Approximate calculation of natural frequencies of oscillations of the plate with variable cross-section of the discrete-continuous inter-resonance vibrating table

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dc.citation.epage50
dc.citation.issue2
dc.citation.journalTitleУкраїнський журнал із машинобудування і матеріалознавства
dc.citation.spage41
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorLanets, Oleksii
dc.contributor.authorMaistruk, Pavlo
dc.contributor.authorMaistruk, Volodymyr
dc.contributor.authorDerevenko, Iryna
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2023-09-15T06:38:02Z
dc.date.available2023-09-15T06:38:02Z
dc.date.created2022-02-22
dc.date.issued2022-02-22
dc.description.abstractProblem statement. To ensure highly efficient inter-resonance modes of operation of vibrating equipment, the oscillating masses of the system must have certain inertia-rigid parameters, as well as a certain frequency of natural oscillations. The disadvantage of highly efficient inter-resonance oscillatory systems is that the third reactive mass must be small, and therefore the use of complex and large structures is impossible. Therefore, it is best to use the reactive mass as a continuous section. The continuous section, which is a flexible body, optimally combines inertial and rigid parameters. Scientific works have already considered the design of the vibrating table, in which the continuous section is an ordinary rectangular plate hinged in the intermediate mass. This decision looks quite promising. However, likely, the rectangular shape of the plate is not the best option to ensure maximum energy efficiency. Purpose. Extend the method of calculating the natural frequency of oscillations of the plates by the approximate Rayleigh-Ritz method using the general hyperboloid equation to plates with variable cross-section for the proposed types of plates and check the results with the calculation in Ansys software. Methodology. The calculations of the plates were performed using the basic principles of the theory of oscillations, in particular the Rayleigh-Ritz method in the software product MathCAD. Findings (results) and originality (novelty). Two types of elastic plates with variable cross-sections are considered. In the first case, the shape of the plate was given by quadratic functions, in the second case, it was described by trigonometric functions of cosine. In both cases, the same conditions of attachment in the intermediate mass were observed. The calculation of the first natural frequency of oscillations of the considered plates was performed using the approximate Rayleigh-Ritz method with the assumption that the deflection of the plates occurs on the surface of the hyperboloid. The reliability of the obtained results was verified by numerical calculation in the software product Ansys. Practical value. It is assumed that the proposed types of plates can increase the dynamic potential of the vibrating machine. Scopes of further investigations. For further study of the considered types of plates as a continuous section of the inter-resonance vibrating machine, it is necessary to calculate their deflections at forced oscillations.
dc.format.extent41-50
dc.format.pages10
dc.identifier.citationApproximate calculation of natural frequencies of oscillations of the plate with variable cross-section of the discrete-continuous inter-resonance vibrating table / Oleksii Lanets, Pavlo Maistruk, Volodymyr Maistruk, Iryna Derevenko // Ukrainian Journal of Mechanical Engineering and Materials Science. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 8. — No 2. — P. 41–50.
dc.identifier.citationenApproximate calculation of natural frequencies of oscillations of the plate with variable cross-section of the discrete-continuous inter-resonance vibrating table / Oleksii Lanets, Pavlo Maistruk, Volodymyr Maistruk, Iryna Derevenko // Ukrainian Journal of Mechanical Engineering and Materials Science. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 8. — No 2. — P. 41–50.
dc.identifier.doidoi.org/10.23939/10.23939/ujmems2022.02.041
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/60085
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofУкраїнський журнал із машинобудування і матеріалознавства, 2 (8), 2022
dc.relation.ispartofUkrainian Journal of Mechanical Engineering and Materials Science, 2 (8), 2022
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dc.relation.references[2] O. Lanets, P. Maistruk, “Obhruntuvannya parametriv trymasovoyi mizhrezonansnoyi vibratsiynoyi mashyny z inertsiynym pryvodom” [“Adjustment of parameters of three – mass interresonant vibrating machines with an inertial exciters”], Industrial Process Automation in Engineering and Instrumentation, vol. 53, pp. 13–22, 2019. [in Ukrainian].
dc.relation.references[3] O. Lanets, O. Kachur, V. Borovets, P. Dmyterko, I. Derevenko, A. Zvarich, “Vstanovlennya vlasnoyi chastoty kontynualʹnoyi dilyanky mizhrezonansnoyi vibromashyny z vykorystannyam nablyzhenoho metodu ReleyaRittsa” [“Establishment of the original frequency of the continual section of the interreson research machine Rayleigh–Ritz method”], Industrial Process Automation in Engineering and Instrumentation, vol. 54, pp. 5–15, 2020. [in Ukrainian].
dc.relation.references[4] P. Maistruk, O. Lanets, V. Stupnytskyy, “Approximate Calculation of the Natural Oscillation Frequency of the Vibrating Table in Inter-Resonance Operation Mode”, Strojnícky časopis – Journal of Mechanical Engineering, vol. 71(2), pp. 151–166, 2021.
dc.relation.references[5] A. Saeed, H. Hassan, E. Wael, “Vibration attenuation using functionally graded material”, World Academy of Science, Engineering and Technology vol. 7(6), pp. 1111–1120, 2013.
dc.relation.references[6] A. K. Sharma, P. Sharma, P. S. Chauhan, S. S Bhadoria, “Study on Harmonic Analysis of Functionally Graded Plates Using Fem”, International Journal of Applied Mechanics and Engineering vol. 23(4), pp. 941–961, 2018.
dc.relation.references[7] K. Taehyun, L. Usik, “Vibration Analysis of Thin Plate Structures Subjected to a Moving Force Using Frequency-Domain Spectral Element Method”, Shock and Vibration vol. 2018, pp. 1–27, 2018.
dc.relation.references[8] J. N. Reddy, “Theory and Analysis of Elastic Plates and Shells”, 2-nd ed., CRC Press, Boca Raton, USA, 2007.
dc.relation.references[9] S. P. Timoshenko, S. Woinowsky-Krieger, “Theory of Plates and Shells”, 2-nd ed., McGraw-Hill, New York, USA, 1959.
dc.relation.references[10] Y. P. Sun, C. W. Min, J. Li, Z. L. Teng, “The Finite Element Analysis of Sandwich Variable CrossSection Plate Bending Performance”, Advanced Materials Research Vols. 335–336, pp. 659–662, 2011.
dc.relation.references[11] M. Ece, M. Aydogdu, V. Taskin, “Vibration of a variable cross-section beam”, Mechanics Research Communications, vol. 34, pp. 78–84, 2007.
dc.relation.references[12] S. K. Jena, S. Chakraverty, “Free Vibration Analysis of Variable Cross-Section Single-Layered Graphene Nano-Ribbons (SLGNRs) Using Differential Quadrature Method”, Frontiers in Built Environment, vol. 4, article 63, 2018.
dc.relation.references[13] M. Boiangiu, V. Ceausu, C.D. Untaroiu, “A transfer matrix method for free vibration analysis of EulerBernoulli beams with variable cross section”, Journal of Vibration and Control, vol. 22(11) pp. 2591–2602, 2016.
dc.relation.references[14] E. Demir, H. Çallioğlu, M. Sayer, “Vibration analysis of sandwich beams with variable cross section on variable Winkler elastic foundation׆, Science and Engineering of Composite Materials, vol. 20(4), pp. 359–370, 2013.
dc.relation.references[15] S. Zolkiewski, “Vibrations of beams with a variable cross-section fixed on rotational rigid disks”, Latin American Journal of Solids and Structures, vol. 10, pp. 39–57, 2013.
dc.relation.references[16] J. Feng, Z. Chen, S. Hao, K. Zhang, “An Improved Analytical Method for Vibration Analysis of Variable Section Beam”, Mathematical Problems in Engineering, vol. 2020, article ID 3658146, 2020.
dc.relation.referencesen[1] O. Lanets, Osnovy rozrakhunku ta konstruyuvannya vibratsiynykh mashyn. Knyha 1. Teoriya ta praktyka stvorennya vibratsiynykh mashyn z harmoniynym rukhom robochoho orhana [Fundamentals of analysis and design of vibrating machines. Book 1. Theory and Practice of Development of Vibratory Machines with Harmonic Motion of the Working Element Body]. Lviv, Ukraine: Lviv Polytechnic Publishing House, 2018. [in Ukrainian].
dc.relation.referencesen[2] O. Lanets, P. Maistruk, "Obhruntuvannya parametriv trymasovoyi mizhrezonansnoyi vibratsiynoyi mashyny z inertsiynym pryvodom" ["Adjustment of parameters of three – mass interresonant vibrating machines with an inertial exciters"], Industrial Process Automation in Engineering and Instrumentation, vol. 53, pp. 13–22, 2019. [in Ukrainian].
dc.relation.referencesen[3] O. Lanets, O. Kachur, V. Borovets, P. Dmyterko, I. Derevenko, A. Zvarich, "Vstanovlennya vlasnoyi chastoty kontynualʹnoyi dilyanky mizhrezonansnoyi vibromashyny z vykorystannyam nablyzhenoho metodu ReleyaRittsa" ["Establishment of the original frequency of the continual section of the interreson research machine Rayleigh–Ritz method"], Industrial Process Automation in Engineering and Instrumentation, vol. 54, pp. 5–15, 2020. [in Ukrainian].
dc.relation.referencesen[4] P. Maistruk, O. Lanets, V. Stupnytskyy, "Approximate Calculation of the Natural Oscillation Frequency of the Vibrating Table in Inter-Resonance Operation Mode", Strojnícky časopis – Journal of Mechanical Engineering, vol. 71(2), pp. 151–166, 2021.
dc.relation.referencesen[5] A. Saeed, H. Hassan, E. Wael, "Vibration attenuation using functionally graded material", World Academy of Science, Engineering and Technology vol. 7(6), pp. 1111–1120, 2013.
dc.relation.referencesen[6] A. K. Sharma, P. Sharma, P. S. Chauhan, S. S Bhadoria, "Study on Harmonic Analysis of Functionally Graded Plates Using Fem", International Journal of Applied Mechanics and Engineering vol. 23(4), pp. 941–961, 2018.
dc.relation.referencesen[7] K. Taehyun, L. Usik, "Vibration Analysis of Thin Plate Structures Subjected to a Moving Force Using Frequency-Domain Spectral Element Method", Shock and Vibration vol. 2018, pp. 1–27, 2018.
dc.relation.referencesen[8] J. N. Reddy, "Theory and Analysis of Elastic Plates and Shells", 2-nd ed., CRC Press, Boca Raton, USA, 2007.
dc.relation.referencesen[9] S. P. Timoshenko, S. Woinowsky-Krieger, "Theory of Plates and Shells", 2-nd ed., McGraw-Hill, New York, USA, 1959.
dc.relation.referencesen[10] Y. P. Sun, C. W. Min, J. Li, Z. L. Teng, "The Finite Element Analysis of Sandwich Variable CrossSection Plate Bending Performance", Advanced Materials Research Vols. 335–336, pp. 659–662, 2011.
dc.relation.referencesen[11] M. Ece, M. Aydogdu, V. Taskin, "Vibration of a variable cross-section beam", Mechanics Research Communications, vol. 34, pp. 78–84, 2007.
dc.relation.referencesen[12] S. K. Jena, S. Chakraverty, "Free Vibration Analysis of Variable Cross-Section Single-Layered Graphene Nano-Ribbons (SLGNRs) Using Differential Quadrature Method", Frontiers in Built Environment, vol. 4, article 63, 2018.
dc.relation.referencesen[13] M. Boiangiu, V. Ceausu, C.D. Untaroiu, "A transfer matrix method for free vibration analysis of EulerBernoulli beams with variable cross section", Journal of Vibration and Control, vol. 22(11) pp. 2591–2602, 2016.
dc.relation.referencesen[14] E. Demir, H. Çallioğlu, M. Sayer, "Vibration analysis of sandwich beams with variable cross section on variable Winkler elastic foundation׆, Science and Engineering of Composite Materials, vol. 20(4), pp. 359–370, 2013.
dc.relation.referencesen[15] S. Zolkiewski, "Vibrations of beams with a variable cross-section fixed on rotational rigid disks", Latin American Journal of Solids and Structures, vol. 10, pp. 39–57, 2013.
dc.relation.referencesen[16] J. Feng, Z. Chen, S. Hao, K. Zhang, "An Improved Analytical Method for Vibration Analysis of Variable Section Beam", Mathematical Problems in Engineering, vol. 2020, article ID 3658146, 2020.
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.rights.holder© Lanets O., Maistruk P., Maistruk V., Derevenko I., 2022
dc.subjectinter-resonance vibrating machine
dc.subjectcontinuous member
dc.subjectelastic plate
dc.subjectthe natural frequency of body oscillations
dc.subjectRayleigh-Ritz method
dc.titleApproximate calculation of natural frequencies of oscillations of the plate with variable cross-section of the discrete-continuous inter-resonance vibrating table
dc.typeArticle

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Ukrainian Journal of Mechanical Engineering and Materials Science. – 2022. – Vol. 8, No. 2