This paper presents a new numerical tool for evaluating the vibration frequencies and mode shapes of masonry buildings in the presence of cracks. The algorithm has been implemented within the NOSA-ITACA code, which models masonry as a nonlinear elastic material with zero tensile strength. Some case studies are reported, and the differences between linear and nonlinear behaviour are highlighted.
DimarogonasAD.Vibration of cracked structures: a state of art review. Eng Fract Mech1996; 55(5): 831–857.
2.
SalawuOS.Detection of structural damage through changes in frequency: a review. Eng Struct1997; 19(9): 718–723.
3.
Dos SantosFLMPeetersBVan der AuweraerHet al. Vibration-based damage detection for a composite helicopter main rotor blade. Case Stud Mech Syst Signal Process2016; 3: 22–27.
4.
AgarwaliSChaudhuriSR.Damage detection in large structures using mode shapes and its derivatives. Int J Res Eng Technol2015; 4(Special Issue 13): 80–87.
5.
WahabMMA.Effect of modal curvatures on damage detection using model updating. Mech Syst Signal Process2001; 15(2): 439–445.
6.
AzzaraRMZaccarelliLMorelliAet al. Seismic monitoring of the Asinelli and Garisenda medieval towers in Bologna (Italy), an instrumental contribution to the engineering modeling direct to their protection. In: Proceedings of the Second International Conference on Protection of Historical Constructions, 2014.
7.
GentileCSaisiACabboiA. Dynamic monitoring of a masonry tower. In: Proceedings of the 8th International Conference on Structural Analysis of Historical Constructions, SAHC 2012, 2012.
8.
RamosLFMarquesLLourenoPBet al. Monitoring historical masonry structures with operational modal analysis: two case studies. Mech Syst Signal Process2010; 24: 1291–1305.
9.
AbbiatiGCeravoloRSuraceC.Time-dependent estimators for on-line monitoring of full-scale structures under ambient excitation. Mech Syst Signal Process2015; 60–61: 166–181.
10.
RamosLFDe RoeckGLourenoPBet al. Damage identification on arched masonry structures using ambient and random impact vibrations. Eng Struct2010; 32: 146–162.
11.
SaisiAGentileCGuidobaldiM.Post-earthquake continuous dynamic monitoring of the Gabbia Tower in Mantua, Italy. Constr Build Mater2015; 48: 1273–1285.
RenWXDe RoeckG.Structural damage identification using modal data. II: Test verification. J Struct Eng2002; 128(1): 96–104.
14.
JayanthanMSrinivasV.Structural damage identification based on finite element model updating. J Mech Eng Autom2015; 5(3B): 59–63.
15.
PinedaP.Collapse and upgrading mechanisms associated to the structural materials of a deteriorated masonry tower. Nonlinear assessment under different damage and loading levels. Eng Fail Anal2016; 63: 72–93.
16.
BuiTTLimamABuiQB.Characterisation of vibration and damage in masonry structures: experimental and numerical analysis. Eur J Environ Civil Eng2014; 18(10): 1118–1129.
17.
CaktiESaygiliOLemosJVet al. A parametric study of the earthquake behaviour of masonry minarets. In: Proceedings of the Tenth US National Conference on Earthquake Engineering Frontiers of Earthquake Engineering, 10NCEE, 2014.
18.
GirardiMLucchesiM.Free flexural vibrations of masonry beam-columns. J Mech Mater Struct2010; 5(1): 143–159.
19.
Del PieroG. Constitutive equations and compatibility of external loads for linear elastic masonry-like materials. Meccanica1989; 24: 150–162.
20.
Di PasqualeS. New trends in the analysis of masonry structures. Meccanica1992; 27: 173–184.
21.
LucchesiMPadovaniCPasquinelliGet al. Masonry constructions: mechanical models and numerical applications (Lecture Notes in Applied and Computational Mechanics, vol. 39). Berlin: Springer-Verlag, 2008.
22.
BinanteVGirardiMPadovaniCet al. NOSA-ITACA 1.1, www.nosaitaca.it/software (2017, accessed 15 March 2017).
23.
MMS Lab. Mechanics of Materials and Structures Laboratory, http://www.nosaitaca.it (2017, accessed 15 March 2017).
24.
HarakSSSharmaSCHarshaSP.Modal analysis of prestressed draft pad of freight wagons using finite element method. J Mod Transport2015; 23(1): 43–49.
25.
NobleDNogalMO’ConnorAJet al. The effect of post-tensioning force magnitude and eccentricity on the natural bending frequency of cracked post-tensioned concrete beams. J Phys Conf Ser2015; 628(1): 012047.
26.
PorcelliMBinanteVGirardiMet al. A solution procedure for constrained eigenvalue problems and its application within the structural finite-element code NOSA-ITACA. Calcolo2015; 52(2): 167–186.
27.
AzzaraRMDe RoeckGGirardiMet al. Assessment of the dynamic behaviour of an ancient masonry tower in Lucca via ambient vibrations. In: Van BalenKVerstryngeE (eds) Structural analysis of historical constructions – anamnesis, diagnosis, therapy, controlsBoca Raton: CRC Press, 2016, 669–675.
28.
BrinckerRVenturaC.Introduction to operational modal analysis. Chichester: John Wiley & Sons, 2015.
29.
PadovaniCSilhavyM.On the derivative of the stress–strain relation in a no-tension material. Math Mech Solids2017; 52(2): 1606–1618.
30.
LucchesiMPadovaniCPasquinelliGet al. Static analysis of masonry vaults, constitutive model and numerical analysis. J Mech Mater Struct2007; 2(2): 221–224.
31.
BernardeschiKPadovaniCPasquinelliG.Numerical modelling of the structural behaviour of Buti’s bell tower. J Cult Heritage2004; 5(4): 371–378.
BatheKJWilsonEL.Numerical methods in finite element analysis. Upper Saddle River: Prentice-Hall, 1976.
34.
CloughRWPenzienJ.Dynamics of structures. New York: McGraw–Hill Inc., 1975.
35.
NayfehAH.Nonlinear interactions. New York: John Wiley & Sons Inc., 2000.
36.
GirardiMPadovaniCPellegriniD.The NOSA-ITACA code for the safety assessment of ancient constructions: a case study in Livorno. Adv Eng Software2015: 89; 64–76.
37.
KarnovskyIA.Theory of arched structures: strength, stability, vibration. New York: Springer, 2012.
38.
GurtinME. The linear theory of elasticity. In: TruesdellC (ed.) Encyclopedia of physics, Vol. VIa/2, mechanics of solids II. Berlin: Springer-Verlag, 1972.
