PDF(757 KB)
Numerical solution method for fundamental frequency and mode shape of Euler-Bernoulli beam based on Monte Carlo method
- Zhu Lei1,2, Zhang Jianxun1,2, Sun Hailin3
Author information
+
1Beijing Advanced Innovation Center for Future Urban Design, Beijing University of Civil Engineering and Architecture, Beijing 100044, China;
2School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China;
3China Architecture Design and Research Group, Beijing 100044, China
Show less
History
+
Received |
Revised |
Published |
30 Nov 2023 |
11 Mar 2024 |
01 Jun 2024 |
Issue Date |
|
09 Jul 2024 |
|
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
This is a preview of subscription content, contact
us for subscripton.
References
[1] Rao C K, Mirza S.A note on vibrations of generally restrained beams[J].Journal of Sound & Vibration, 1989, 130(3):453-465. DOI:10.1016/0022-460X(89)90069-2.
[2] Piccardo G, Tubino F.Dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads[J].Structural Engineering & Mechanics, 2012, 44(5):681-704. DOI:10.12989/sem.2012.44.5.681.
[3] Bokaian A.Natural frequencies of beams under compressive axial loads[J].Journal of Sound and Vibration, 1988, 126(1):49-65. DOI:10.1016/0022-460X(88)90397-5.
[4] Li S, Xie L L, Bao Y Q.Analysis of beam with variable cross-section by using direct element-based equilibrium framework[J].Chinese Journal of Computational Mechanics, 2009, 26(2):226-231. DOI:10.1109/CLEOE-EQEC.2009.5194697. (in Chinese)
[5] Shahba A, Rajasekaran S.Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials[J].Applied Mathematical Modelling, 2012, 36(7):3094-3111. DOI:10.1016/j.apm.2011.09.073.
[6] Özdemir Ö, Kaya M O.Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli-Euler beam by differential transform method[J].Journal of Sound & Vibration, 2006, 289(1/2):413-420. DOI:10.1016/j.jsv.2005.01.055.
[7] Şimşek M,Kocatirkş T,Akba Ş.Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory[J].Composite Structures, 2013, 95:740-747. DOI:10.1016/j.compstruct.2012.08.036.
[8] Huang Y, Li X F.A new approach for free vibration of axially functionally graded beams with non-uniform cross-section[J].Journal of Sound & Vibration, 2010, 329(11):2291-2303. DOI:10.1016/j.jsv.2009.12.029.
[9] Jin W Y, Dennis B H, Wang B P.Improved sensitivity and reliability analysis of nonlinear Euler-Bernoulli beam using a complex variable semi-analytical method[C]//ASME International Design Engineering Technical Conferences & Computers & Information in Engineering Conferences. San Diego, CA, USA, 2010:375-380. DOI:10.1115/DETC2009-87593.
[10] Abdollahi M, Attarnejad R.Dynamic analysis of dam-reservoir-foundation interaction using finite difference technique[J].Journal of Central South University of Technology, 2012, 19(5):1399-1410. DOI:10.1007/s11771-012-1156-5.
[11] Liu J, Zhou S J, Dong M L, et al.Three-node Euler-Bernoulli beam element based on positional FEM[J].Procedia Engineering, 2012, 29:3703-3707. DOI:10.1016/j.proeng.2012.01.556.
[12] Shang H Y, Machado R D, Abdalla Filho J E. Dynamic analysis of Euler-Bernoulli beam problems using the generalized finite element method[J].Computers & structures, 2016, 173:109-122. DOI:10.1016/j.compstruc.2016.05.019.
[13] Miletic M, Arnold A.Euler-Bernoulli beam with boundary control: Stability and FEM[J].PAMM, 2011, 11(1):681-682.DOI:10.1002/pamm.201110330.
[14] Banerjee J R, Ananthapuvirajah A.Free flexural vibration of tapered beams[J]. Computers & Structures, 2019, 224:106106. DOI:10.1016/j.compstruc.2019.106106.
[15] Lee J W, Lee J Y.Free vibration analysis using the transfer-matrix method on a tapered beam[J].Computers & Structures, 2016, 164:75-82.DOI:10.1016/j.compstruc.2015.11.007.
[16] Zheng Z, Guo N S, Sun Y Z, et al.Mechanical response analysis on cement concrete pavement structure considering interlayer slip[J].Journal of Southeast University(Natural Science Edition), 2023, 53(4):655-663. DOI:10.3969/j.issn.1001-0505.2023.04.011. (in Chinese)
[17] Kang Z T, Wang Z Y, Zhou B, et al.Study on size-dependent bending behavior of axially functionally graded microbeams via nonlocal strain gradient theory[J].Journal of Southeast University(English Edition), 2019, 35(4):453-463. DOI:10.3969/j.issn.1003-7985.2019.04.008.
[18] Niu J, Wang L H, Zong Z H, et al.Damage identification method of beam type structures considering proportional damping[J]. Journal of Southeast University(Natural Science Edition), 2018, 48(3):496-505. DOI:10.3969/j.issn.1001-0505.2018.03.018. (in Chinese)
[19] Clough R W, Penzien J, Griffin D S.Dynamics of structures[M].Berkeley, CA, USA: Computers & Structures, Inc., 2003:377-382.
[20] Jonkman J, Butterfield S, Musial W, et al.Definition of a 5-MW reference wind turbine for offshore system development[R].Golden, CO, USA: National Renewable Energy Laboratory, 2009.