ЦЕНТРАЛЕН ПОДХОД НА КРАЙНИТЕ РАЗЛИКИ ЗА ОТЧИТАНЕ НА СВОБОДНИТЕ ВИБРАЦИИ НА ДВОЙНО КОНУСОВИДНИ КОНЗОЛНИ ГРЕДИ С ЕЛАСТИЧНА ОСНОВА И ЗАОСТРЕ

Nebojša Zdravković; Milomir Gašić; Mile Savković; Goran Marković

Научен доклад ID 1200 : 2015/3

ЦЕНТРАЛЕН ПОДХОД НА КРАЙНИТЕ РАЗЛИКИ ЗА ОТЧИТАНЕ НА СВОБОДНИТЕ ВИБРАЦИИ НА ДВОЙНО КОНУСОВИДНИ КОНЗОЛНИ ГРЕДИ С ЕЛАСТИЧНА ОСНОВА И ЗАОСТРЕ

Nebojša Zdravković, Milomir Gašić, Mile Savković, Goran Marković

Проблемът, произтичащ от свободните вибрации на двойно-конусовидните конзолни греди с еластична основа и заострени краища, се решава успешно чрез построяването на алгебрични равенства с помощта на модела на крайните разлики. Използването на правилните диференциални уравнения, отчитащи втъзките между променливите, дискретизирани с помощта на метода на крайните разлики, съответства на определени точки от координатната система. Влиянието на неподвижността на формата на обекта е дискретизирана в зависимост от връзките между променливите в уравнението. Проблемът, свързан с отчитане на граничните стойности, се решава с построяването на матрица, която се състои от алгоритъм, който се решава чрез техническата програма MATLAB. С цел сравнение на получените резултати, подобен алгоритъм е създаден и решен чрез ANSYS. Тествани са голям брой стойности с неизмерима скованост и обем. Представеният модел отчита естествената честота на параметрите, което до голяма степен се доближава до резултатите, получени при модела на симулация на крайните елементи.

• Презареди статията • Open/Download as PDF

свободни вибрации двойно-конусовидни конзолни греди ограничен метод Теория на Ойлер – Бернули еластична основа заострени краища.free vibrations double-tapered cantilever beam finite difference method Euler–Bernoulli theory elastic foundation tNebojša Zdravković Milomir Gašić Mile Savković Goran Marković

BIBLIOGRAPHY

[1] Laura PAA, Gutierrez RH. Vibrations of an elastically restrained cantilever beam of varying cross-section with tip mass of finite length. Journal of Sound and Vibration 108(1), 123–131 (1986).

[2] W.L. Craver Jr., P. Jampala. Transverse Vibrations of a Linearly Tapered Cantilever Beam With Constraining Springs. Journal of Sound and Vibration 166(3), 521–529 (1993).

[3] R.O. Grossi, B. del V. Arenas. A variational approach to the vibration of tapered beams with elastically restrained ends. Journal of Sound and Vibration 195(3), 507–511 (1996).

[4] N.M. Auciello. Transverse vibrations of a linearly tapered cantilever beam with tip mass of rotatory inertia and eccentricity. Journal of Sound and Vibration 194(1), 25–34 (1996).

[5] N.M. Auciello, G. Nolè. Vibrations of a cantilever tapered beam with varying section properties and carrying a mass at the free end. Journal of Sound and Vibration 214(1), 105–119 (1998).

[6] D. Zhou, Y.K. Cheung. The free vibration of a type of tapered beams. Computer Methods in Applied Mechanics and Engineering. 188, 203–216 (2000).

[7] N.M. Auciello. On the transverse vibrations of non-uniform beams with axial loads and elastically restrained ends. International Journal of Mechanical Sciences 43, 193–208 (2001)

[8] S. Naguleswaran. Vibration of an Euler–Bernoulli beam on elastic end supports and with up to three step changes in cross-section. International Journal of Mechanical Sciences 44, 2541–2555 (2002)

[9] S. Naguleswaran. Vibration and stability of an Euler–Bernoulli beam with up to three-step changes in cross-section and in axial force. International Journal of Mechanical Sciences 45, 1563–1579 (2003)

[10] Q.S. Li, L.F. Yang, Y.L. Zhao, G.Q. Li. Dynamic analysis of non-uniform beams and plates by finite elements with generalized degrees of freedom. International Journal of Mechanical Sciences 45, 813–830 (2003)

[11] H. Qiao, Q.S. Li, G.Q. Li. Vibratory characteristics of flexural non-uniform Euler–Bernoulli beams carrying an arbitrary number of spring–mass systems. International Journal of Mechanical Sciences 44, 725–743 (2002)

[12] Jong-Shyong Wu, Chin-Tzu Chen. An exact solution for the natural frequencies and mode shapes of an immersed elastically restrained wedge beam carrying an eccentric tip mass with mass moment of inertia. Journal of Sound and Vibration 286, 549–568 (2005)

[13] Michael A. Koplow, Abhijit Bhattacharyya, Brian P. Mann. Closed form solutions for the dynamic response of Euler–Bernoulli beams with step changes in cross section. Journal of Sound and Vibration 295, 214–225 (2006)

[14] R.D. Firouz-Abadi, H. Haddadpour, A.B. Novinzadeh. An asymptotic solution to transverse free vibrations of variable-section beams. Journal of Sound and Vibration 304, 530–540 (2007)

[15] J.W. Jaworski, E.H. Dowell. Free vibration of a cantilevered beam with multiple steps: Comparison of several theoretical methods with experiment. Journal of Sound and Vibration 312, 713–725 (2008)

[16] M.S. Abdel-Jaber et al. Nonlinear natural frequencies of an elastically restrained tapered beam. Journal of Sound and Vibration 313, 772–783 (2008)

[17] Jung-Chang Hsu, Hsin-Yi Lai, C.K. Chen. Free vibration of non-uniform Euler–Bernoulli beams with general elastically end constraints using Adomian modified decomposition method. Journal of Sound and Vibration 318, 965–981 (2008)

[18] E. J. Sapountzakis, D. G. Panagos. Nonlinear analysis of beams of variable cross section, including shear deformation effect. Archive of Applied Mechanics. 78, 687–710 (2008)

[19] Yong Huang, Xian-Fang Li. A new approach for free vibration of axially functionally graded beams with non-uniform cross-section. Journal of Sound and Vibration 329, 2291–2303 (2010)

[20] Korak Sarkar, Ranjan Ganguli. Closed-form solutions for non-uniform Euler–Bernoulli free–free beams. Journal of Sound and Vibration 332, 6078–6092 (2013)

[21] S. Rajasekaran. Buckling and vibration of axially functionally graded nonuniform beams using differential transformation based dynamic stiffness approach. Meccanica 48, 1053–1070 (2013)

[22] Samir AL-Sadder, Raid A. Othman AL-Rawi. Finite difference scheme for large-deflection analysis of non-prismatic cantilever beams subjected to different types of continuous and discontinuous loadings. Archive of Applied Mechanics 75, 459–473 (2006)

[23] J. Awrejcewicz, A.V. Krysko, J. Mrozowski, O.A. Saltykova, M.V. Zhigalov. Analysis of regular and chaotic dynamics of the Euler–Bernoulli beams using finite difference and finite element methods. Acta Mechanica Sinica 27(1), 36–43 (2011)

[24] Meirovitch L. Fundamentals of vibrations. McGraw-Hill, New York (2001)

[25] Yong Huang, Ling-E Yang, Qi-Zhi Luo. Free vibration of axially functionally graded Timoshenko beams with non-uniform cross-section. Composites: Part B 45, 1493–1498 (2013)