Обобщенная формула для оценки основного тона консольного стержня с точечными массами
DOI:
https://doi.org/10.26577/JMMCS.2023.v118.i2.07Ключевые слова:
треугольная пластина, численный метод, метод сеток, прогиб, изгибная жесткость, стержневая аналогия, редукционный коэффициент.Аннотация
В данной работе исследован изгиб консольных треугольных пластин при одинаковых углах наклона боковых кромок к основанию. Из-за сложности граничных условий применен численный метод конечных разностей с применением сетки из разносторонних треугольни- ков, хорошо вписывающийся в контур пластины. Для решения проблемы острого угла у вершины пластины применен способ совмещения результатов расчета консольного стержня переменной изгибной жесткости с аналогичными результатами расчета треугольной опертой по контуру пластины с использованием коэффициента редукции. Приведены результаты прогибов консольной треугольной пластины при различных углах наклона боковых кромок к основанию. Теоретические положения и прикладные результаты данного исследования могут быть использованы как в научных изысканиях, так и в инженерном проектировании.
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[4] Korobko A.V., Kalashnikova N.G., Abashin E.G. Transverse bending and free vibrations of elastic isotropic plates in the form of isosceles triangles. Construction and reconstruction, 2021, No. 6, pp. 20 - 27. https://doi.org/10.33979/2073-7416- 2021-98-6-20-27
[5] Korobko A.V., Chernyaev A.A., Shlyakhov S.V. Application of the MICF method for calculating triangular and quadrangular plates using widely known geometric parameters. Construction and reconstruction, 2016, No. 4, pp. 19 - 28.
[6] Saliba H.T. Triangular elements and the superposition techniques in till free vibration analysis of plates. Mecanique industrielle et materiaux (11th Colloquium on Vibrations, Shocks and Noise), 1996, No. 49 (4), pp. 168 - 170.
[7] Korobko A.V. Calculation of triangular plates by interpolation method by the shape coefficient using affine
transformations. News of higher educational institutions. Aviation technology, 2003, No. 2, pp. 13 - 16.
[8] Korobko V.I., Savin S.Yu. Free vibrations of triangular orthotropic plates with homogeneous and combined boundary conditions. Construction and reconstruction, 2013, No. 2, pp. 33 - 40.
[9] Korobko V.I., Savin S.Yu., Boyarkina S.V. Bending of triangular orthotropic plates with homogeneous and combined boundary conditions. Construction and Reconstruction, 2012, No. 1, pp. 7 - 13.
[10] Muromsky A.S., Korobko A.V. Calculation of triangular plates using affine transformations. Proceedings of the 55th International scientific and technical conference of young scientists (doctoral students, postgraduates and students) "Actual problems of modern construction St. Petersburg, 2001.
[11] Vlasov V.I., Gorshkov A.B., Kovalev R.V., Lunev V.V. Thin triangular plate with a blunted vertex in a viscous hypersonic flow. 2009, No. 4, pp. 134 - 145.
[12] Grigorenko O.Y., Borisenko M.Y., Boichuk O.V. et al. Free vibrations of triangular plates with a hole*. Int Appl Mech., 2021, No. 57, pр. 534 - 542. https://doi.org/10.1007/s10778-021-01104-3.
[13] Dongze He, Tao Liu, Bin Qin, Qingshan Wang, Zhanyu Zhai, Dongyan Shi. In-plane modal studies of arbitrary laminated triangular plates with elastic boundary constraints by the Chebyshev-Ritz approach. Composite Structures, 2021. DOI: 10.1016/j.compstruct.2021.114138.
[14] Iman Dayyani, Masih Moore, Alireza Shahidi. Unilateral buckling of point-restrained triangular plates. Thin-Walled Structures, 2013, Vol. 66, pр 1 - 8.
[15] Cai D., Wang X., Zhou G. Static and free vibration analysis of thin arbitrary-shaped triangular plates under various boundary and internal supports, Thin-Walled Structures, 2021, Vol. 162, No. 107592.
[16] Varvak P.M., Varvak L.P. Method of grids in problems of calculation for building structures. Moscow, Stroyizdat, 1977, 154 p.
[17] Karamansky T.D. Numerical methods of structural mechanics. Moscow, Stroyizdat, 1980, 434 p.
[18] Akhmediev S.K. Analytical and numerical methods for calculating machine-building and transport constructions and structures (textbook). Karaganda, KarTU, 2016, 158 p.
[19] Akhmediev S.K. Calculations of triangular plates. Karaganda, KarTU, 2006, 86 p.
[20] Nuguzhinov Z.S., Akhmediyev S.K., Donenbayev B.S., Kurokhtin A.Yu., Khabidolda O. Comparative analysis of designing wall panels with hole based on one-dimensional and two-dimensional computer models. IOP Conf. Series: Materials Science and Engineering, 2018, 456 012082. DOI:10.1088/1757-899X/456/1/012082
[21] Kasimov A.T., Yessenbayeva G.A., Zholmagambetov S.R., Khabidolda O. Investigation of layered orthotropic structures based on one modified refined bending theory. Eurasian Physical Technical Journal, 2021, Vol.18, No. 4(38), pp. 37 - 44. DOI 10.31489/2021No4/37-44
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Как цитировать
Akhmediyev, S. K., Khabidolda, O., Vatin, N. I., Yessenbayeva, G. A., & Muratkhan, R. (2023). Обобщенная формула для оценки основного тона консольного стержня с точечными массами. Вестник КазНУ. Серия математика, механика, информатика, 118(2), 64–73. https://doi.org/10.26577/JMMCS.2023.v118.i2.07
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Механика
