Academy of Sciences 116, Nr. 4 (07.01.2019): 1152–61. http://dx.doi.org/10.1073/pnas.1815735116.

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Prostate cancer and benign prostatic hyperplasia are common genitourinary diseases in aging men. Both pathologies may coexist and share numerous similarities, which have suggested several connections or some interplay between them. However, solid evidence confirming their existence is lacking. Recent studies on extensive series of prostatectomy specimens have shown that tumors originating in larger prostates present favorable pathological features. Hence, large prostates may exert a protective effect against prostate cancer. In this work, we propose a mechanical explanation for this phenomenon. The mechanical stress fields that originate as tumors enlarge have been shown to slow down their dynamics. Benign prostatic hyperplasia contributes to these mechanical stress fields, hence further restraining prostate cancer growth. We derived a tissue-scale, patient-specific mechanically coupled mathematical model to qualitatively investigate the mechanical interaction of prostate cancer and benign prostatic hyperplasia. This model was calibrated by studying the deformation caused by each disease independently. Our simulations show that a history of benign prostatic hyperplasia creates mechanical stress fields in the prostate that impede prostatic tumor growth and limit its invasiveness. The technology presented herein may assist physicians in the clinical management of benign prostate hyperplasia and prostate cancer by predicting pathological outcomes on a tissue-scale, patient-specific basis.
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26

Fa-rong, Yuan, und Sun Hua-dong. „Transient temperature fields and residual stress fields of metallic materials under welding“. Applied Mathematics and Mechanics 12, Nr. 6 (Juni 1991): 595–99. http://dx.doi.org/10.1007/bf02015573.

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27

Sloan, James V., Alejandro A. Pacheco Sanjuan, Zhengfei Wang, Cedric M. Horvath und Salvador Barraza-Lopez. „Discrete Gauge Fields for Graphene Membranes under Mechanical Strain“. MRS Proceedings 1549 (2013): 31–34. http://dx.doi.org/10.1557/opl.2013.1030.

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ABSTRACTMechanical strain creates strong gauge fields in graphene, offering the possibility of controlling its electronic properties. We developed a gauge field theory on a honeycomb lattice valid beyond first-order continuum elasticity. Along the way, we resolve a recent controversy on the theory of strain engineering in graphene: there are no K-point dependent gauge fields.
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28

Кайнц, Д. І., А. А. Горват und Ю. С. Наконечний. „Dielectric properties in electric SbSJ, mechanical and temperature fields“. Scientific Herald of Uzhhorod University.Series Physics 5 (31.12.1999): 44–49. http://dx.doi.org/10.24144/2415-8038.1999.5.44-49.

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29

Inoue, Tatsuo. „Macro- and microscopic simulation of materio-thermo-mechanical fields“. Metals and Materials 4, Nr. 3 (Mai 1998): 227–34. http://dx.doi.org/10.1007/bf03187767.

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30

Mao, Yu, Y. Liu und Hai Lin. „Angular momenta in fields from a rotational mechanical antenna‡“. Journal of Physics Communications 5, Nr. 12 (01.12.2021): 125012. http://dx.doi.org/10.1088/2399-6528/ac41a9.

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Abstract Mechanic antennas provide opportunities for human portable, VLF communications, where a rotational dipole emits EM signals with angular momenta. In this paper we analytically derive the electromagnetic fields from a rotational electric dipole using Fourier transform method, and find that the radiated fields from the rotational electric dipole carries nonzero energy flow density in both orbital and spin angular momentum (AM) parts by their flux tensors. Intuitively, a dipole circulating on the transverse plane induces a longitudinal orbital angular momentum and a longitudinal spin angular momentum. And the binding force for the rotational electric dipole is then shown to result mainly from the Coulomb fields. We believe that our work will contributes to novel communication designs for portable mechanic antennas.
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31

Dmitriyev, V. P. „Towards an exact mechanical analogy of particles and fields“. Il Nuovo Cimento A 111, Nr. 5 (Mai 1998): 501–11. http://dx.doi.org/10.1007/bf03185584.

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32

Berezin, K. V., A. V. Novoselova, M. L. Chernavina, V. I. Berezin und V. V. Novoselov. „Calculation of Scale Factors for Quantum-mechanical Force Fields“. Series Physics 15, Nr. 4 (10.12.2015): 41–44. http://dx.doi.org/10.18500/1817-3020-2015-15-4-41-44.

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33

Giese, Timothy J., und Darrin M. York. „Quantum mechanical force fields for condensed phase molecular simulations“. Journal of Physics: Condensed Matter 29, Nr. 38 (17.08.2017): 383002. http://dx.doi.org/10.1088/1361-648x/aa7c5c.

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34

Vshivkov, Sergei A., Sergei G. Kulichikhin und Elena V. Rusinova. „Phase transitions in polymer solutions induced by mechanical fields“. Russian Chemical Reviews 67, Nr. 3 (31.03.1998): 233–43. http://dx.doi.org/10.1070/rc1998v067n03abeh000319.

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35

Panchenko, Yurii N. „Vibrational spectra and scaled quantum-mechanical molecular force fields“. Journal of Molecular Structure 567-568 (Juni 2001): 217–30. http://dx.doi.org/10.1016/s0022-2860(01)00555-5.

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36

Zhang, Pei, Joon Hock Yeo und Ned HC Hwang. „INVESTIGATION OF SHEAR FIELDS ACROSS MECHANICAL HEART VALVE MODEL“. ASAIO Journal 51, Nr. 2 (März 2005): 42A. http://dx.doi.org/10.1097/00002480-200503000-00165.

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37

Mansori, Mohamed El, und Barney E. Klamecki. „Magnetic Field Effects in Machining Processes and on Manufactured Part Mechanical Characteristics“. Journal of Manufacturing Science and Engineering 128, Nr. 1 (20.07.2005): 136–45. http://dx.doi.org/10.1115/1.2113007.

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A review of research results demonstrating that magnetic fields applied to machining processes and mechanically manufactured parts can have beneficial effects is presented, an explanatory mechanistic model is described, and the model is used to interpret some results. The magnetic field-material interaction model shows an exponential dependence of material behavior and mechanical property changes on applied field strength and material magnetostrictive characteristics. Implications for use of magnetic fields to manipulate tribological processes, control machining processes, and alter material properties are that low field strengths can be useful for treating materials that have large magnetostrictive stain and high magnetic saturation level.
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38

Roberts, Mark D. „Quantum imploding scalar fields“. Royal Society Open Science 5, Nr. 10 (Oktober 2018): 180692. http://dx.doi.org/10.1098/rsos.180692.

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The d’Alembertian □ ϕ = 0 has the solution ϕ = f ( v )/ r , where f is a function of a null coordinate v , and this allows creation of a divergent singularity out of nothing. In scalar-Einstein theory a similar situation arises both for the scalar field and also for curvature invariants such as the Ricci scalar. Here what happens in canonical quantum gravity is investigated. Two minispace Hamiltonian systems are set up: extrapolation and approximation of these indicates that the quantum mechanical wave function can be finite at the origin.
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39

Naidu, V. G., M. L. Mittal und B. Nageswara Rao. „Boundary layer heat transfer with electromagnetic fields“. Acta Mechanica 68, Nr. 3-4 (September 1987): 277–86. http://dx.doi.org/10.1007/bf01190889.

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40

Treede, R. D., R. A. Meyer und J. N. Campbell. „Comparison of heat and mechanical receptive fields of cutaneous C-fiber nociceptors in monkey“. Journal of Neurophysiology 64, Nr. 5 (01.11.1990): 1502–13. http://dx.doi.org/10.1152/jn.1990.64.5.1502.

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1. Receptive-field properties were investigated in cutaneous C-fiber nociceptive afferents (CMH) responsive to mechanical and heat stimuli. Teased-fiber techniques were used to record from 28 CMHs that innervated the hairy skin of upper or lower limb in anesthetized monkeys. 2. The response to mechanical stimuli was studied with the use of calibrated von Frey probes. The response to heat stimuli was studied with the use of a laser thermal stimulator that provided stepped increases in skin temperature with rise times to the desired temperature near 100 ms. The size of the receptive field (RF) for mechanical stimuli was determined by use of a suprathreshold stimulus that consisted of a 0.5-mm-diam probe that exerted a 200-mN force (10 bar). The size of the heat RF was determined by use of a 49 degrees C stimulus applied to a 7.5-mm-diam area for 1 s. 3. Heat thresholds were determined with an ascending series of stimulus intensities and were found to be stable over many hours: they ranged from 37 to 46 degrees C (mean, 41.1 degrees C). Mechanical thresholds ranged from 1.3 to 7.3 bar (mean, 3.3 bar). There was no correlation between mechanical and heat thresholds. Both thresholds extended well below the corresponding psychophysical pain thresholds in the literature. This suggests that spatial and/or temporal summation of C-fiber input are important for pain induced by either stimulus modality. 4. Mechanical RF diameters ranged from 3.3 to 9.6 mm (mean, 4.7 mm); heat RF diameters ranged from punctate (less than 1 mm) to 9.5 mm (mean, 4.3 mm). There was a significant linear correlation between mechanical and heat RF sizes with a slope of one. The distance between the center of the mechanical RF and the center of the heat RF along one axis ranged from 0 to 1.1 mm (mean, 0.4 mm). These data indicate that the heat RFs coincided with the mechanical RFs. 5. Within the mechanical RF determined with the suprathreshold stimuli, all CMHs had one or more punctate areas of maximal mechanical sensitivity where mechanical threshold was lowest. Heat excitability extended greater than 2 mm beyond these mechanically sensitive spots. Because lateral transmission of the heat stimulus is small, this indicates that heat transduction occurs outside the regions of maximal mechanical sensitivity. 6. Both the threshold to heat and the response magnitude at suprathreshold intensities depended on the percentage of the RF area overlapped by the heat stimulus. This indicates that multiple transducer sites probably contribute to the total evoked response.(ABSTRACT TRUNCATED AT 400 WORDS)
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41

Plenkin, A. V. „Multiscale analysis of gas dynamic fields“. Moscow University Mechanics Bulletin 66, Nr. 2 (April 2011): 40–43. http://dx.doi.org/10.3103/s0027133011020038.

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42

Nowicki, Marcin, und Witold Respondek. „Mechanical state-space linearization of mechanical control systems and symmetric product of vector fields“. IFAC-PapersOnLine 54, Nr. 19 (2021): 204–9. http://dx.doi.org/10.1016/j.ifacol.2021.11.079.

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43

Rameswara Reddy, Y. „Composite Laminates for Aerospace and Packaging Fields“. Asian Review of Mechanical Engineering 12, Nr. 1 (21.06.2023): 39–43. http://dx.doi.org/10.51983/arme-2023.12.1.3674.

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Composite materials have become increasingly popular and widely used in the present world due to their unique combination of properties that cannot be achieved by any single material. In the current study the mechanical properties of composite laminates (Jute, palm and banana fibers) were fabricated by varying groundnut husk and seashell powders quantities (5, 10, 15 and 20gms) in epoxy resin using hand layup technique. In according to the ASTM standards, a mixture of Epoxy (LY556) and Hardener (araldite) HY951 is used. The ratio of epoxy to hardener is 10:1. The material will be properly mixed for some time before being used to create laminates. Samples were fabricated with different compositions of jute, palm and banana fibers. Tensile, Compression properties of laminates were analyzed by testing composite laminates on universal testing machine. In this context the weight ratio of groundnut husk to seashell powder is 2:1. Analysis states that both the powders have impact on the mechanical properties of laminates. The impact of groundnut husk powder is slightly more on the laminates mechanical properties (tensile, compression) when related to seashell powder.
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44

Serajzadeh, Siamak. „Thermo-Mechanical Modeling of Hot Forging Process“. Journal of Engineering Materials and Technology 126, Nr. 4 (01.10.2004): 406–12. http://dx.doi.org/10.1115/1.1631029.

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In the present study, a mathematical model has been developed to evaluate temperature and strain fields as well as dynamic and static microstructural changes during the nonisothermal forging process. To do so, a finite element analysis and a microstructural model based on Bergstrom’s model have been coupled for predicting temperature history, velocity and strain fields as well as phase transformations within the metal during and after hot forging. To verify the results of the model, theoretical predictions for loadstroke behavior and austenite grain size have been compared with experimental results for two grades of steel.
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45

CARLEY, M. „PROPELLER NOISE FIELDS“. Journal of Sound and Vibration 233, Nr. 2 (Juni 2000): 255–77. http://dx.doi.org/10.1006/jsvi.1999.2797.

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46

Alrbaihat, Mohammad. „Mechanochemical Synthesis of Dendrimers as Nanocarriers: A Review“. Advanced Materials Research 1175 (20.02.2023): 37–46. http://dx.doi.org/10.4028/p-a610b7.

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The process of mechanically activating chemical bonds usually involves applying external force. Since mechanical chemistry can be performed without solvents or with minimal amounts of solvent (catalytic quantities), it has become an imperative synthetic tool in multiple fields (e.g., physics, chemistry, and materials science) and is an attractive greener method for preparing diverse molecules. Catalysis, organic synthesis, solid-state medicinal preparation, metal complex synthesis, and many other chemistry fields have benefited from sustainable methods. The purpose of this paper is to shed light on the benefits of using mechanochemical methods to produce a pharmaceutical crystal that is composed of dendrimer nanocrystals. Consequently, we describe and examine the importance of mechanical procedures in forming dendrimers and pharmaceutical crystals in this review.
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47

Toussaint, Evelyne, Michel Grédiac und Fabrice Pierron. „The virtual fields method with piecewise virtual fields“. International Journal of Mechanical Sciences 48, Nr. 3 (März 2006): 256–64. http://dx.doi.org/10.1016/j.ijmecsci.2005.10.002.

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48

Hu, Zheng, Ming Han, Zhen Chuan Song und Ke Yan Ning. „Numerical Investigation on Thermo Mechanical Behavior in Wet Multidisc Friction Pairs System“. Applied Mechanics and Materials 697 (November 2014): 177–80. http://dx.doi.org/10.4028/www.scientific.net/amm.697.177.

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In order to research the thermomechanical behavior of multidisc friction pairs system, three dimensional model is established for numerical simulation under simulated braking process. Based on some accurate boundary conditions, the temperature fields and thermal stress fields of friction discs and separator discs are simulated using finite element method. The temperature fields and contact stress fields of friction disc and separator discs are obtained, and their regularities of distribution are studied spatially and historically. To verify the simulation results, an experimental investigation is carried out. The results offered references for analyzing failure forms and causes of the wet multidisc friction pairs system.
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Wang, Xu, und Peter Schiavone. „Asymptotic elastic fields near an interface anticrack tip“. Acta Mechanica 230, Nr. 12 (25.09.2019): 4385–89. http://dx.doi.org/10.1007/s00707-019-02522-8.

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50

Gavrikov, Mikhail Borisovich. „Variational principle for local fields“. Keldysh Institute Preprints, Nr. 14 (2021): 1–39. http://dx.doi.org/10.20948/prepr-2021-14.

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The simplest variational problems (with free, fixed boundaries, the Bolz problem) in Banach spaces are considered. Necessary conditions for a local extremum in these problems are derived. An important class of Lagrangian mechanical systems is considered – local loaded fields, for which the Lagrangian has the form of an integral functional. Necessary conditions for the action functional – the Euler-Ostrogradsky equations and transversality conditions – are obtained. The equations of the theory of elasticity and Maxwell electrodynamics are derived from the variational principle for local fields.
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