2021
Journal article
Open Access
The natural frequencies of masonry beams
Girardi M.
Nonlinear dynamics FOS: Computer and information sciences Finance Computer Science - Computational Engineering Computational Engineering Masonry structures and Science and Science (cs.CE) Slender masonry Mechanical Engineering Linear perturbation
The present paper aims at analytically evaluating the natural frequencies of cracked slender masonry elements. The problem is dealt with in the framework of linear perturbation, and the small oscillations of the structure are studied under loaded conditions, after the equilibrium for permanent loads has been achieved. A masonry beam element made of no-tension (masonry-like) material is considered, and some explicit expressions of the beam's fundamental frequency as a function of the external loads and the amplitude of imposed deformations are derived. The analytical results are validated via finite-element analysis.
Source: Archive of applied mechanics (1991) (2021): 2369–2379. doi:10.1007/s00419-021-01887-4
Publisher: Springer, Berlin , Germania
[1] H. Abdel-Jaber and B. Glisic. Monitoring of prestressing forces in prestressed concrete structures { An overview. Structural Control and Health Monitoring 2019; 26:e2374.
[2] Agarwali S, Chaudhuri SR. Damage detection in large structures using mode shapes and its derivatives. International Journal of Research in Engineering and Technology 2015; 4, Special Issue 13.
[3] R. Barsotti and S. Bennati. A simple and e ective nonlinear elastic one-dimensional model for the structural analysis of masonry arches. Meccanica 2018; 53: 1899-1915.
[4] E.B Becker, G.F. Carey, J.T. Oden. Finite Elements: An Introduction Prentice{Hall, Inc., New Jersey, 1981.
[5] Bui TT, Limam A, Bui QB. Characterisation of vibration and damage in masonry structures: experimental and numerical analysis. European Journal of Environmental and Civil Engineering 2014; 18(10), 1118{1129.
[6] R.W. Clough, J. Penzien. Dynamics of Structures Mc{Graw Hill, Inc., 1975.
[7] A. De Falco and M. Lucchesi. Stability of columns with no tension strenght and bounded compressive strenght and deformability. part i: large eccentricity. International Journal of Solids and Structures 2002; 39:6191{ 6210.
[8] A. De Falco and M. Lucchesi. No tension beam-columns with bounded compressive strength and deformability undergoing eccentric vertical loads. International Journal of Mechanical Sciences 2007; 49(1): 54-74.
[9] G. Del Piero. Constitutive equation and compatibility of the external loads for linear elastic masonry{like materials. Meccanica 1989; 24: 150-162.
[10] M. Girardi and M. Lucchesi. Free exural vibrations of masonry beam-columns. Journal of Mechanics of Materials and Structures, 2010; 5(1): 143-159.
[11] M. Girardi. On the dynamic behaviour of masonry beam-columns: An analytical approach. European Journal of Mechanics, A/Solids, 2014; 45: 174-184.
[12] M. Girardi, C. Padovani and D. Pellegrini. Modal analysis of masonry structures. Mathematics and Mechanics of Solids, 2019; 24(3):616{636.
[13] J.E. Mottershead and M.I. Friswell. Model updating in structural dynamics: A survey. Journal of Sound and Vibration, 1993; 167 (2): 347{375.
[14] B. Peeters and G. De Roeck. One-year monitoring of the Z24-bridge: Environmental e ects versus damage events. Earthquake Engineering and Structural Dynamics, 2001; 30 (2): 149{171.
[15] M. Lucchesi and B.L. Pintucchi. A numerical model for non-linear dynamic analysis of masonry slender structures. European Journal of Mechanics A/Solids 2007; 26: 88-105.
[16] M. Lucchesi, C. Padovani, G. Pasquinelli, N. Zani. Masonry constructions: mechanical models and numerical applications Lecture Notes in Applied and Computational Mechanics, Vol. 39, Springer{Verlag, 2008.
[17] E. Hamed, Y. Frostig. Free vibrations of cracked prestressed concrete beams. Engineering Structures 2004; 26: 1611{1621.
[18] M.G. Masciotta, D. Pellegrini, D. Brigante, A. Barontini, P.B. Lourenco, M. Girardi, M., C. Padovani, G. Fabbrocino, G. (2020). Dynamic characterization of progressively damaged segmental masonry arches with one settled support: experimental and numerical analyses. Frattura ed Integrita Strutturale 2020; 14(51), 423-441.
[19] Noble D, Nogal M, O'Connor AJ, Pakrashi V. The e ect of post-tensioning force magnitude and eccentricity on the natural bending frequency of cracked post-tensioned concrete beams, Journal of Physics. Conference Series 628, 2015. IOPscience.
[20] D. Pellegrini, M. Girardi, M. Lourenco, P.B. Masciotta, M.G., Mendes N., Padovani C., Ramos L.F. Modal analysis of historical masonry structures: Linear perturbation and software benchmarking. Construction and Building Materials, 2018; 189,1232-1250.
[21] Pineda P. Collapse and upgrading mechanisms associated to the structural materials of a deteriorated masonry tower. Nonlinear assessment under di erent damage and loading levels. Engineering Failure Analysis 2016; 63:72{93, Elsevier.
[22] B.L. Pintucchi. Vibrazioni trasversali di elementi monodimensionali non resistenti a trazione in direzione longitudinale, Ph.D. thesis, Universita degli Studi di Firenze, 2001.
[23] Ramos LF, De Roeck G, Lourenco PB, Campos{Costa A. Damage identi cation on arched masonry structures using ambient and random impact vibrations. Engineering Structures 2010; 32: 146{162, Elsevier.
[24] Salawu OS. Detection of structural damage through changes in frequency: a review. Engineering Structures 1997; 19(9): 718{723, Elsevier.
[25] N. Zani. A constitutive equation and a closed-form solution for no-tension beams with limited compressive strength. European Journal of Mechanics A/Solids 23, 2004; 23: 467-484. Istituto di Scienza e Tecnologie dell'Informazione "A. Faedo", CNR Via G. Moruzzi 1, Pisa, 56124, Italy Email address: Maria.Girardi@isti.cnr.it
[2] Agarwali S, Chaudhuri SR. Damage detection in large structures using mode shapes and its derivatives. International Journal of Research in Engineering and Technology 2015; 4, Special Issue 13.
[3] R. Barsotti and S. Bennati. A simple and e ective nonlinear elastic one-dimensional model for the structural analysis of masonry arches. Meccanica 2018; 53: 1899-1915.
[4] E.B Becker, G.F. Carey, J.T. Oden. Finite Elements: An Introduction Prentice{Hall, Inc., New Jersey, 1981.
[5] Bui TT, Limam A, Bui QB. Characterisation of vibration and damage in masonry structures: experimental and numerical analysis. European Journal of Environmental and Civil Engineering 2014; 18(10), 1118{1129.
[6] R.W. Clough, J. Penzien. Dynamics of Structures Mc{Graw Hill, Inc., 1975.
[7] A. De Falco and M. Lucchesi. Stability of columns with no tension strenght and bounded compressive strenght and deformability. part i: large eccentricity. International Journal of Solids and Structures 2002; 39:6191{ 6210.
[8] A. De Falco and M. Lucchesi. No tension beam-columns with bounded compressive strength and deformability undergoing eccentric vertical loads. International Journal of Mechanical Sciences 2007; 49(1): 54-74.
[9] G. Del Piero. Constitutive equation and compatibility of the external loads for linear elastic masonry{like materials. Meccanica 1989; 24: 150-162.
[10] M. Girardi and M. Lucchesi. Free exural vibrations of masonry beam-columns. Journal of Mechanics of Materials and Structures, 2010; 5(1): 143-159.
[11] M. Girardi. On the dynamic behaviour of masonry beam-columns: An analytical approach. European Journal of Mechanics, A/Solids, 2014; 45: 174-184.
[12] M. Girardi, C. Padovani and D. Pellegrini. Modal analysis of masonry structures. Mathematics and Mechanics of Solids, 2019; 24(3):616{636.
[13] J.E. Mottershead and M.I. Friswell. Model updating in structural dynamics: A survey. Journal of Sound and Vibration, 1993; 167 (2): 347{375.
[14] B. Peeters and G. De Roeck. One-year monitoring of the Z24-bridge: Environmental e ects versus damage events. Earthquake Engineering and Structural Dynamics, 2001; 30 (2): 149{171.
[15] M. Lucchesi and B.L. Pintucchi. A numerical model for non-linear dynamic analysis of masonry slender structures. European Journal of Mechanics A/Solids 2007; 26: 88-105.
[16] M. Lucchesi, C. Padovani, G. Pasquinelli, N. Zani. Masonry constructions: mechanical models and numerical applications Lecture Notes in Applied and Computational Mechanics, Vol. 39, Springer{Verlag, 2008.
[17] E. Hamed, Y. Frostig. Free vibrations of cracked prestressed concrete beams. Engineering Structures 2004; 26: 1611{1621.
[18] M.G. Masciotta, D. Pellegrini, D. Brigante, A. Barontini, P.B. Lourenco, M. Girardi, M., C. Padovani, G. Fabbrocino, G. (2020). Dynamic characterization of progressively damaged segmental masonry arches with one settled support: experimental and numerical analyses. Frattura ed Integrita Strutturale 2020; 14(51), 423-441.
[19] Noble D, Nogal M, O'Connor AJ, Pakrashi V. The e ect of post-tensioning force magnitude and eccentricity on the natural bending frequency of cracked post-tensioned concrete beams, Journal of Physics. Conference Series 628, 2015. IOPscience.
[20] D. Pellegrini, M. Girardi, M. Lourenco, P.B. Masciotta, M.G., Mendes N., Padovani C., Ramos L.F. Modal analysis of historical masonry structures: Linear perturbation and software benchmarking. Construction and Building Materials, 2018; 189,1232-1250.
[21] Pineda P. Collapse and upgrading mechanisms associated to the structural materials of a deteriorated masonry tower. Nonlinear assessment under di erent damage and loading levels. Engineering Failure Analysis 2016; 63:72{93, Elsevier.
[22] B.L. Pintucchi. Vibrazioni trasversali di elementi monodimensionali non resistenti a trazione in direzione longitudinale, Ph.D. thesis, Universita degli Studi di Firenze, 2001.
[23] Ramos LF, De Roeck G, Lourenco PB, Campos{Costa A. Damage identi cation on arched masonry structures using ambient and random impact vibrations. Engineering Structures 2010; 32: 146{162, Elsevier.
[24] Salawu OS. Detection of structural damage through changes in frequency: a review. Engineering Structures 1997; 19(9): 718{723, Elsevier.
[25] N. Zani. A constitutive equation and a closed-form solution for no-tension beams with limited compressive strength. European Journal of Mechanics A/Solids 23, 2004; 23: 467-484. Istituto di Scienza e Tecnologie dell'Informazione "A. Faedo", CNR Via G. Moruzzi 1, Pisa, 56124, Italy Email address: Maria.Girardi@isti.cnr.it
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BibTeX entry
@article{oai:it.cnr:prodotti:446155,
title = {The natural frequencies of masonry beams},
author = {Girardi M.},
publisher = {Springer, Berlin , Germania},
doi = {10.1007/s00419-021-01887-4 and 10.48550/arxiv.2012.05704},
journal = {Archive of applied mechanics (1991)},
pages = {2369–2379},
year = {2021}
}CNR authorsLaboratories
0000-0002-7358-5607CNR ExploRA
ISTI Repository
DOI
ISTI Repository
DOI
10.1007/s00419-021-01887-4
10.48550/arxiv.2012.05704
arXiv.org e-Print Archive
Archive of Applied Mechanics
link.springer.com