Optimal design for eigen-frequencies of a longitudinal bar using Pontryagin's maximum principle considering the influence of concentrated mass
Abstract
Keywords
Full Text:
PDFReferences
A. DasGupta and P. Hagedorn. Vibrations and waves in continuous mechanical systems. Wiley, New York, (2007). doi:10.1002/9780470518434.
Y. Yi, W. Seemann, R. Gausmann, and J. Zhong. Development and analysis of a longitudinal and torsional type ultrasonic motor with two stators. Ultrasonics, 43, (8), (2005), pp. 629–634. doi:10.1016/j.ultras.2005.03.007.
V. K. Astashev and V. I. Babitsky. Ultrasonic processes and machines: dynamics, control and applications. Springer Science & Business Media, (2007). doi:10.1007/978-3-540-72061-4.
H. Al-Budairi, M. Lucas, and P. Harkness. A design approach for longitudinaltorsional ultrasonic transducers. Sensors and Actuators A: Physical, 198, (2013), pp. 99–106. doi:10.1016/j.sna.2013.04.024.
Y. Kubojima and S. Sonoda. Measuring Youngs modulus of a wooden bar using longitudinal vibration without measuring its weight. European Journal of Wood and Wood Products, 73, (3), (2015), pp. 399–401. doi:10.1007/s00107-015-0884-2.
C. Szymczak. Optimal design of thin walled I beams for extreme natural frequency of torsional vibrations. Journal of Sound and Vibration, 86, (2), (1983), pp. 235–241. doi:10.1016/0022-460x(83)90751-4.
C. Szymczak. Optimal design of thin-walled I beams for a given natural frequency of torsional vibrations. Journal of Sound and Vibration, 97, (1), (1984), pp. 137–144. doi:10.1016/0022-460x(84)90474-7.
T. M. Atanackovic and S. S. Simic. On the optimal shape of a Pfl¨ uger column. European Journal of Mechanics-A/Solids, 18, (5), (1999), pp. 903–913. doi:10.1016/s0997-7538(99)00128-x.
V. B. Glavardanov and T. M. Atanackovic. Optimal shape of a twisted and compressed rod. European Journal of Mechanics-A/Solids, 20, (5), (2001), pp. 795–809. doi:10.1016/s0997-7538(01)01165-2.
T. M. Atanackovic and D. J. Braun. The strongest rotating rod. International Journal of Non-Linear Mechanics, 40, (5), (2005), pp. 747–754. doi:10.1016/j.ijnonlinmec.2004.09.002.
T. M. Atanackovic and B. N. Novakovic. Optimal shape of an elastic column on elastic foundation. European Journal of Mechanics-A/Solids, 25, (1), (2006), pp. 154–165. doi:10.1016/j.euromechsol.2005.06.008.
T. M. Atanackovic. Optimal shape of a strongest inverted column. Journal of Computational and Applied Mathematics, 203, (1), (2007), pp. 209–218. doi:10.1016/j.cam.2006.03.019.
T. M. Atanackovic. Optimal shape of a rotating rod with unsymmetrical boundary conditions. Journal of Applied Mechanics, 74, (6), (2007), pp. 1234–1238. doi:10.1115/1.2744041.
Z. D. Jelicic and T. M. Atanackovic. Optimal shape of a vertical rotating column. International Journal of Non-Linear Mechanics, 42, (1), (2007), pp. 172–179. doi:10.1016/j.ijnonlinmec.2006.10.020.
D. J. Braun. On the optimal shape of compressed rotating rod with shear and extensibility. International Journal of Non-Linear Mechanics, 43, (2), (2008), pp. 131–139. doi:10.1016/j.ijnonlinmec.2007.11.001.
T. M. Atanackovic, B. B. Jakovljevic, and M. R. Petkovic. On the optimal shape of a column with partial elastic foundation. European Journal of Mechanics-A/Solids, 29, (2), (2010), pp. 283–289. doi:10.1016/j.euromechsol.2009.08.003.
V. B. Glavardanov, D. T. Spasic, and T. M. Atanackovic. Stability and optimal shape of Pfluger micro/nano beam. International Journal of Solids and Structures, 49, (18), (2012), pp. 2559–2567. doi:10.1016/j.ijsolstr.2012.05.016.
T. M. Atanackovic, B. N. Novakovic, and Z. Vrcelj. Shape optimization against buckling of micro-and nano-rods. Archive of Applied Mechanics, 82, (10-11), (2012), pp. 1303–1311. doi:10.1007/s00419-012-0661-1.
M.-Q. Le, D.-T. Tran, and H.-L. Bui. Optimal design of a torsional shaft system using Pontryagins maximum principle. Meccanica, 47, (5), (2012), pp. 1197–1207. doi:10.1007/s11012-011-9504-3.
Refbacks
- There are currently no refbacks.
Editorial Office of Vietnam Journal of Mechanics 3rd Floor, A16 Building, 18B Hoang Quoc Viet Street, Cau Giay District, Hanoi, Vietnam Tel: (+84) 24 3791 7103 Email: vjmech@vjs.ac.vn |