[en] Transverse vibrations of beams are an interesting topic for numerous engineering fields. The equations of motion develop under various assumptions and associate a frequency equation. This paper expresses the frequency equation for two specific models, using the Timoshenko beam theory. The first model is a typical cantilever beam with an additional mass attached to the free end. The second model considers a beam partially clamped at the base and with an elastic connection of the additional mass to the free end. The relevance of the used theory is discussed and the importance of each term of the equation is studied. These models find applications in unreinforced masonry. They are indeed fitted to identify, from white noise tests, equivalent mechanical properties of unreinforced load-bearing clay masonry walls including soundproofing devices in the perspective of modelling these elements with a macro-scale approach. Discrepancies with respect to current standards are underscored.
Disciplines :
Civil engineering
Author, co-author :
Mordant, Christophe
Degée, Hervé ; Université de Liège - ULiège > Département ArGEnCo > Département Argenco : Secteur A&U
Denoël, Vincent ; Université de Liège - ULiège > Département ArGEnCo > Analyse sous actions aléatoires en génie civil
Language :
English
Title :
Identification of equivalent mechanical properties for unreinforced masonry walls
Publication date :
2017
Journal title :
International Journal of Masonry Research and Innovation
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Ansari, M., Jalili, N. and Esmailzadeh, E. (2011) 'Exact frequency analysis of a rotating cantilever beam with tip mass subjected to torsional-bending vibrations', Journal of Vibration and Acoustics, Vol. 133, No. 4, p.041003.
Braga, F. and Liberatore D. (1990) 'A finite element for the analysis of the response of masonry buildings', Proceedings of 5th North American masonry conference. University of Illinois at Urbana-Champaign, 3-6 June.
Bruch Jr, J.C. and Mitchell, T.P. (1987) 'Vibrations of a mass-loaded clamped-free Timoshenko beam', Journal of Sound and Vibration, Vol. 114, No. 2, pp.341-345.
Calio, I. and Greco, A. (2012) 'Free vibrations of Timoshenko beam-columns on Pasternak foundations', Journal of Vibration and Control, Vol. 19, No. 5, pp.686-696. doi:10.1177/ 1077546311433609.
da Porto, F., Grendene, M. and Modena, C. (2009) 'Estimation of load reduction factors for clay masonry walls', Earthquake Engineering & Structural Dynamics, Vol. 38, No. 10, pp.1155-1174. doi:10.1002/eqe.887.
Esmailzadeh, E. and Ohadi, A.R. (2000) 'Vibration and stability analysis of non-uniform Timoshenko beams under axial and distributed tangential loads', Journal of Sound and Vibration, Vol. 236, No. 3, pp.443-456. doi:10.1006/jsvi.2000.2999. http://linkinghub.elsevier.com/retrieve/pii/S0022460X00929997
Farchaly, S. and Shebl, M. (1995) 'Exact frequency and mode shape formulae for studying vibration and stability of Timoshenko beam system', Journal of Sound and Vibration, Vol. 180, pp.205-227. http://www.sciencedirect.com/science/article/pii/S0022460X85700752
Gregoire, Y. (2007) 'Compressive strength of masonry according to eurocode 6: a contribution to the study of the influence of shape factors', Masonry International, Vol. 20, No. 2, p.69.
Han, S., Benaroya, H. and Wei, T. (1999) 'Dynamics of transversely vibrating beams using four engineering theories', Journal of Sound and Vibration, Vol. 225, pp.935-988. http://www.sciencedirect.com/science/article/pii/S0022460X99922575
Hernández-Urrea, J. and Dario Aristizábal-Ochoa, J. (2008) 'Static and dynamic stability of an elastically restrained Beck column with an attached end mass', Journal of Sound and Vibration, Vol. 312, Nos. 4-5, pp.789-800. doi:10.1016/j.jsv.2007.11.014. http://linkinghub.elsevier.com/retrieve/pii/S0022460X0700908X
Lagomarsino, S., Penna, A., Galasco, A. and Cattari, S. (2013) 'Tremuri program: an equivalent frame model for the nonlinear seismic analysis of masonry buildings', Engineering Structures, Vol. 56, pp.1787-1799.
Lee, T. and Lakes, R. (1997) 'Anisotropic polyurethane foam with poisson'sratio greater than 1', Journal of Materials Science, Vol. 32, No. 9, pp.2397-2401.
Low, K. (1999) 'Comparisons of experimental and numerical frequencies for classical beams carrying a mass in-span', International Journal of Mechanical Sciences, Vol. 41, No. 12, pp.1515-1531. doi:10.1016/S0020-7403(98)00103-9. http://linkinghub.elsevier.com/retrieve/pii/S0020740398001039
Low, K.H. (2000) 'A modified Dunkerley formula for eigenfrequencies of beams carrying concentrated masses', International Journal of Mechanical Sciences, Vol. 42, pp.1287-1305.
Li, X. (2013) 'Free vibration of axially loaded shear beams carrying elastically restrained lumped-tip masses via asymptotic timoshenko beam theory', Journal of Engineering Mechanics, Vol. 139, No. 4, pp.418-428. doi:10.1061/(ASCE)EM.1943-7889.0000403.
Li, X-F., Kang, Y-A. and Wu, J-X. (2013a) 'Exact frequency equations of free vibration of exponentially functionally graded beams', Applied Acoustics, Vol. 74, No. 3, pp.413-420. doi:10.1016/j.apacoust.2012.08.003. http://linkinghub.elsevier.com/retrieve/pii/ S0003682X12002538
Kappos, A.J., Penelis, G.G. and Drakopoulos, C.G. (2002) 'Evaluation of simplified models for lateral load analysis of unreinforced masonry buildings', Journal of structural Engineering, Vol. 128, No. 7, pp.890-897.
Khaji, N., Shafiei, M. and Jalalpour, M. (2009) 'Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions', International Journal of Mechanical Sciences, Vol. 51, Nos. 9-10, pp.667-681. doi:10.1016/j.ijmecsci.2009.07.004. http://linkinghub.elsevier.com/retrieve/pii/S0020740309001398
Majkut, L. (2009) 'Free and forced vibrations of timoshenko beams described by single difference equation', Journal of Theoretical and Applied Mechanics, Vol. 47, No. 1, pp.193-210. http://yadda.icm.edu.pl/baztech/element/bwmeta1.element.baztech-article-BWM4-0019-0012
Mordant, C. (2016) Unreinforced Clay Masonry Structures: Advanced Characterisation of the Seismic Behaviour Including Acoustic Issues, Doctoral Dissertation, University of Liège and Hasselt Uniersity.
Mordant, C., Dietz, M.S., Taylor, C.A., Plumier, A. and Degée, H. (2014) 'Seismic behavior of thin-bed layered unreinforced clay masonry shear walls including soundproofing elements', Seismic Evaluation and Rehabilitation of Structures, Springer, Berlin, pp.77-93.
Naguleswaran, S. (2003) 'Vibration and stability of an Euler-Bernoulli beam with up to three-step changes in cross-section and in axial force', International Journal of Mechanical Sciences, Vol. 45, No. 9, pp.1563-1579. doi:10.1016/j.ijmecsci.2003.09.001. http://linkinghub.elsevier.com/retrieve/pii/S0020740303001577
Oguamanam, D. (2003) 'Free vibration of beams with finite mass rigid tip load and flexural-torsional coupling', International Journal of Mechanical Sciences, Vol. 45, Nos. 6-7, pp.963-979. doi:10.1016/j.ijmecsci.2003.09.014.
Penna, A., Lagomarsino, S. and Galasco, A. (2013) 'A nonlinear macroelement model for the seismic analysis of masonry buildings', Earthquake Engineering & Structural Dynamics, Vol. 43, No. 2, pp.159-179. doi:10.1002/eqe.2335. http://doi.wiley.com/10.1002/eqe.2335
Salarieh, H. and Ghorashi, M. (2006) 'Free vibration of Timoshenko beam with finite mass rigid tip load and flexural-torsional coupling', International Journal of Mechanical Sciences, Vol. 48, No. 7, pp.763-779. doi:10.1016/j.ijmecsci.2006.01.008. http://linkinghub.elsevier.com/retrieve/pii/S0020740306000269
Strutt, J.W. (1877) The theory of sound, London, Macmillan and co, p.370.
Timoshenko, S.P. (1921) 'On the correction for shear of the differential equation for transverse vibrations of bars of uniform cross-section', Philosophical Magazine, Series 6, Vol. 41, pp.744-746.
Timoshenko, S.P. (1922) 'X. On the transverse vibrations of bars of uniform cross-section', The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 43, No. 253, pp.125-131.
Timoshenko, S.P. and Goodier, J.N. (1987) Theory of Elasticity, 3rd ed., McGraw-Hill Book Company, New-York.
Zhang, H., Kang, Y. and Li, X. (2013) 'Stability and vibration analysis of axially-loaded shear beam-columns carrying elastically restrained mass', Applied Mathematical Modelling, Vol. 37, Nos. 16-17, pp.8237-8250. doi:10.1016/j.apm.2013.03.050. http://linkinghub.elsevier.com/retrieve/pii/S0307904X13002242
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
