Please use this identifier to cite or link to this item: `https://hdl.handle.net/11147/2505`
 Title: Coupled out of plane vibrations of spiral beams for micro-scale applications Authors: Karami, M. A.Yardımoğlu, BülentInman, Daniel J. Keywords: Equations of motionEnergy harvestingFunction evaluationRayleigh's methodFundamental frequencies Publisher: Academic Press Inc. Source: Karami, M. A., Yardımoğlu, B., and Inman, D. J.(2010). Coupled out of plane vibrations of spiral beams for micro-scale applications. Journal of Sound and Vibration, 329(26), 5584-5599. doi:10.1016/j.jsv.2010.07.013 Abstract: An analytical method is proposed to calculate the natural frequencies and the corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equations and the boundary conditions are derived using Hamilton's principle. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the derivative of the radius terms have negligible effect on structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joined together to approximate the slow change of radius along the spiral. The equations of motion are formulated in non-dimensional form and the effect of all the key parameters on natural frequencies is presented. Non-dimensional curves are used to summarize the results for clarity. We also solve the governing equations using Rayleigh's approximate method. The fundamental frequency results of the exact and Rayleigh's method are in close agreement. This to some extent verifies the exact solutions. The results show that the vibration of spirals is mostly torsional which complicates using the spiral beam as a host for a sensor or energy harvesting device. URI: http://doi.org/10.1016/j.jsv.2010.07.013http://hdl.handle.net/11147/2505 ISSN: 0022-460X1095-8568 Appears in Collections: Mechanical Engineering / Makina MühendisliğiScopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications CollectionWoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

###### Files in This Item:
File Description SizeFormat

CORE Recommender

#### SCOPUSTM Citations

29
checked on Sep 13, 2024

#### WEB OF SCIENCETM Citations

26
checked on Sep 14, 2024

#### Page view(s)

174
checked on Sep 16, 2024

264
checked on Sep 16, 2024