Optimization of Location and Stiffness of an Intermediate Support to Maximize the First Natural Frequency of a Beam with Tip Mass-With Application
Subject Areas :
vibration and control
Hossein Ebrahimi
1
,
Farshad Kakavand
2
,
Hassan 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
Received: 2021-06-22
Accepted : 2021-11-10
Published : 2022-03-01
Keywords:
References:
Courant, R., Hilbert, D., Methods of Mathematical Physics, Interscience Publishers, New York, 1953.
Olhoff, N., Akesson, B., Minimum Stiffness of Optimally Located Supports for Maximum Value of Column Buckling Loads, Structural Optimization, Vol. 3, No. 3, 1991, pp. 163-175, https://doi.org/10.1007/BF01743073.
Wang, D., Friswell, M., and Lei, Y., Maximizing the Natural Frequency of a Beam with an Intermediate Elastic Support, Journal of Sound and Vibration, Vol. 291, No. 3, 2006, pp. 1229–1238, https://doi.org/10.1016/j.jsv.2005.06.028.
Wang, C., Minimum Stiffness of an Internal Elastic Support to Maximize the Fundamental Frequency of a Vibrating Beam, Journal of Sound and Vibration, Vol. 259, No. 1, 2003, pp. 229–232, https://doi.org/10.1006/jsvi.2002.5100.
Rao, C. K., Frequency Analysis of Clamped-Clamped Uniform Beams with Intermediate Elastic Support, Journal of Sound and Vibration, Vol. 133, No. 3, 1989, pp. 502–509, https://doi.org/1016/0022-460X(89)90615-9.
Szelag, D., Mroz, Z., Optimal Design of Vibrating Beams with Unspecified Support Reactions, Computer Methods in Applied Mechanics and Engineering, Vol. 19, No. 3, 1979, pp. 333–349, https://doi.org/10.1016/0045-7825(79)90063-X.
Albarracı́n, C. M., Zannier, L., and Grossi, R., Some Observations in the Dynamics of Beams with Intermediate Supports, Journal of Sound and Vibration, Vol. 271, No. 1-2, 2004, pp. 475–480, http://dx.doi.org/10.1016/S0022-460X(03)00631-X.
Wang, D., Optimal Design of Structural Support Positions for Minimizing Maximal Bending Moment, Finite Elements in Analysis and Design, Vol. 43, No. 2, 2006, pp. 95–102, https://doi.org/10.1016/j.finel.2006.07.004.
Motaghian, S., Mofid, M., and Alanjari, P., Exact Solution to Free Vibration of Beams Partially Supported by an Eastic Foundation, Scientia Iranica, Vol. 18, No. 4, 2011, pp. 861-866, https://doi.org/10.1016/j.scient.2011.07.013.
Aydin, E., Minimum Dynamic Response of Cantilever Beams Supported by Optimal Elastic Springs, Structural Engineering and Mechanics, Vol. 51, No. 3, 2014, pp. 377–402, https://doi.org/10.12989/sem.2014.51.3.377.
Goel, R., Vibrations of a Beam Carrying a Concentrated Mass, Journal of Applied Mechanics, Vol. 40, No. 3, 1973, pp. 821-832, https://doi.org/10.1115/1.3423102.
Laura, P., Pombo, J., and Susemihl, E., A Note on the Vibrations of a Clamped-Free Beam with a Mass at the Free End, Journal of Sound and Vibration, Vol. 37, No. 2, 1974, pp. 161-168, https://doi.org/10.1016/S0022-460X(74)80325-1.
Bruch, J., Mitchell, T., Vibrations of a Mass-Loaded Clamped-Free Timoshenko Beam, Journal of Sound and Vibration, Vol. 114, No. 2, 1987, pp. 341-345, https://doi.org/10.1016/S0022-460X(87)80158-X.
Murgoze, M., On the Eigenfrequencies of a Cantilever Beam with Attached Tip Mass and a Spring-Mass System, Journal of Sound and Vibration, Vol. 190, No. 2, 1996, pp. 146-162, https://doi.org/10.1006/jsvi.1996.0053.
Salarieh, H., Ghorashi, M., Free Vibration of Timoshenko Beam with Finite Mass Rigid Tip Load and Flexural–Torsional Coupling, International Journal of Mechanical Sciences, Vol. 48, No. 7, 2006, pp. 763-779, https://doi.org/10.1016/j.ijmecsci.2006.01.008.
Magrab, E. B., Natural Frequencies and Mode Shapes of Timoshenko Beams with Attachments, Journal of Vibration and Control, Vol. 13, No. 7, 2007, pp. 905-934, https://doi.org/10.1177/1077546307078828.
Kukla, S., Free Vibrations of Axially Loaded Beams with Concentrated Masses and Intermediate Elastic Supports, Journal of Sound and Vibration, Vol. 172, No. 4, 1994, pp. 449–458, https://doi.org/10.1006/jsvi.1994.1163.
Lin, H. P., Chang, S., Free Vibration Analysis of Multi-Span Beams with Intermediate Flexible Constraints, Journal of Sound and Vibration, Vol. 281, No. 2, 2005, pp. 155–169, https://doi.org/10.1016/j.jsv.2004.01.010.
Lin, H. Y., Tsai, Y. C., Free Vibration Analysis of a Uniform Multi-Span Beam Carrying Multiple Spring–Mass Systems, Journal of Sound and Vibration, Vol. 302, No. 3, 2007, pp. 442–456, https://doi.org/10.1016/j.jsv.2006.06.080.
Lin, H. Y., Dynamic Analysis of a Multi-Span Uniform Beam Carrying a Number of Various Concentrated Elements, Journal of Sound and Vibration, Vol. 309, No. 1, 2008, pp. 262–275, https://doi.org/10.1016/j.jsv.2007.07.015.
Kim, T., Lee, U., Dynamic Analysis of a Multi-Span Beam Subjected to a Moving Force Using the Frequency Domain Spectral Element Method, Computers and Structures, Vol. 192, 2017, pp. 181–195,https://doi.org/10.1016/j.compstruc.2017.07.028.
Han, S. M., Benaroya, H., and Wei, T., Dynamics of Transversely Vibrating Beams Using Four Engineering Theories, Journal of Sound and Vibration, Vol. 225, No. 5, 1999, pp. 935–988, https://doi.org/10.1006/jsvi.1999.2257.
Zohoor, H., Kakavand, F., Vibration of Euler–Bernoulli Beams in Large Overall Motion on Flying Support Using Finite Element Method, Scientia Iranica, Vol. 19, No. 4, 2012, pp. 1105–1116, https://doi.org/10.1016/j.scient.2012.06.019.
