APPLICATION OF GENERALIZED EQUATIONS OF THE FINITE DIFFERENCE METHOD AS PART OF THE ANALYSIS OF SLABS RESTING ON ELASTIC FOUNDATIONS

Vestnik MGSU 4/2012
  • Gabbasov Radek Fatykhovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Professor, Construction and Theoretical Mechanics Departmenе, Moscow State University of Civil Engineering (National Research University) (MGSU), .
  • Uvarova Nataliya Borisovna - Moscow State University of Civil Engineering (MSUCE) Candidate of Technical Sciences, Professor, Department of Structural Mechanics, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 102 - 107

Generalized equations of the finite difference method are used to analyze bended slabs resting on elastic foundations. The algorithm makes it possible to take account of the finite discontinuity of the function, its first derivative and the right part of the differential equation without getting any points outside of the contour or a fine grid involved in the analysis. The examples have proven the high accuracy of the proposed analysis that employs a coarse grid and a simple algorithm.
It is noteworthy that the algorithm of the analysis is developed with a view to the employment of computer-aided methods and with due account for a substantial number of subsettings. The examples provided in the article are solely designated to illustrate the operation of the proposed algorithm. They demonstrate that even if the number of subsettings is minimal, generalized equations of the method of finite differences are capable of generating the results that make it possible to assess the stress-strained state of a slab.

DOI: 10.22227/1997-0935.2012.4.102 - 107

References
  1. Gabbasov R.F., Mussa Sali. Obobshchennye uravneniya metoda konechnykh raznostey i ikh primenenie k raschetu izgibaemykh plastin peremennoy zhestkosti [Generalized Equations of the Method of Finite Differences and Their Application to Analysis of Bent Slabs of Variable Rigidity]. Izvestiya VUZov, Stroitel'stvo [News of Higher Education Institutions. Construction]. 2004, no. 5, pp. 17—22.
  2. Timoshenko S.P., Voynovskiy-Kriger S. Plastinki i obolochki [Plates and Envelopes]. Moscow, Nauka Publ., 1966
  3. Gabbasov R.F., Gabbasov A.R., Filatov V.V. Chislennoe postroenie razryvnykh resheniy zadach stroitel'noy mekhaniki [Numerical Structure of Discontinuous Solutions of Problems of Structural Mechanics]. Moscow, ASV Publ., 2008, 277 p.

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Eigenfunction of the Laplace operator in +1-dimentional simplex

Vestnik MGSU 11/2014
  • Ovchintsev Mikhail Petrovich - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Higher Mathematics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sitnikova Elena Georgievna - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Professor, Department of Higher Mathematics, Moscow State University of Civil Engineering (MGSU), .

Pages 68-73

In order to find eigenfunction of the Laplace operator in regular
n+1-dimensional simplex the barycentric coordinates are used. For obtaining this result we need some formulas of the analytical geometry. A similar result was obtained in the earlier papers of the author in a tetrahedron from
R
3 and in gipertetrahedron from
R
4. Let П be unlimited cylinder in the space
R
n, its cross-section with hyperplane has a special form. Let
L be a second order linear differential operator in divergence form, which is uniformly elliptic and η is its ellipticity constant. Let
u be a solution of the mixed boundary value problem in Π with homogeneous Dirichlet and Neumann data on the boundary of the cylinder. In some cases the eigenfunction of the Laplace operator allows us to continue this solution from the cylinder Π to the whole space
R
n with the same ellipticity constant. The obtained result allows us to get a number of various theorems on the solution growth for mixed boundary value problem for linear differential uniformly elliptical equation of the second order, given in unlimited cylinder with special cross-section. In addition we consider
n-1-dimensional hill tetrahedron and the eigenfunction for an elliptic operator with constant coefficients in it.

DOI: 10.22227/1997-0935.2014.11.68-73

References
  1. Sitnikova E.G. Sobstvennaya funktsiya operatora Laplasa v gipertetraedre [Eigenfunction of the Laplace Operator in the Tetrahedron]. Integratsiya, partnerstvo i innovatsii v stroitel’noy nauke i obrazovanii : sbornik trudov Mezhdunaridnoy nauchnoy konferentsii [Integration, Partnership and Innovations in Construction Science and Education : Collection of Works of International Scientific Conference]. Moscow, MGSU, 2011, pp. 755—758. (In Russian).
  2. Sitnikova E.G. Neskol’ko teorem tipa Fragmena-Lindelefa dlya ellipticheskogo uravneniya vtorogo poryadka [Several Theorems of Phragmen-Lindelof Type for the Second Order Differential Equation]. Voprosy matematiki i mekhaniki sploshnykh sred : sbornik nauchnykh trudov [Problems of Continuum Mathematics and Mechanics: Collection of Works]. Moscow, MGSU Publ., 1984, pp. 98—104. (In Russian).
  3. Sitnikova E.G. Sobstvennaya funktsiya operatora Laplasa v tetraedre [Eigenfunction of the Laplace Operator in the Tetrahedron]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, no. 4, pp. 80—82. (In Russian).
  4. Mikhaylov V.P. Differentsial’nye uravneniya v chastnykh proizvodnykh [Differential Equations in Partial Derivatives]. Moscow, Nauka Publ., 1976, 391 p. (In Russian).
  5. Mikhlin S.G. Kurs matematicheskoy fiziki [Course in Mathematical Physics]. Moscow, Nauka Publ., 1968, 576 p. (In Russian).
  6. Lazutkin V.F. Ob asimptotike sobstvennykh funktsiy operatora Laplasa [On Asymptotics of Eigenfunctions of the Laplace Operator]. Doklady AN SSSR [Reports of the Academy of Sciences of the USSR]. 1971, vol. 200, no. 6, pp. 1277—1279. (In Russian).
  7. Lazutkin V.F. Sobstvennye funktsii s zadannoy kaustikoy [Eigenfunctions with Preassigned Caustic Curve]. Zhurnal vychislitel’noy matematiki i matematicheskoy fiziki [Computational Mathematics and Mathematical Physics]. 1970, vol. 10, no. 2, pp. 352—373. (In Russian).
  8. Lazutkin V.F. Asimptotika serii sobstvennykh funktsiy operatora Laplasa, otvechayushchey zamknutoy invariantnoy krivoy «billiardnoy zadachi» [Asymptotics of Eigenfunctions Series of the Laplace Operator Matching Closed Invariant Curve of a "Billiard problem"]. Problemy matematicheskoy fiziki [Mathematical Physics Problems]. 1971, no. 5, pp. 72—91. (In Russian).
  9. Lazutkin V.F. Postroenie asimptotiki serii sobstvennykh funktsiy operatora Laplasa, otvechayushchey ellipticheskoy periodicheskoy traektorii «billiardnoy zadachi» [Asymptotics Creation of Eigenfunctions Series of the Laplace Operator Matching Elliptical Periodic Path of a "Billiard problem"]. Problemy matematicheskoy fiziki [Mathematical Physics Problems]. 1973, no. 6, pp. 90—100. (In Russian).
  10. Apostolova L.N. Initial Value Problem for the Double-Complex Laplace Operator. Eigenvalue Approaches. AIP Conf. Proc. 2011, vol. 1340, no. 1, pp. 15—22. DOI: http://dx.doi.org/10.1063/1.3567120.
  11. Pomeranz K.B. Two Theorems Concerning the Laplace Operator. AIP Am. J. Phys. 1963, vol. 31, no. 8, pp. 622—623. DOI: http://dx.doi.org/10.1119/1.1969694.
  12. Iorgov N.Z., Klimyk A.U. A Laplace Operator and Harmonics on the Quantum Complex Vector Space. AIP J. Math. Phys. 2003, vol. 44, no. 2, pp. 823—848.
  13. Fern?ndez C. Spectral concentration for the Laplace operator in the exterior of a resonator. AIP J. Math. Phys. 1985, vol. 26, no. 3, pp. 383—384. DOI: http://dx.doi.org/10.1063/1.526618.
  14. Davis H.F. The Laplace Operator. AIP Am. J. Phys. 1964, 32, 318. DOI: http://dx.doi.org/10.1119/1.1970275. Date of access: 25.03.2012.
  15. Gorbar E.V. Heat Kernel Expansion for Operators Containing a Root of the Laplace Operator. AIP J. Math. Phys. 1997, vol. 38, no. 3, pp. 1692. DOI: http://dx.doi.org/10.1063/1.531823. Date of access: 25.03.2012.

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Consideration of reflected wavesas part of analysis of plane elements

Vestnik MGSU 3/2013
  • Loktev Aleksey Alekseevich - Moscow State University of Civil Engineering (МGSU) +7 (499) 183-24-01, Moscow State University of Civil Engineering (МGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Stepanov Roman Nikolaevich - Moscow State University of Civil Engineering (МGSU) Candidate of Technical Sciences, Associate Professor, Department of Theoretical Mechanics and Aerodynamics; +7 (499) 183-24-01, Moscow State University of Civil Engineering (МGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 72-80

The authors study the distribution pattern of wave surfaces inside the orthotropic plate having curvilinear anisotropy. Dynamic behavior of the target is described by wave equations taking account of the transverse shear and rotational inertia of transverse cross-sections and of the ability to simulate the process of propagation of elastic waves. These equations are solved using the asymptotic method employed for decomposition of unknown values into time and spatial value series.The problem is resolved to identify the stress values in the points of interaction between direct waves and those reflected by the bottom face of the plate. Description of patterns of propagation of wave fronts inside the target requires a clear understanding of the nature of each wave, its velocity, etc.The research completed by the co-authors has proven that any increase in the thickness of a plate increases maximal stresses in the area of wave formation, while stresses in points of interaction between elastic waves go down, and peak stresses involving transverse waves go down more intensively. Nonetheless, any encounter between direct and reflected waves may either increase, or reduce the final values of principal stresses.The methodology developed by the authors may be employed to identify the coordinates of the points of maximal stresses occurring in medium thickness reinforced orthotropic plates. Awareness of these coordinates makes it possible to identify the appropriate diameter and patterns of arrangement of reinforcing elements.

DOI: 10.22227/1997-0935.2013.3.72-80

References
  1. Thomas T.Y. Plastic Flow and Fracture in Solids. New York, L., Acad. Press, 1961.
  2. Malekzadeh K., Khalili M.R., Mittal R.K. Response of Composite Sandwich Panels with Transversely Flexible Core to Low Velocity Transverse Impact: A New Dynamic Model. International Journal of Impact Engineering. 2007, vol. 34, pp. 522—543.
  3. Rossikhin Yu.A., Shitikova M.V. A Ray Method of Solving Problems Connected with a Shock Interaction. Acta Mechanica, 1994, vol. 102, no. 1-4, pp. 103—121.
  4. Loktev A.A. Udarnoe vzaimodeystvie tverdogo tela i uprugoy ortotropnoy plastinki [Impact Interaction between a Solid Body and an Elastic Orthotropic Plate]. Mekhanika kompozitsionnykh materialov i konstruktsiy [Mechanics of Composite Materials and Structures]. 2005, vol. 11, no. 4, pp. 478—492.
  5. Erofeev V.I., Kazhaev V.V., Semerikova N.P. Volny v sterzhnyakh. Dispersiya. Dissipatsiya. Nelineynost’ [Waves inside Rods. Dispersion. Dissipation. Non-linearity.]. Moscow, FIZMATLIT Publ., 2002, 208 p.
  6. Eliseev V.V. Mekhanika uprugikh tel [Mechanics of Elastic Bodies]. St.Petersburg, SPbGTU Publ., 1999, 341 p.
  7. Biryukov D.G., Kadomtsev I.G. Uprugoplasticheskiy neosesimmetrichnyy udar parabolicheskogo tela po sfericheskoy obolochke [Elastoplastic Assymmetric Concussion of a Parabolic Body against a Spherical Shell]. Prikladnaya mekhanika i tekhnicheskaya fizika [Applied Mechanics and Applied Physics]. 2005, vol. 46, no. 1, pp. 181—186.
  8. Loktev A.A. Dinamicheskiy kontakt udarnika i uprugoy ortotropnoy plastinki pri nalichii rasprostranyayushchikhsya termouprugikh voln [Dynamic Contact between a Striker and an Elastic Orthotropic Plate Subject to Existence of Evolving Thermoelastic Waves]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 2008, vol. 72, no. 4, pp. 652—658.
  9. Rossikhin Yu.A., Shitikova M.V. The Ray Method for Solving Boundary Problems of Wave Dynamics for Bodies Having Curvilinear Anisotropy. Acta Mechanica, 1995, vol. 109, no. 1-4, pp. 49—64.
  10. Olsson R., Donadon M.V., Falzon B.G. Delamination Threshold Load for Dynamic Impact on Plates. International Journal of Solids and Structures. 2006, vol. 43, pp. 3124—3141.
  11. Achenbach J.D., Reddy D.P. Note on Wave Propagation in Linear Viscoelastic Media. Z. Angew. Math. Phys. 1967, vol. 18, pp. 141—144.
  12. Al-Mousawi M.M. On Experimental Studies of Longitudinal and Flexural Wave Propagations. An Annotated Bibliography. Applied Mechanics Reviews, 1986, vol. 39, no. 6, pp. 853—864.
  13. Karagiozova D. Dynamic Buckling of Elastic-plastic Square Tubes under Axial Impact. I. Stress Wave Propagation Phenomenon. International Journal of Impact Engineering. 2004, vol. 30, pp. 143—166.
  14. Kukudzjanov V.N. Investigation of Shock Wave Structure in Elasto-visco-plastic Bar Using the Asymptotic Method. Archive of Mechanics, 1981, vol. 33, no. 5, pp. 739—751.
  15. Sun C.T. Transient Wave Propagation in Viscoelastic Rods. ASME. Ser. E, J. Appl. Mech. 1970, vol. 37, pp. 1141—1144.
  16. Olsson R. Mass Criterion for Wave Controlled Impact Response of Composite Plates. Composites. Part A. 2000, vol. 31, pp. 879—887.
  17. Tan T.M., Sun C.T. Wave Propagation in Graphite/Epoxy Laminates due to Impact. NASA CR, 1982, 168057.

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Continuation of the solution of an elliptic equation and mathematical tesselations

Vestnik MGSU 10/2014
  • Ovchintsev Mikhail Petrovich - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Higher Mathematics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sitnikova Elena Georgievna - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Professor, Department of Higher Mathematics, Moscow State University of Civil Engineering (MGSU), .

Pages 48-53

In the following article the authors continue investigating elliptical equation. Let P be an unlimited cylinder in the space R3, the cross-section of which is a regular dodecagon. The authors have previously estimated linear self-conjugate uniformly elliptic equation of second order in the cylinder and obtained theorems on the growth of the solution in bounded domain. In order to prove the theorems we have to continue solving the differential equation and its coefficients for the whole space Rn.
Let L be a second order linear differential operator in a divergence form which is uniformly elliptic and h is its ellipticity constant. Let u be a solution of the mixed boundary value problem in P for the equation Lu=0 (u>0) with homogeneous Dirichlet and Neumann data on the boundary of the cylinder.
In this paper the solution for mixed boundary value problem is continued from the cylinder to the whole space R3.
The solution of the mixed problem has connection with the notion of the mathematical tessellation. This tessellation is a sum of nonintersecting regular dodecagons and triangles filling the whole space R2

DOI: 10.22227/1997-0935.2014.10.48-53

References
  1. Sitnikova E.G. Neskol’ko teorem tipa Fragmena — Lindelefa dlya ellipticheskogo uravneniya vtorogo poryadka [Several Theorems of Phragmen-Lindelof Type for the Second Order Differential Equation]. Voprosy matematiki i mekhaniki sploshnykh sred: sbornik trudov [Problems of Mathematics and Mechanics of Continuous Media: Collection of Works]. Moscow, MGSU Publ., 1984, pp. 98—104. (in Russian)
  2. Landis E.M. O povedenii resheniy ellipticheskikh uravneniy vysokogo poryadka v neogranichennykh oblastyakh [On Solutions Behavior of High Order Elliptic Equations in Unbounded Domains]. Trudy MMO [Works of Moscow Mathematical Society]. Moscow, MGU Publ., 1974, vol. 31, pp. 35—58. (in Russian)
  3. Brodnikov A.P. Sobstvennye funktsii i sobstvennye chisla operatora Laplasa dlya treugol’nikov [Eigenfunctions and Eigenvalues of the Laplace Operator for Triangles]. Available at: http://chillugy.narod.ru/Mathematics/laplas/start/start.html. Date of access: 17.02.2014. (in Russian)
  4. Kolmogorov A.N. Parkety iz pravil’nykh mnogougol’nikov [Tesselations of the Regular Polygons]. Kvant [Quantum]. 1970, no. 3. Available at: http://kvant.mccme.ru/1970/03/parkety_iz_pravilnyh_mnogougol.htm. Date of access: 17.02.2014. (in Russian)
  5. Mikhaylov O. Odinnadtsat’ pravil’nykh parketov [Eleven Regular Tessellation]. Kvant [Quantum]. 1979, no. 2. Available at: http://kvant.mccme.ru/1979/02/odinnadcat_pravilnyh_parketov.htm. Date of access: 17.02.2014. (in Russian)
  6. Sitnikova E.G. Prodolzhenie obobshchennogo resheniya kraevoy zadachi [Continuation of the Generalized Solution for the Boundary Value Problem]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2007, no. 1, pp. 16—18. (in Russian)
  7. Mikhaylov V.P. Differentsial’nye uravneniya v chastnykh proizvodnykh [Differential Equations in Partial Derivatives]. Moscow, Nauka Publ., 1976, 391 p. (in Russian)
  8. Mikhlin S.G. Kurs matematicheskoy fiziki [Course in Mathematical Physics]. Moscow, Nauka Publ., 1968, 576 p. (in Russian)
  9. Petrovskiy N.G. Lektsii ob uravneniyakh s chastnymi proizvodnymi [Lections on the Equations with Partial Derivatives]. 3rd edition, Moscow, Fizmatgiz Publ., 1961, 401 p. (in Russian)
  10. Lazutkin V.F. Ob asimptotike sobstvennykh funktsiy operatora Laplasa [On the Asymptotics of Eigenfunctions of Laplace Operator]. Doklady AN SSSR [Proceedings of the USSR Academy of Sciences]. 1971, vol. 200, no. 6, pp. 1277—1279. (in Russian)
  11. Jiaquan Liu, Zhi-Qiang Wang, Xian Wu. Multibump Solutions for Quasilinear Elliptic Equations with Critical Growth. AIP. J. Math. Phys. 2013, no. 54, 121501. Available at: http://scitation.aip.org/content/aip/journal/jmp/54/12/10.1063/1.4830027. Date of access: 17.02.2014. DOI: http://dx.doi.org/10.1063/1.4830027.
  12. Chavey D. Tilings by Regular Polygons—II: A Catalog of Tilings. Computers & Mathematics with Applications. 1989, vol. 17, no. 1—3, pp. 147—165. DOI: http://dx.doi.org/10.1016/0898-1221(89)90156-9.
  13. Grünbaum B., Shephard G.C. Tilings And Pattern. New York, W.H. Freeman and Company, 1987, 700 p.
  14. Berger R. The Undecidability of the Domino Problem. Memoirs of the American Mathematical Society. 1966, no. 66, pp. 1—72.
  15. Penrose R. Pentaplexity: A Class of Non-Periodic Tilings of the Plane. The Mathematical Intelligencer. 1979, vol. 2, no. 1, pp. 32—37. DOI: http://dx.doi.org/10.1007/BF03024384.

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Fluctuations of the membrane with piecewise smooth contour and mixed boundary conditions

Vestnik MGSU 11/2015
  • Algazin Sergey Dmitrievich - Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences (IPMekh RAN) leading research worker, chief research worker, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences (IPMekh RAN), 101-1 Prospekt Vernadskogo str., Moscow, 119526, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 29-37

The eigenvalue problem for the two-dimensional operator Laplace is classical in mathematics and physics. However, computing methods for calculation of eigenvalues have still many problems, especially in applications to acoustic and electromagnetic wave guides. The investigated below two-dimensional spectral for the Laplace operator have been previously considered by the author only in smooth areas. The solutions of these tasks (eigen functions) are infinitely differentiated or. even analytical and therefore in order to create effective algorithms it is necessary to consider this enormous a priori information. Traditional methods of finite differences and finite elements almost do not practically use the information on smoothness of the decision, i.e. these are methods with saturation. The term “saturation” was entered by K.I. Babenko. Using the method of computing experiment the author investigates the task about fluctuations of the membrane with the piecewise smooth contour for two-dimensional area, obtained by conformal representation of the square. It is shown that eigen functions are infinitely differentiated. Therefore, numerical algorithms without saturation are applicable. In article the calculation algorithm of eigenvalues in this two-dimensional area is developed, which allows determining up to 10 natural frequencies with the accuracy acceptable for practice on the grid 10×10.

DOI: 10.22227/1997-0935.2015.11.29-37

References
  1. Algazin S.D. Chislennye algoritmy klassicheskoy matematicheskoy fiziki [Numerical Algorithms of Classical Mathematical Physics]. Moscow, Dialog-MIFI Publ., 2010, 240 p. (In Russian)
  2. Babenko K.I. Osnovy chislennogo analiza [Fundamentals of Numerical Analysis]. 2nd edition, revised and enlarged. Moscow; Izhevsk, RKhD Publ., 2002, 847 p. (In Russian)
  3. Algazin S.D., Babenko K.I., Kosorukov A.L. O chislennom reshenii zadachi na sobstvennye znacheniya [On the Numerical Solution of the Task on Eigenvalues]. Moscow, 1975, 57 p. (Preprint. IPM; no. 108, 1975). (In Russian)
  4. Algazin S.D. Vychislenie sobstvennykh chisel i sobstvennykh funktsiy operatora Laplasa (Lap123) [Calculation of Eigenvalues and Eigenfunctions of Laplace Operator]. SVIDETEL’’STVO o gosudarstvennoy registratsii programmy dlya EVM № 2012617739. Zaregistrirovana v Reestre programm dlya EVM [Certificate on State Registration of the Computer Program № 2012617739. Registered in Software Registration Book]. August 27, 2012, 18 p. (In Russian)
  5. Kuttler J.R., Sigillito V.G. Eigenvalues of the Laplacian in Two Dimensions. SIAM Review. Apr. 1984, vol. 26, no. 2, pp. 163—193. DOI: http://dx.doi.org/10.1137/1026033

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SOLUTION TO THE BOUNDARY PROBLEM OF HEAT AND WATER TRANSMISSION IN A LAYER OF A LOOSE DISPERSE MATERIAL EXEMPLIFIED BY MILLED PEAT EXPOSED TO INFRARED HEATING

Vestnik MGSU 6/2012
  • Pavlov Mikhail Vasil'evich - Vologda State Technical University (VoSTU) Senior Lecturer, Department of Heat, Supply and Ventilation, Vologda State Technical University (VoSTU), 15 Lenina st., Vologda, 160000, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Karpov Denis Fedorovich - Vologda State Technical University» (VoSTU) Senior Lecturer, Department of Heat/Gas Supply and Ventilation, Vologda State Technical University» (VoSTU), 15 Lenin st., Vologda, 160000, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sinitsyn Anton Alexandrovich - Vologda State Technical University (VoSTU) Candidate of Technical Sciences, Associated Professor, Department of Heat, Supply and Ventilation, Vologda State Technical University (VoSTU), 5 Lenina st., Vologda, 160000, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 92 - 98

Maintenance of appropriate thermal and humidity modes of soil is the main condition of intensive growth and development of plants. It is feasible in the event that the temperature and humidity patterns of the soil environment can be projected in time and registered at different depths. Towards this end, the author proposes three alternative solutions to the boundary problem of heat and water transmission in a layer of a loose disperse material exemplified by milled peat. Each solution is based on the operation of a source of infrared radiation. The research results are benchmarked against the experimental data, and thereafter, the list of optimal solutions and substantiations is composed.

DOI: 10.22227/1997-0935.2012.6.92 - 98

References
  1. Mikhaylov Yu.A., Glazunov Yu.T. Variatsionnye metody v teorii nelineynogo teplo- i massoperenosa [Variation Methods in the Theory of Nonlinear Heat and Mass Transfer]. Riga, Zinatne Publ., 1985, 190 p.
  2. Lykov A.V. Teplomassoobmen [Heat and Mass Exchange]. Moscow, Energiya Publ., 1972, 560 p.
  3. Lykov A.V., Mikhailov J.A. Teorija perenosa jenergii i veshchestva [Theory of Energy and Substance Transfer]. Minsk, AN BSSR Publ., 1963, 332 p.
  4. Tsoy P.V. Metody rascheta otdel’nyh zadach teplomassoperenosa [Methods of Resolution of Particular Problems of Heat and Mass Transfer]. Moscow, Energiya Publ., 1971, 384 p.
  5. Igonin V.I., Pavlov M.V., Karpov D.F., Ivanov M.I. Eksperimental’no-raschetnoe opredelenie temperaturoprovodnosti i teploprovodnosti frezernogo torfa metodom mgnovennoy plastiny [Experimental and Analytical Identification of Temperature and Thermal Conductivity of Milled Peat through the Employment of an Instant Plate Method]. Vuzovskaya nauka — regionu [High School Science: Contributions to Regions]. Proceedings of the ninth All-Russian scientific and technical conference. Vologda, VoSTU, 2011, vol. 1, pp. 166—170.

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