Increasing the Fundamental Frequency of the Cantilever Rotating Beam by Placing the Intermediate Elastic Support with Minimum Stiffness at the Optimum Point Based on the Courant’s Maximum–Minimum Theorem using Finite-Element Analysis Software
محورهای موضوعی :
vibration and control
Mehdi Asgarikia
1
,
Farshad Kakavand
2
,
Hasan Seidi
3
1 - Department of Mechanical Engineering,
Takestan Branch, Islamic Azad University, Takestan, Iran
2 - Department of Mechanical Engineering, Takestan Branch, Islamic Azad University, Takestan, Iran
3 - Department of Mechanical Engineering,
Takestan Branch, Islamic Azad University, Takestan, Iran
تاریخ دریافت : 1399/09/20
تاریخ پذیرش : 1400/02/11
تاریخ انتشار : 1400/06/10
کلید واژه:
Intermediate Elastic Support,
Rotating Beam,
Damping Wire,
Stiffness,
Fundamental Frequency,
Blade,
چکیده مقاله :
: In this paper, the effect of the optimal position and minimum stiffness of the elastic middle support on increasing the fundamental frequency of a rotating cantilever beam is investigated based on the Courant’s maximum–minimum theorem using ABAQUS finite element software. First, the software analysis results are compared with the numerical analysis results for a non-rotating cantilever beam to confirm the accuracy of the software model. Next, by placing the middle elastic support at the optimal point selected based on the Courant theorem, the minimum stiffness of the elastic intermediate support for the maximum fundamental frequency of the rotating console beam was obtained. The results of this study prove that the Courant’s maximum–minimum theorem is completely valid for rotating cantilever beams and can be used to improve the vibrational behavior of rotating engineering components. Finally, the minimum diameter of damping wire for the turbomachine blade is calculated as a practical application of the minimum stiffness of the intermediate elastic support for the rotating beam.
منابع و مأخذ:
Lord, R., Theory of Sound, 2nd ed, Dover, New York, USA, 1, 1894, pp 480.
Courant, R., Zeitschrift.l~r Angewandte Mathematik und Mechanik 2, Zur Theorie der kleinen Schwingungen, Germany, 1922, pp. 278-285.
Akesson, B., Olhoff, N., Minimum Stiffness of Optimally Located Supports for Maximum Value of Beam Eigenfrequencies, Journal of Sound and Vibration, 120, No. 3, 1988, pp. 457-463. https://doi.org/ 10.1016/s0022-460x (88)80218-9
Rao, C. K., Frequency Analysis of Clamped–Clamped Uniform Beams with Intermediate Elastic Support, Journal of Sound and Vibration, 133, 1989, pp. 502–509.
Albarracı´n, C. M., Zannier, L., and Grossi, R. O., Some Observations in The Dynamics of Beams with Intermediate Supports, Journal of Sound and Vibration, 271, 2004, pp. 475–480.
Wang, D., Friswell, M. I., and Lei, Y., Maximizing the Natural Frequency of a Beam with an Intermediate Elastic Support, Journal of Sound and Vibration, 291, 2006, pp. 1229-1238.
Lin, S. C., K. M. Hsiao., Vibration Analysis of a Rotating Timoshenko Beam, Journal of Sound and Vibration, 240, No. 2, 2001, pp. 303-322.
Stoykov, S., P. Ribeiro., Vibration Analysis of Rotating 3D Beams by The P-Version Finite Element Method, Finite Elements in Analysis and Design, 65, 2013, pp. 76-88.
Cheng, Jianlian, Hui, X., and Anzhi, Y., Frequency Analysis of a Rotating Cantilever Beam Using Assumed Mode Method with Coupling Effect, Mechanics Based Design of Structures and Machines, 34, No. 1, 2006, pp. 25-47.
Salarieh, H., Ghorashi. M., Free Vibration of Timoshenko Beam with Finite Mass Rigid Tip Load and Flexural–Torsional Coupling, International Journal of Mechanical Sciences, 48, No. 7, 2006, pp. 763-779.
Ansari, M., Esmailzadeh, E., and Jalili, N., Exact Frequency Analysis of a Rotating Cantilever Beam with Tip Mass Subjected to Torsional-Bending Vibrations, Journal of Vibration and Acoustics, 133, No. 4, 2011, pp. 1003-1014.
Bambill, D. V., Rossit, C. A., Rossi, R. E., Felix, D. H., and Ratazzi, A. R., Transverse Free Vibration of Non-Uniform Rotating Timoshenko Beams with Elastically Clamped Boundary Conditions, Meccanica, 48, No. 6, 2013, pp. 1289-1311.
Tang, A. Y., Li, X. F., Wu, J. X., and Lee., K. Y., Flapwise Bending Vibration of Rotating Tapered Rayleigh Cantilever Beams, Journal of Constructional Steel Research, 112, 2015, pp. 1-9.
Chen, Y., Juan Z., and Hong Z., Free Vibration Analysis of Rotating Tapered Timoshenko Beams via Variational Iteration Method, Journal of Vibration and Control, 23, No. 2, 2017, pp. 220-234.
Ajinkya, B., Abhjit, S., Natural Frequencies of a Rotating Curved Cantilever Beam: A Perturbation Method-Based Approach, Journal of Mechanical Engineering Science, 2020, pp. 1–14.
