nach oben

Meccanica

Erschienen in:

27.01.2021 | Modelling and analysis of mechanical systems dynamics

An interval framework for uncertain frequency response of multi-cracked beams with application to vibration reduction via tuned mass dampers

verfasst von: Roberta Santoro, Giuseppe Failla

Erschienen in: Meccanica | Ausgabe 4/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The paper addresses the frequency response of beams in presence of open cracks with interval parameters. On adopting the standard Euler–Bernoulli beam theory, every crack is modelled as a linearly-elastic rotational spring whose stiffness and position are treated as uncertain-but-bounded parameters. A two-step method is proposed to calculate the bounds of all response variables. First, the sensitivity functions of the response are calculated as every uncertain parameter varies within the respective interval. Next, the bounds of the response are computed by either a sensitivity-based method or a global optimization technique, the former if the response is monotonic with respect to all uncertain parameters and the latter if the response is non-monotonic with respect to even one parameter only. The method relies on analytical forms for all response variables and the associated sensitivity functions. The applications focus on the frequency response of multi-cracked beams equipped with tuned mass dampers, showing potential and accuracy of the method.

Vorheriger Artikel Kinematics of the motorcar body side deformation process during front-to-side vehicle collision and the emergence of a hazard to car occupants

Nächster Artikel Kinematic analysis of a rolling tensegrity structure with spatially curved members

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

Cacciola P, Muscolino G (2002) Dynamic response of a rectangular beam with a known non-propagating crack of certain or uncertain depth. Comput Struct 80(27):2387–2396. https://doi.org/10.1016/S0045-7949(02)00255-9CrossRef

Muscolino G, Santoro R (2019) Dynamics of multiple cracked prismatic beams with uncertain-but-bounded depths under deterministic and stochastic loads. J Sound Vib 443:717–731. https://doi.org/10.1016/j.jsv.2018.11.029CrossRef

Santoro R, Muscolino G (2019) Dynamics of beams with uncertain crack depth: stochastic versus interval analysis. Meccanica 54(9):1433–1449. https://doi.org/10.1007/s11012-019-01024-0MathSciNetCrossRef

Soize C (2013) Stochastic modeling of uncertainties in computational structural dynamics-recent theoretical advances. J Sound Vib 332(10):2379–2395. https://doi.org/10.1016/j.jsv.2011.10.010CrossRef

Soize C, Capiez-Lernout E, Durand J-F, Fernandez C, Gagliardini L (2008) Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation. Comput Methods Appl Mech Eng 198(1):150–163. https://doi.org/10.1016/j.cma.2008.04.007CrossRefMATH

Beck JL, Katafygiotis LS (1998) Updating models and their uncertainties. I: Bayesian statistical framework. J Eng Mech 124(4):455–461. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:4(455)CrossRef

Spall JC (2003) Introduction to stochastic search and optimization. Wiley, HobokenCrossRef

Soize C (2001) Maximum entropy approach for modeling random uncertainties in transient elastodynamics. J Acoust Soc Am 109(5):1979–1996. https://doi.org/10.1121/1.1360716CrossRef

Soize C (2005) Random matrix theory for modeling uncertainties in computational mechanics. Comput Methods Appl Mech Eng 194(12–16):1333–1366. https://doi.org/10.1016/j.cma.2004.06.038MathSciNetCrossRefMATH

10.

Soize C (2008) Construction of probability distributions in high dimension using the maximum entropy principle: applications to stochastic processes, random fields and random matrices. Int J Numer Methods Eng 76(10):1583–1611. https://doi.org/10.1002/nme.2385MathSciNetCrossRefMATH

11.

Soize C, Ghanem R (2004) Physical systems with random uncertainties: chaos representation with arbitrary probability measure. SIAM J Sci Comput 26(2):395–410. https://doi.org/10.1137/S1064827503424505MathSciNetCrossRefMATH

12.

Soize C (2009) Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions. Int J Numer Methods Eng 81(8):939–970. https://doi.org/10.1002/nme.2712MathSciNetCrossRefMATH

13.

Carlin BP, Louis TA (2009) Bayesian methods for data analysis, 3rd edn. CRC Press, Boca RatonMATH

14.

Savvas D, Papaioannou I, Stefanou G (2020) Bayesian identification and model comparison for random property fields derived from material microstructure. Comput Methods Appl Mech Eng 365:113026. https://doi.org/10.1016/j.cma.2020.113026MathSciNetCrossRefMATH

15.

Soize C (2011) A computational inverse method for identification of non-Gaussian random fields using the Bayesian approach in very high dimension. Comput Methods Appl Mech Eng 200(45–46):3083–3099. https://doi.org/10.1016/j.cma.2011.07.005MathSciNetCrossRefMATH

16.

Ghanem R, Spanos PD (1991) Stochastic finite elements: a spectral approach. Springer-Verlag, BerlinCrossRef

17.

Stefanou G, Papadrakakis M (2007) Assessment of spectral representation and Karhunen–Loève expansion methods for the simulation of Gaussian stochastic fields. Comput Methods Appl Mech Eng 196(21–24):2465–2477. https://doi.org/10.1016/j.cma.2007.01.009CrossRefMATH

18.

Stefanou G (2009) The stochastic finite element method: past, present and future. Comput Methods Appl Mech Eng 198(9–12):1031–1051. https://doi.org/10.1016/j.cma.2008.11.007CrossRefMATH

19.

Stefanou G, Savvas D, Papadrakakis M (2017) Stochastic finite element analysis of composite structures based on mesoscale random fields of material properties. Comput Methods Appl Mech Eng 326:319–337. https://doi.org/10.1016/j.cma.2017.08.002MathSciNetCrossRefMATH

20.

Soize C (2015) Polynomial Chaos expansion of a multimodal random vector SIAM/ASA. J Uncertain Quantif 3(1):34–60. https://doi.org/10.1137/140968495MathSciNetCrossRefMATH

21.

Kleiber M, Hien TD (1992) The stochastic finite element method (basic perturbation technique and computer implementation) Chichester. Wiley, West SussexMATH

22.

Kamiński M (2006) On generalized stochastic perturbation-based finite elements. Commun Numer Methods Eng 22(1):23–31. https://doi.org/10.1002/cnm.795MathSciNetCrossRefMATH

23.

Kamiński M (2010) Generalized stochastic perturbation technique in engineering computations. Math Comput Model 51(3–4):272–285. https://doi.org/10.1016/j.mcm.2009.08.014MathSciNetCrossRefMATH

24.

Kamiński M (2010) Potential problems with random parameters by the generalized perturbation-based stochastic finite element method. Comput Struct 88(7–8):437–445. https://doi.org/10.1016/j.compstruc.2009.12.005MathSciNetCrossRef

25.

Papadrakakis M, Papadopoulos V (1996) Robust and efficient methods for stochastic finite element analysis using Monte Carlo simulation. Comput Methods Appl Mech Eng 134:325–340. https://doi.org/10.1016/0045-7825(95)00978-7MathSciNetCrossRefMATH

26.

Elishakoff I, Ohsaki M (2010) Optimization and anti-optimization of structures under uncertainty. Imperial College Press, LondonCrossRef

27.

Moore RE (1966) Interval analysis. Prentice-Hall, Englewood CliffsMATH

28.

Hansen ER (1975) A generalized interval arithmetic. In: Nickel K. (eds) Interval mathematics. Lecture notes in computer science, 29: 7–18 Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07170-9_2

29.

Stolfi J, De Figueiredo LH (2003) An introduction to affine arithmetic. TEMA Tend Mat Apl Comput 4:297–312MathSciNetMATH

30.

Elishakoff I, Miglis Y (2012) Overestimation-free computational version of interval analysis. Int J Comput Methods Eng Sci Mech 13(5):319–328. https://doi.org/10.1080/15502287.2012.683134MathSciNetCrossRef

31.

Muscolino G, Sofi A (2012) Stochastic response of structures with uncertain-but-bounded parameters via improved interval analysis. Probab Eng Mech 28:152–163. https://doi.org/10.1016/j.probengmech.2011.08.011CrossRef

32.

Muhanna RL, Mullen RL (2001) Uncertainty in mechanics: problems-interval-based approach. J Eng Mech. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:6(557)CrossRef

33.

Moens D, Vandepitte D (2005) A survey of non-probabilistic uncertainty treatment in finite element analysis. Comput Methods Appl Mech Eng 194:1527–1555. https://doi.org/10.1016/j.cma.2004.03.019CrossRefMATH

34.

Chen SH, Lian HD, Yang XW (2002) Dynamic response analysis for structures with interval parameters. Struct Eng Mech 13:299–312. https://doi.org/10.12989/sem.2002.13.3.299CrossRef

35.

Qiu ZP, Wang XJ (2003) Comparison of dynamic response of structures with uncertain-but-bounded parameters using non probabilistic interval analysis method and probabilistic approach. Int J Solids Struct 40(20):5423–5439. https://doi.org/10.1016/S0020-7683(03)00282-8CrossRefMATH

36.

Qiu Z, Wang XJ (2005) Parameter perturbation method for dynamic response of structures with uncertain-but-bounded parameters based on interval analysis. Int J Solids Struct 42(18–19):4958–4970. https://doi.org/10.1016/j.ijsolstr.2005.02.023CrossRefMATH

37.

Qiu ZP, Ma L, Wang XJ (2009) Non-probabilistic interval analysis method for dynamic response analysis of nonlinear systems with uncertainty. J Sound Vib 319:531–540. https://doi.org/10.1016/j.jsv.2008.06.006CrossRef

38.

Wu J, Zhang Y, Chen L, Luo Z (2013) A Chebyshev interval method for nonlinear dynamic systems under uncertainty. Appl Math Model 37:4578–4591. https://doi.org/10.1016/j.apm.2012.09.073MathSciNetCrossRefMATH

39.

Xu M, Du J, Chen J, Wang C, Li Y (2018) An iterative dimension-wise approach to the structural analysis with interval uncertainties. Int J Comput Methods 15(06):1850044. https://doi.org/10.1142/S0219876218500445MathSciNetCrossRefMATH

40.

Muscolino G, Sofi A (2013) Bounds for the stationary stochastic response of truss structures with uncertain-but-bounded parameters. Mech Syst Signal Process 37:163–181. https://doi.org/10.1016/j.ymssp.2012.06.016CrossRef

41.

Muscolino G, Santoro R, Sofi A (2014) Explicit frequency response functions of discretized structures with uncertain parameters. Comput Struct 133:64–78. https://doi.org/10.1016/j.compstruc.2013.11.007CrossRef

42.

Muscolino G, Santoro R, Sofi A (2014) Explicit sensitivities of the response of discretized structures under stationary random processes. Probab Eng Mech 35:82–95. https://doi.org/10.1016/j.probengmech.2013.09.006CrossRef

43.

Dong W, Shah HC (1987) Vertex method for computing functions of fuzzy variables. Fuzzy Sets Syst 24(1):65–78. https://doi.org/10.1016/0165-0114(87)90114-XMathSciNetCrossRefMATH

44.

Hanss M (2003) The extended transformation method for the simulation and analysis of fuzzy-parameterized models. Int J Uncertain Fuzziness Knowl Based Syst 11(6):711–727. https://doi.org/10.1142/S0218488503002491MathSciNetCrossRefMATH

45.

Muscolino G, Santoro R (2017) Explicit frequency response function of beams with crack of uncertain depth. Proced Eng 199:1128–1133. https://doi.org/10.1016/j.proeng.2017.09.239CrossRef

46.

Cannizzaro F, Impollonia N, Caddemi S, Caliò I (2020) Explicit dynamic response of damaged beams with application to uncertain and identification problems. J Sound Vib 487:115608. https://doi.org/10.1016/j.jsv.2020.115608CrossRef

47.

Santoro R, Failla G, Muscolino G (2020) Interval static analysis of multi-cracked beams with uncertain size and position of cracks. Appl Math Model 86:92–114. https://doi.org/10.1016/j.apm.2020.03.049MathSciNetCrossRef

48.

Rizos PF, Aspragathos N, Dimarogonas AD (1990) Identification of crack location and magnitude in a cantilever beam from the vibration modes. J Sound Vib 138(3):381–388. https://doi.org/10.1016/0022-460X(90)90593-OCrossRef

49.

Ostachowicz WM, Krawczuk M (1991) Analysis of the effect of cracks on the natural frequencies of a cantilever beam. J Sound Vib 150(2):191–201. https://doi.org/10.1016/0022-460X(91)90615-QCrossRef

50.

Chondros TG, Dimarogonas AD, Yao J (1998) A continuous cracked beam vibration theory. J Sound Vib 215(1):17–34. https://doi.org/10.1006/jsvi.1998.1640CrossRefMATH

51.

Fernandez-Saez J, Rubio L, Navarro C (1999) Approximate calculation of the fundamental fre-quency for bending vibrations of cracked beams. J Sound Vib 225(2):345–352. https://doi.org/10.1006/jsvi.1999.2251CrossRef

52.

Shifrin EI, Ruotolo R (1999) Natural frequencies of a beam with an arbitrary number of cracks. J Sound Vib 222(3):409–423. https://doi.org/10.1006/jsvi.1998.2083CrossRef

53.

Zhao X, Zhao YR, Gao XZ, Li XY, Li YH (2016) Green’s functions for the forced vibrations of cracked Euler–Bernoulli beams. Mech Syst Signal Process 68–69:155–175. https://doi.org/10.1016/j.ymssp.2015.06.023CrossRef

54.

Caddemi S, Caliò I (2009) Exact closed-form solution for the vibration modes of the Euler–Bernoulli beam with multiple open cracks. J Sound Vib 327(3–5):473–489. https://doi.org/10.1016/j.jsv.2009.07.008CrossRef

55.

Caddemi S, Morassi A (2013) Multi-cracked Euler–Bernoulli beams: mathematical modeling and exact solutions. Int J Solids Struct 50(6):944–956. https://doi.org/10.1016/j.ijsolstr.2012.11.018CrossRef

56.

Failla G (2016) An exact generalised function approach to frequency response analysis of beams and plane frames with the inclusion of viscoelastic damping. J Sound Vib 360:171–202. https://doi.org/10.1016/j.jsv.2015.09.006CrossRef

57.

Failla G (2019) An exact modal analysis approach to vibration analysis of structures with mass-spring subsystems and rotational joints. J Sound Vib 438:191–219. https://doi.org/10.1016/j.jsv.2018.09.025CrossRef

58.

Den Hartog JP (1962) Mechanical vibrations. McGraw-Hill, New YorkMATH

59.

Housner GW et al (1997) Structural control: past, present and future. J Eng Mech 123(9):897–971. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:9(897)CrossRef

60.

Spencer BF, Nagarajaiah S (2003) State of the art of structural control. J Struct Eng 129(7):845–856. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:7(845)CrossRef

61.

Adam C, Di Lorenzo S, Failla G, Pirrotta A (2017) On the moving load problem in beam structures equipped with tuned mass dampers. Meccanica 52:3101–3115. https://doi.org/10.1007/s11012-016-0599-4MathSciNetCrossRefMATH

62.

Failla G, Di Paola M, Pirrotta A, Burlon A, Dunn I (2019) Random vibration mitigation of beams via tuned mass dampers with spring inertia effects. Meccanica 54:1365–1383. https://doi.org/10.1007/s11012-019-00983-8MathSciNetCrossRef

63.

Santoro R, Failla G (2019) Effect of uncertainty in dynamic response of multi-cracked beams. In: 15th international conference—dynamical systems—theory and applications, December 2–5, 2019, Łódź, Poland (Abstract)

64.

Yavari A, Sarkani S, Moyer ET (2000) On applications of generalized functions to beam bending problems. Int J Solids Struct 37(40):5675–5705. https://doi.org/10.1016/S0020-7683(99)00271-1MathSciNetCrossRefMATH

65.

Yavari A, Sarkani S (2001) On applications of generalized functions to the analysis of Euler–Bernoulli beam-columns with jump discontinuities. Int J Mech Sci 43:1543–1562. https://doi.org/10.1016/S0020-7403(00)00041-2CrossRefMATH

66.

Falsone G (2002) The use of generalised functions in the discontinuous beam bending differential equation. Int J Eng Educ 18(3):337–343

67.

Palmeri A, Cicirello A (2011) Physically-based Dirac’s delta functions in the static analysis of multi-cracked Euler–Bernoulli and Timoshenko beams. Int J Solids Struct 48(14–15):2184–2195. https://doi.org/10.1016/j.ijsolstr.2011.03.024CrossRef

68.

Burlon A, Failla G, Arena F (2017) Coupled bending and torsional free vibrations of beams with in-span supports and attached masses. Eur J Mech A/Solids 66:387–411. https://doi.org/10.1016/j.euromechsol.2017.07.015MathSciNetCrossRefMATH

69.

Pownuk A. (2004) Efficient method of solution of large scale engineering problems with interval parameters. In: Muhanna RL, Mullen RL (eds) Proc. NSF workshop on reliable engineering computing (REC2004), Savannah, GA, USA

70.

Qiu Z, Elishakoff I (1998) Antioptimization of structures with large uncertain-but-non random parameters via interval analysis. Comput Methods Appl Mech Eng 152:361–372CrossRef

71.

Santoro R, Muscolino G, Elishakoff I (2015) Optimization and anti-optimization solution of combined parameterized and improved interval analyses for structures with uncertainties. Comput Struct 149:31–42. https://doi.org/10.1016/j.compstruc.2014.11.006CrossRef

72.

Li Y, Xu YL (2018) Increasing accuracy in the interval analysis by the improved format of interval extension based on the first order Taylor series. Mech Syst Signal Process 104:744–757. https://doi.org/10.1016/j.ymssp.2017.11.037CrossRef

73.

Slepyan LI (2018) Structural discontinuity as generalized strain and Fourier transform for discrete-continuous systems. Int J Eng Sci 130:199–214. https://doi.org/10.1016/j.ijengsci.2018.06.004MathSciNetCrossRefMATH

Titel: An interval framework for uncertain frequency response of multi-cracked beams with application to vibration reduction via tuned mass dampers
verfasst von: Roberta Santoro
Giuseppe Failla
Publikationsdatum: 27.01.2021
Verlag: Springer Netherlands
Erschienen in: Meccanica / Ausgabe 4/2021
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-020-01290-3

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 4/2021

Nonlinear modeling and analysis of rotors supported by magnetorheological squeeze film journal bearings

Resonance study of spring pendulum based on asymptotic solutions with polynomial approximation in quadratic means

Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Comparison of a modified vibro-impact nonlinear energy sink with other kinds of NESs

Kinematics of the motorcar body side deformation process during front-to-side vehicle collision and the emergence of a hazard to car occupants

A novel identification procedure from ambient vibration data

Premium Partner

Marktübersichten