# Department of Mechanics

The Department of Mechanics is part of the Faculty of Technical Sciences at the University of Novi Sad, Serbia

An interesting problem...

# Euler's disk...

Mechanics is a science that deals with the motion and deformation of bodies under the action of forces. Its essential ingredients are axioms, theorems, proofs, definitions, principles, but at the heart of it, what mechanics really consist of, are problems and solutions.

## Forthcomming events

**September 2007 · 17-23, Applications of Fractional Calculus in Mechanics**

Summer school sponsored by DAAD Foundation ...

**September 2007 · Symmetries and Mechanics**

Conferrence organized by PMF and FTN

Novi Sad...

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### 1991-2000

- L. Cveticanin and R. Maretic: Dynamic analysis of a cutting mechanism. Mechanism and Machine Theory, 2000, 35, 1391- 1411.
- R. Maretic: Vibration and Stability of Rotating Plates with Elastic Edge Supports. Journal of Sound and Vibration, 1998, 210, 291- 294.
- Teodor M. Atanackovic, Djordje S. Djukic and S. E. Jones, On the Rotating Rod With Shear and Extensibility, Int. J. Non-Linear Mechanics, 33, 4, 1998, 593-606.
- Dj. S. Djukic and S. E. Jones, The Necessary Conditions for Plane Motion of a Rigid Body, The International Journal of Mechanical Engineering Education, 26, 1, 1998, 71-74.
- Djordje S. Djukic, S. E. Jones, A Note on the Axioms of Statics, The International Journal of Mechanical Engineering Education, 25, 4, 1997, 327-330.
- L. J. Cveticanin, T. M. Atanackovic, Dj. S. Djukic, Beck's Rod With Shear, Compressibility and Pulsating Force, Continuum Mech. Thermodyn. 8, 1996, 103-113.
- Dj. S. Djukic and T. M. Atanackovic, Heavy Horizontal Rod With Shear and Compressibility, International Journal for Engineering Analysis and Design, 2, 1995, 57-70.
- Dj. Djukic, T. Atanackovic, A Note on the Ritz Approach to the Extremal Curves, Teorijska i primenjena mehanika, 20, 1994, 59-68.
- Dj. S. Djukic and T. M. Atanackovic, Stability of a vertically positioned heavy rotating rod, Continuum Mech. Thermodyn., Springer-Verlag, 5, 1993, 51-65.
- Dj. S. Djukic and T. M. Atanackovic, Effect of Shear on Simple Buckling Problem, Journal of Engineering Mechanics, American Society of Civil Engineers, New York, 119, 5, 1993, 1108-1115.
- Djordje S. Djukic, Adiabatic Invariants for the Nonconservative Kepler's Problem, Celestial Mechanics and Dynamical Astronomy, Kluwer Academic Publishers, Netherlands, 56, 1993, 523-540.
- T. M. Atanackovic and Dj. S. Djukic, Negativism: A Nonlinear Version, Journal of Applied Mechanics, 60, 1993, 241-244.
- T. M. Atanackovic, Dj. S. Djukic and A. M. Strauss, Instability by Extension of an Extensible Elastic Column, Zeitschrift fňr Angewandte Mathematik und Mechanik, Dresden, 72, 1992, 209-218.
- Teodor Atanackovic and Djordje Djukic, The influence of shear and extensibility on the stability of a heavy rotating rod, Dynamics and Stability of Systems, Oxford University Press, Vol. 7, No. 4, 1992, 207-218.
- Dj. S. Djukic and T. M. Atanackovic, Extremum Variational Principle for an Inextensible Rotating Rod, Int. J. Non-Linear Mechanics, Pergamon Press, 27, 1992, 591-595.
- T. M. Atanackovic and Dj. S. Djukic, The Influence of Shear on the Stability of a Pfluger Column, Journal of Sound and Vibration, Academic Press, 144, 3, 1991, 531-535.
- T. M. Atanackovic, Dj. S. Djukic and S. E. Jones, Effect of shear on stability and non-linear behavior of a rotating rod, Archive of Applied Mechanics, Springer-Verlag, 61, 1991, 285-294.
- Dj. S. Djukic, Extremal variational principles, 19-th Yugoslav Congress of Theoretical and Applied Mechanics, general lecture, Ohrid, General lecture, 1990, 57-72.
- T. M. Atanackovic and Dj. S. Djukic, An extremum variational principle for some non-linear diffusion problems, Int. J. Heat Mass Transfer, Pergamon Press, 33, 6, 1990, 1081-1085.
- Dj. S. Djukic, T. M. Atanackovic and A. M. Strauss, An always extremum variational principle for classical mechanics via a canonical transformation, Int. J. Non-linear Mechanics, Pergamon Press, 25, 5, 1990, 583-595.
- T. M. Atanackovic and D. T. Spasic, (1999): ''On the Impact of Elasctic Bodies with Adhesive Forces'', Meccanica, 34, 367-377, Kluwer AP
- Petrović Lj. and Spasić D. T. (1998): "Investigation of the bond strength of various composites to tooth structure", Proceedings of 5th International Conference on Composites Engineering, Las Vegas, 723-724
- Atanackovic T. M., Guran A. and Spasic D. T. (1998): "A variational principle for equation of Hertz's theory of impact", Proceedings of First International Symposium on Impact and Friction of Solids, Structures and Inteligent Mashines: Theory and Applications in Engineering and Science, Birkhauser Boston.
- Milanov V., Milutinović M. and Spasić D. T. (1998): "One Problem of Linear Optimization for Vojvodina Region", Proceedings of 3rd International Interdisciplinary Regional Research, Novi Sad, 195-197.
- Vujanović B.D. and Spasić D.T. (1997): "Optimization Methods - Part I: Applied Calculus of Variations with Elements of Analytical Mechanics - Part II: Fundamentals of Optimal Control Theory", Novi Sad University Press, Novi Sad, (
**book**- 484 pages in Serbian). - Stojsic Dj., Spasic D., Obradovic M., Benc D., Jung R., Srdic S., Bikicki M., Dodic S. , Stojsic-Milosavljevic A., (1997): "Does left ventricular hypertrophy correlates with aortic regurgitations?", 10th Annual Meeting of Mediterranean Association of Cardiology and Cardiatic Surgery, Beirut-Lebanon (Research done at Institute of Cardiovascular Diseases, Sremska Kamenica)
- Spasić, D. T. (1997), "Optimal design of elastic columns for maximal buckling load",
**book chapter**in Volume 3 of Stability, Vibration and Control of Systems, A. Guran and D. Inman Eds. Birkhauser Boston - Kovac M., Stojsic A., Jancic B., Grujic S., Stojsic Dj., Spasic D., Cikos J., (1997): "Quantification of mitral regurgitation with 2D and Doppler echocardiography", 9th International Congress on Echocardiography "Clinical Cardiology", Book of Abstracts, Roma (Italy) 1997, pp. 111, (Research done at Institute of Cardiovascular Diseases, Sremska Kamenica YU)
- D. T. Spasic and B. V. Glavardanov, (1996): ''Stability of a rigid sphere supported by a thin elastic column'', Eur. J. Mech., A/Solids, 15, 2, 337-350, Gauthier-Villars
- Spasić D.T. (1995): "On nonlinear oscillatory motion with force acting on nonconvex domain", Proceedings of 21st, Yugoslav Congress of Applied Mechanics, Nis, (in Serbian).
- T. M. Atanackovic and D. T. Spasic, (1994): ''A model for plane elastica with simple shear deformation pattern'', Acta Mechanica 104, 241-253, Springer-Verlag
- Spasić D.T. (1994): "Optimal shape of water tower against buckling", Proceedings of Symposia in Mechanics, Novi Sad, (in Serbian).
- D.T. Spasic, (1993), "On stability of a compressed and twisted linearly elastic rod", University of Novi Sad,
**PhD Thesis**, written under direction of Prof. Dr.-Ing. Teodor M. Atanacković, - T. M. Atanackovic and D. T. Spasic, (1991): ''Effect of shear and compressibility on stability of a heavy column with an end load'', Q. J. Mech. appl. Math., 44, 4, 601-617, Oxford UP
- B. Vujanović, D.T. Spasić, Metodi optimizacije, Univerzitet u Novom Sadu, Fakultet tehničkih nauka, Novi Sad, 1997.
- B. Vujanović, Teorija oscilacija, Univerzitet u Novom Sadu, Fakultet tehničkih nauka, 1995.
- B.D. Vujanović and B.S. Baclic, Variational solutions of transient heat conduction through the bodies of finite length, Advances in Heat Transfer, J.P. Hartnett and T.F. Irvine, Jr., Editors, Vol. 24, 39-99, Academic Press, 1994. Boston.
- T.M. Atanackovic, B.D. Vujanović and B.S. Baclic, A variational principle motivated by the optimal rod theory, Acta Mechanica, 139, 57-71, 2000.
- B.Vujanović, A.M.Strauss, S.E.Jones, P.P.Gillis, Polynomial conservation laws of the generalized Emden-Fowler equation, International Journal of Non-Linear Mechanics, Vol. 33, No. 2, 377-384, 1998.
- B.D.Vujanović, B.S.Bačlić, O kanonskim bilinearnim formama varijacionih principa u provođenju toplote, skup "300 godina optimizacije", Odeljenje Tehničkih najuka SANU - Matematički institut SANU, Decembar 1997.
- B.Vujanović, T.Kawaguchi, S.Simic, A Class of Conservation Laws of Linear Time-Dependent Dynamical Systems, Tensor, Vol. 58, No. 3, 1997.
- B.D.Vujanović, B.S.Bačlić, O jednoj bilinearnoj formi varijacionog principa sa išćezavajućim parametrom, 22. Jugoslovenski kongres teorijske i primenjene mehanike, Zbornik radova, Vrnjačka Banja, 1997.
- B.Vujanović, B.S.Baclic, A bilinear form of the variational principle with vanishing parameter, Archive of Applied Mechanics, 68, (1998), 122-127, Springer, 1998.
- B.Vujanović, Conservation laws of nonconservative dynamical systems via Hamel's variational principle, Bulletin T.CXI de L'Academie Serbe des Sciences et des Arts, Classe des Sciences Mathematiques et naturelles, 21, 31-46, 1996.
- B.Vujanović, Conservation Laws and Reduction to Quadratures of the Generalized Time-Dependent Duffing Equation, International Journal of Non-Linear Mechanics, Vol. 30, No. 6, 783-792, 1995.
- B.Vujanović, Application of the Field-Momentum Method to Rheonomic Dynamics, International Journal of Non-Linear Mechanics, Vol. 29, No. 44, 515-528, 1994.
- B.D.Vujanović and B.S.Baclic, Variational solutions of transient heat conduction through the bodies of finite length, Advances in Heat Transfer, J.P. Hartnett and T.F. Irvine, Jr., Editors, Vol. 24, 39-99, Academic Press, 1994. Boston.
- B.D.Vujanović, A variational approach to transient heat transfer theory, štampano u monografiji: Advances in Thermodynamics, Vol. 6, Flow, Diffusion and Rate Processes Edited by. S.Sienintycz and P.Salamon, Taylor and Frances, New York, 1992, pp. 200-217.
- B.D.Vujanović, Application of the Hamilton-Jacobi method to the study of rheo-linear oscillators, Acta Mechanica, 93, 179-190, 1992.
- B.D.Vujanović, Conservation laws of rheo-linear dynamical systems with one and two-degrees of freedom, International Journal of Nonlinear Mechanics, Vol. 27, pp. 309-322, 1992.
**T. Atanackovic**,*Stability Theory of Elastic Rods*. World Scientific, 1997**T. M. Atanackovic**, A. Guran,*Theory of Elasticity for Scientists and Engineers*. Birkhauser, 2000.**T.Atanackovic**, On a bending problem for shape memory materials. Journal of the Mechanical Behaviour of Materials 11, 1-6 (2000).- B. S. Baclic and
**T. M. Atanackovic**, Stability and creep of a Fractional order viscoelastic rod. Bull. de l'Académie Serbe des Sciences et des Arts. Classe des Sciences mathématiques et naturelles 25, 115-131 (2000). - V. B. Glavardanov and
**T. M. Atanackovic**, Stability of a pipe through which a sring is pulled. Int. J. Non-Linear Mechanics Mechanics 35, 7-20 (2000). **T. M. Atanackovic**, B. D. Vujanovic and B. S. Baclic, , A Variational principle motivated by the optimal rod Theory. Acta Mechanica, 139, 57-71 (2000).**T. M. Atanackovic**, R. B. Maretic and J. M. Milidragovic, On the Stability of an Elastic rod positioned on elastic half Space. Archive of Applied Mechanics, 69, 94-104 (1999).- L. J. Cveticanin and
**T. M. Atanackovic**, On Beck's column with shear and compressibility. Structural Engineering and Mechanics, 6, 747-756 (1998). - L.J. Cveticanin,
**T. M. Atanackovic**, Leipholz Column with Shear and Compressibility. Journal of Eng. Mechanics (ASCE), 124, 146-151 (1998). - A. Guran and
**T.M. Atanackovic**, Fluid conveying pipe with shear and compressibility. Eur. J. Mech., A/Solids, 17, 121 - 137 (1997). **T.M. Atanackovic**, D.S. Djukic and S.E. Jones, On the rotating rod with shear and extensibility. Int. J. Non-Linear Mechanics 33, 593-606 (1998).**T.M. Atanackovic**, On the rotating rod with shear and extensibility. Continuum Mech. Thermodyn. 9, 143-153 (1997).**T.M. Atanackovic**, On the rotating rod with variable cross-section. Archive of Applied Mechanics 67, 447-456 (1997).**T.M. Atanackovic**, Buckling of a compressible elastic ring. Acta Mechanica. 127, 121-134 (1998).- L. Cveticanin and
**T. Atanackovic**, Vibrations of a finite length beam with an axially movable load. Eur. J. Mech., A/Solids, 15, 667-680 (1996). **T.M. Atanackovic**and V. Glavardanov, Twisted axially loaded rod with shear and compressibility. Acta Mechanica, 119, 119-130 (1996).**T.M. Atanackovic**and L.J. Cveticanin, Dynamics of Plane Motion of an Elastic Rod. Journal of Applied Mechanics (transactions of ASME), 63 392-398 (1996).- Dj.S. Djukic and
**T.M. Atanackovic**, Heavy horizontal rod with shear and compressibility. Int. J. Engineering Analysis and design, 2, 57-70 (1995). **T.M. Atanackovic**and I. Müller, A New form of ther Coherency Energy in Pseudoelasticity. Meccanica, 30, 467-474 (1995).- L.J. Cveticanin,
**T.M. Atanackovic**and Dj.S. Djukic, Beck's rod with shear, compressibility and pulsating force. Continuum Mech. Thermodyn. 8, 103-113 (1996). - L. Cveticanin and R. Maretic: A Van der Pol Absorber for rotor vibrations. Journal of Sound and Vibration, 1994, 173 (2), 145- 155.
**T.M. Atanackovic**and D.T. Spasic, A Model for plane elastica with simple shear deformation pattern. Acta Mechanica, 104, 241-253 (1994).- Dj.S. Djukic and
**T.M. Atanackovic**, Stability of a vertically positioned heavy rotating rod. Continuum Mech. Thermodyn. 5, 51-65 (1993). **T.M. Atanackovic**and Dj.S. Djukic, Negativism: A Nonlinear Version. Journal of Applied Mechanics (transactions of ASME), 60, 241-243 (1993).- Dj.S. Djukic and
**T.M. Atanackovic**, Effect of Shear on Simple Buckling Problem. Journal of Engineering Mechanics (transactions of ASCE), 119, 1109-1115 (1993). **T.M. Atanackovic**, Dj.S. Djukic and A.M. Strauss, Instability by Extension of an Extensible Elastic column. Zeitschrift Angew. Math. Mech. (ZAMM), 72, 209-218 (1992).- Dj.S. Djukic and
**T.M. Atanackovic**, Extremum variational principle for an inextensible rotating rod. Int. J. Non-Linear Mechanics, 27, 591-595 (1992). **T.M. Atanackovic**and Dj.S. Djukic, The influence of shear and extensibility on the stability of a heavy rotating rod. Dynamics and Stability of Systems, 7, 207-218 (1992).- Dj.S Djukic,
**T.M. Atanackovic**and A.M. Strauss, An always extremun principle for classical mechanics via a canonical transformation. Int. J. Non-Linear Mechanics, 25, 583-595 (1991). **T.M. Atanackovic**and Dj.S. Djukic, The influence of shear on the stability of a Pfluger column. Journal of Sound and Vibration, 144, 531-535 (1991).**T.M. Atanackovic**, Dj.S. Djukic and S.E. Jones, Effect of shear on stability and nonlinear behavior of a rotating rod. Archive of Applied Mechanics, 61, 285-294 (1991).**T.M. Atanackovic**and D.T. Spasic, Effect of shear and compressibility on stability of a heavy column with an end load. Q. Jl. Mech. App. Math. 44, 601-617 (1991).**T.M. Atanackovic**and L.J. Cveticanin, Pfluger rod with shear and extensibility. Archive of Applied Mechanics, 64, 497-508 (1994).- L. Cveticanin and
**T.M. Atanackovic**, Non-Linear vibration of an Extensible elastic beam. Journal of Sound and Vibration, 177, 159-171 (1994). - B.D. Vujanovic, T. Kawaguchi, S.S. Simic (1997), A Class of Conservation Laws of Linear Time-Dependent Dynamical Systems, TENSOR (NS), 58 (3), pp. 243-252.
- T.M. Atanackovic, S.S. Simic (1999), On the optimal shape of a Pflüger column, European Journal of Mechanics, A/Solids, 18 (5), pp. 903-913.
- S.S. Simic (2000), Cubic invariants of one-dimensional Lagrangian systems, International Journal of Non-Linear Mechanics, 35 (2), pp. 333-345.
- S.S. Simic (2000), A note on generalization of the Lewis invariant and the Ermakov systems, Journal of Physics A: Mathematical and General, 33, pp. 5435-5447.
- S. Simic (2000), On Noetherian Approach to Integrable Cases of the Motion of Heavy Top, Bulletin T.CXXI de l'Academie Serbe des Sciences et des Arts, Classe de Sciences mathématiques et naturelles, Sciences mathématiques, No. 25, pp. 133-156.
- S.S. Simić (1994), O uticaju trenja na optimalni oblik obrtnog tela pri hiperzvučnom strujanju, Simpozijum iz opšte mehanike, Zbornik radova, Novi Sad, 153-160.
- N. Teofanov, S. Simić (1997), Approximate Solutions of Biharmonic Equation Using Wavelet Subspaces, Proceedings of XI Conference on Applied Mathematics, PriM '96, Budva, 411-419.
- S.S. Simić (1997), O nekim uopštenjima Luisovih integrala, Zbornik radova XXII Jugoslovenskog kongresa Teorijske i primenjene mehanike, Vrnjačka Banja '97, A. Opšta mehanika, 150-155.
- N. Teofanov, S. Simić (2001), Approximate Solution of Biharmonic Equation Using Wavelet Subspaces, First SIAM-EMS Conference Applied Mathematics in our Changing World, Poster Session, Berlin.
- L. J. Cveticanin, The Oscillations of a Textile Machine Rotor on Which the Textile is Wound Up, Mechanism and Machine Theory, Vol. 26, No. 3, pp. 253-260, 1991.
- L. Cveticanin, An Approximate Solution for a System of Two Coupled Differential Equations, Journal of Sound and Vibration, Vol. 153, No. 2, pp. 375-380, 1992.
- L. Cveticanin, Approximate Analytical Solutions to a Class of Nonlinear Equations with Complex Functions, Journal of Sound and Vibration, Vol. 157, No. 2, pp. 289-302, 1992.
- L. Cveticanin, Extension of Melnikov Criterion for the Differential Equation with Complex Function, Nonlinear Dynamics, Vol. 4, pp. 139-152, 1993.
- L. Cveticanin, An Asymptotic Solution to Weak Nonlinear Vibrations of the Rotor, Mechanism and Machine Theory, Vol. 28, No. 4, pp. 495-506, 1993.
- L. Cveticanin, The Influence of the Reactive Force on a Nonlinear Oscillator with Variable Parameter, Trans. ASME, J. of Vibrat. and Acoustics, Vol. 114, No. 4, pp. 578-580, 1992.
- L. Cveticanin, An Approximative Solution of a Coupled Differential Equation with Variable Parameter, Trans. ASME, J. of Applied Mechanics, Vol. 60, No. 1, March, pp. 214-217, 1993.
- L. Cveticanin, Adiabatic Invariants of quasi-pure-cubic oscillators, Journal of Sound and Vibration, Vol. 183, No.5, pp.881-888, 1995.
- L. Cveticanin, A note on the stability and instability of the system with variable parameters, Trans. ASME, Journal of Applied Mechanics, Vol. 62, March, pp. 227-229, 1995.
- L. Cveticanin, Chaos in the rotors with slow variable mass, Journal of Sound and Vibration, Vol.185, No.5, pp.897-901, 1995.
- L. Cveticanin, Vibrations of strongly nonlinear rotors with time variable parameters, Machine Vibration, Vol.4, pp.40-45, 1995.
- Baclic, B.S. and Dragutinovic, G.D., "Asymmetric-unbalanced Counterflow Thermal Regenerator Problem: Solution by the Galerkin Method and meaning of dimensional Parameters, Int. J. Heat Mass Transfer, Vol.34, No. 2, 1991, pp. 483-498.
- Vujanovic, B.D., and Baclic, B.S., "Variational Solutions of Transient Heat Conduction Through Bodies of Finite Length", Advances in Heat Transfer, J.P. Hartnett and T.F. Irvine, Jr., eds., Vol. 24, Academic Press, New York, 1994. pp. 39-99.
- Gvozdenac, D.D. and Baclic, B.S. Performances of three-pass crossflow heat exchangers: Inverted order flow arrangements, Heat and Mass Transfer, Vol. 29, No. 6, 1994. pp. 343-347.
- Dragutinovic, G.D., Baclic, B.S., "Interpolation and collocation methods for prediction of thermal regenerator performances", Thermal Science, Vol. 12, No. 4, 1996. pp. 307-327.
- Baclic, B.S., "1-(2N-1) Shell-and-Tube Exchanger Effectiveness: Explicit Equations", Wärme- und Stoffubertragung (Heat and Mass Transfer), Vol. 33 No. 1/2, 1997. pp. 163-165.
- Vujanovic, B.D., Baclic, B. S., "A bilinear form of the variational principle with vanishing parameter", Archive of Applied Mechanics, Vol. 68, No. 2 1998. pp. 122-127.
- Kmecko, I.S., Baclic, B. S.: "Paradoxical Irreversibility of Enthalpy Exchange in some Heat Exchangers", Paper No. 12.4, Proceedings of the International Conference "Heat Exchangers for Sustainable Development" Lisbon, Portugal, 15-18 June 1998, pp. 751-760.
- Baclic, B.S., Heggs, P. J.: "Summary of Galerkin-like Methods for Counterflow Regenerators", Proceedings of the Conference "Mathematics in Heat Transfer", Institute of Mathematics and its Applications, University of Bradford, 29 June - 1 July 1998.
- Baclic, B.S., Heggs, P. J.: "Successive Integral Method for Nonlinear Fin Problems", Proceedings of the Conference "Mathematics in Heat Transfer", Institute of Mathematics and its Applications, University of Bradford, 29 June - 1 July 1998.
- Baclic, B.S., Dragutinovic, G.D. "Operation of Counterflow Regenerators", Book Vol. 4 in Series "Developments in Heat Transfer", Computational Mechanics Publications, Southampton, 1998.