Symmetrical Mechanical System Properties-Based Forced Vibration Analysis
Document Type : Research Paper
Authors
1 Department of Mechanical Engineering, Transilvania University of Brasov, B-dul Eroilor, 29, 500036, Romania
2 Technical Sciences Academy of Romania, Bucharest
3 Department of Mathematics and Computer Science, Transilvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania
4 Academy of Romanian Scientists, Ilfov Street, No. 3, 050045 Bucharest, Romania
Abstract
Mechanical systems with structural symmetries present vibration properties that allow the calculation to be easier and the analysis time to decrease. The paper aims to use the properties involved by the symmetries that exist in mechanical systems for the analysis of the forced response to vibrations. Thus, the study of the properties of systems with symmetries or with identical parts is expanded. Based on a classic model, the characteristic properties that appear in this case are obtained and the advantages of using these properties are revealed. On an example consisting of a truck equipped with two identical engines, the way of applying these properties in the calculation and the resulting advantages is presented.
Keywords
Main Subjects
[1] C. Ambrus, Dynamic Analysis of Stresses in the Motor-Transmission Assembly of Mobile Power Drilling Installations, Ph. D Thesis, Transylvania University of Brasov, Brasov, Romania., 2017.
[2] C. Kaluba, A. Zingoni, Group-Theoretic Buckling Analysis of Symmetric Plane Frames, Journal of Structural Engineering, Vol. 147, pp. 04021153, 10/01, 2021.
[3] D. Holm, T. Schmah, C. Stoica, 2009, Geometric Mechanics and Symmetry,
[4] J. E. Marsden, T. S. Ratiu, 2013, Introduction to mechanics and symmetry: a basic exposition of classical mechanical systems, Springer Science & Business Media,
[5] S. F. Singer, 2004, Symmetry in Mechanics, Springer, Berlin/Heidelberg, Germany, 1ed.
[6] Z. Celep, On the axially symmetric vibration of thick circular plates, Ingenieur-Archiv, Vol. 47, No. 6, pp. 411-420, 1978/11/01, 1978.
[7] A. Zingoni, N. Enoma, Dual-purpose concrete domes: A strategy for the revival of thin concrete shell roofs, in Proceeding of, Elsevier, pp. 2686-2703.
[8] A. Zingoni, N. Enoma, On the strength and stability of elliptic toroidal domes, Engineering Structures, Vol. 207, pp. 110241, 2020.
[9] Y. Chen, J. Feng, Generalized Eigenvalue Analysis of Symmetric Prestressed Structures Using Group Theory, Journal of Computing in Civil Engineering, Vol. 26, pp. 488-497, 07/01, 2012.
[10] E. Zavadskas, R. Bausys, J. Antucheviciene, Civil Engineering and Symmetry, Symmetry, Vol. 11, pp. 501, 04/05, 2019.
[11] L. Codarcea-Munteanu, M. Marin, S. Vlase, The study of vibrations in the context of porous micropolar media thermoelasticity and the absence of energy dissipation, Journal of Computational Applied Mechanics, Vol. 54, No. 3, pp. 437-454, 2023.
[12] I. M. J. J. Ganghoffer, Similarity, Symmetry and Group Theoretical Methods in Mechanics, in International Centre for Mechanical Sciences, Udine, Italy, 2015.
[13] I. G. D. Mangeron, S. Vlase, Symmetrical Branched Systems Vibrations, Sci. Mem. Rom. Acad, Vol. 12, pp. 232-236, 1991.
[14] M. Luminita Scutaru, S. Vlase, M. Marin, Symmetrical Mechanical System Properties-Based Forced Vibration Analysis, Journal of Computational Applied Mechanics, pp. -, 2023.
[15] S. Vlase, M. Marin, M. Scutaru, I. R. Száva, Coupled transverse and torsional vibrations in a mechanical system with two identical beams, AIP Advances, Vol. 7, pp. 065301, 06/01, 2017.
[16] S. M. Abo-Dahab, A. E. Abouelregal, M. Marin, Generalized thermoelastic functionally graded on a thin slim strip non-Gaussian laser beam, Symmetry, Vol. 12, No. 7, pp. 1094, 2020.
[17] S. Vlase, C. Năstac, M. Marin, M. Mihălcică, A method for the study of the vibration of mechanical bars systems with symmetries, ACTA TECHNICA NAPOCENSIS-Series: APPLIED MATHEMATICS, MECHANICS, and ENGINEERING, Vol. 60, No. 4, 2017.
[18] M. Hassan, M. I. Marin, R. Ellahi, S. Z. Alamri, EXPLORATION OF CONVECTIVE HEAT TRANSFER AND FLOW CHARACTERISTICS SYNTHESIS BY Cu–Ag/WATER HYBRID-NANOFLUIDS, Heat Transfer Research, Vol. 49, pp. 1837-1848, 2018.
[19] A. Zingoni, Symmetry recognition in group-theoretic computational schemes for complex structural systems, Computers & Structures, Vol. 94-95, pp. 34-44, 2012/03/01/, 2012.
[20] A. Zingoni, Group-theoretic exploitations of symmetry in computational solid and structural mechanics, International Journal for Numerical Methods in Engineering, Vol. 79, pp. 253-289, 07/16, 2009.
[21] M. Marin, A. Seadawy, S. Vlase, A. Chirila, On mixed problem in thermoelasticity of type III for Cosserat media, Journal of Taibah University for Science, Vol. 16, No. 1, pp. 1264-1274, 2022.
[22] A. Zingoni, Group-theoretic insights on the vibration of symmetric structures in engineering, Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, Vol. 372, pp. 20120037, 02/13, 2014.
[23] T. PERNA, ROLE OF SYMMETRY IN OPTIMIZATION OF FEM SIMULATION CALCULATIONS, MM Science Journal, 2022.
[24] B. Dong, R. Parker, Modal properties of cyclically symmetric systems with central components vibrating as three-dimensional rigid bodies, Journal of Sound and Vibration, Vol. 435, 08/01, 2018.
[25] A. Zingoni, Group-theoretic vibration analysis of double-layer cable nets of D4h symmetry, International Journal of Solids and Structures, Vol. 176-177, pp. 68-85, 2019/11/30/, 2019.
[26] A. Zingoni, On the best choice of symmetry group for group-theoretic computational schemes in solid and structural mechanics, Computers & Structures, Vol. 223, pp. 106101, 10/01, 2019.
[27] D. Bartilson, J. Jang, A. Smyth, Symmetry properties of natural frequency and mode shape sensitivities in symmetric structures, Mechanical Systems and Signal Processing, Vol. 143, pp. 106797, 09/01, 2020.
[28] M. G. Fernández-Godino, S. Balachandar, R. Haftka, On the Use of Symmetries in Building Surrogate Models, Journal of Mechanical Design, Vol. 141, 11/20, 2018.
[29] D. Wang, C. Zhou, J. Rong, Free and forced vibration of repetitive structures, International Journal of Solids and Structures, Vol. 40, pp. 5477-5494, 10/01, 2003.
[30] C. Cai, F. Wu, On the vibration of rotational periodic structures, Acta Scientiarum Naturalium Universitatis Sunyatseni, Vol. 22, No. 3, pp. 1-9, 1983.
[31] C. W. Cai, Y. K. Cheung, H. C. Chan, Uncoupling of dynamic equations for periodic structures, Journal of Sound and Vibration, Vol. 139, No. 2, pp. 253-263, 1990/06/08/, 1990.
[32] H. C. Chan, C. Cai, Y. K. Cheung, 1998, Exact analysis of structures with periodicity using U-transformation, World Scientific,
[33] D. A. Evensen, Vibration analysis of multi-symmetric structures, AIAA Journal, Vol. 14, No. 4, pp. 446-453, 1976.
[34] D. Wang, C.-C. Wang, Natural vibrations of repetitive structures, Journal of Mechanics, Vol. 16, No. 2, pp. 85-95, 2000.
[35] W. Zhong, J. Lin, The eigen-value problem of the chain of identical substructures and the expansion method solution lasted on the eigen-vectors, Acta Mech. Sin, Vol. 23, pp. 72-81, 1991.
[36] L. Brillouin, 1946, Wave Propagation in Periodic Structures, Dover Publications, New York, USA
[37] D. Mead, A general theory of harmonic wave propagation in linear periodic systems with multiple coupling, Journal of Sound and Vibration, Vol. 27, No. 2, pp. 235-260, 1973.
[38] M. Marin, Some estimates on vibrations in thermoelasticity of dipolar bodies, Journal of Vibration and Control, Vol. 16, No. 1, pp. 33-47, 2010.
[39] D. Mead, A. Bansal, Mono-coupled periodic systems with a single disorder: Free wave propagation, Journal of Sound and Vibration, Vol. 61, No. 4, pp. 481-496, 1978.
[40] L. Gry, C. Gontier, DYNAMIC MODELLING OF RAILWAY TRACK: A PERIODIC MODEL BASED ON A GENERALIZED BEAM FORMULATION, Journal of Sound and Vibration, Vol. 199, No. 4, pp. 531-558, 1997/01/30/, 1997.
[41] L. Meirovitch, 2010, Methods of analytical dynamics, Courier Corporation,
[42] W. Zhong, F. W. Williams, On the direct solution of wave propagation for repetitive structures, Journal of Sound and Vibration, Vol. 181, pp. 485-501, 1995.
[43] A. Kaveh, K. Biabani Hamedani, A. Joudaki, M. Kamalinejad, Optimal analysis for optimal design of cyclic symmetric structures subject to frequency constraints, Structures, Vol. 33, pp. 3122-3136, 06/17, 2021.
[44] S. Vlase, M. Marin, M. L. Scutaru, C. Pruncu, Vibration Response of a Concrete Structure with Repetitive Parts Used in Civil Engineering, Mathematics, Vol. 9, No. 5, pp. 490, 2021.
[45] S. Vlase, P. Teodorescu, Elasto-dynamics of a solid with a general ‘rigid’motion using fem model. Part I. Theoretical approach, Rom. J. Phys, Vol. 58, No. 7-8, pp. 872-881, 2013.
[46] J. Zhang, E. Reynders, G. De Roeck, G. Lombaert, Model updating of periodic structures based on free wave characteristics, Journal of Sound and Vibration, Vol. 442, 11/01, 2018.
[47] L.-J. Wu, H.-W. Song, Band gap analysis of periodic structures based on cell experimental frequency response functions (FRFs), Acta Mechanica Sinica, Vol. 35, pp. 156-173, 2019.
[48] M. I. Othman, M. Fekry, M. Marin, Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating, Struct. Eng. Mech, Vol. 73, No. 6, pp. 621-629, 2020.
[49] A. Kaveh, A. Joudaki, Matrix Analysis of Repetitive Circulant Structures: New-block and Near Block Matrices, Periodica Polytechnica Civil Engineering, 05/28, 2019.
[50] R. Antoine, S. Hans, C. Boutin, Asymptotic analysis of high-frequency modulation in periodic systems. Analytical study of discrete and continuous structures, Journal of the Mechanics and Physics of Solids, Vol. 117, 04/01, 2018.
[51] S. Vlase, M. Marin, P. Bratu, O. A. O. SHRRAT, Analysis of Vibration Suppression in Multi-Degrees of Freedom Systems, Romanian Journal of Acoustics and Vibration, Vol. 19, No. 2, pp. 149-156, 2022.
[52] M. Marin, O. Florea, On temporal behaviour of solutions in thermoelasticity of porous micropolar bodies, Analele ştiinţifice ale Universităţii" Ovidius" Constanţa. Seria Matematică, Vol. 22, No. 1, pp. 169-188, 2014.
[53] A. Kaveh, A. Zolghadr, Optimal design of cyclically symmetric trusses with frequency constraints using cyclical parthenogenesis algorithm, Advances in Structural Engineering, Vol. 21, No. 5, pp. 739-755, 2018.
[54] L. Li, B. Cheng, Y. Zhang, H. Qin, Study of a smart platform based on backstepping control method, Earthquake Engineering and Engineering Vibration, Vol. 16, No. 3, pp. 599-608, 2017/07/01, 2017.
[55] Z. Ghemari, S. Belkhiri, Mechanical resonator sensor characteristics development for precise vibratory analysis, Sensing and Imaging, Vol. 22, No. 1, pp. 40, 2021.
[56] H. Çetin, G. G. Yaralioglu, Analysis of Vibratory Gyroscopes: Drive and Sense Mode Resonance Shift by Coriolis Force, IEEE Sensors Journal, Vol. 17, pp. 347-358, 2017.
[57] A. Z. Ter-Martirosyan, A. N. Shebunyaev, V. V. Sidorov, Mathematical Analysis of the Vibratory Pile Driving Rate, Axioms, Vol. 12, No. 7, pp. 629, 2023.
[58] I. Abbas, A. Hobiny, M. Marin, Photo-thermal interactions in a semi-conductor material with cylindrical cavities and variable thermal conductivity, Journal of Taibah University for Science, Vol. 14, No. 1, pp. 1369-1376, 2020.
[59] M. Marin, On the minimum principle for dipolar materials with stretch, Nonlinear Analysis: Real World Applications, Vol. 10, No. 3, pp. 1572-1578, 2009.
[60] M. Rades, Mechanical vibrations II. Structural dynamic modeling, Rumania: University Politehnica Bucharest, pp. 354, 2010.
[61] Shock, V. I. Center, 1986, Shock and Vibration Monograph Series, Shock and Vibration Information Center.,
[62] D. Chen, J. Yang, S. Kitipornchai, Free and forced vibrations of shear deformable functionally graded porous beams, International Journal of Mechanical Sciences, Vol. 108-109, pp. 14-22, 2016/04/01/, 2016.
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Volume 54, Issue 4
December 2023Pages 501-514
- Receive Date: 10 October 2023
- Accept Date: 11 October 2023