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A hybrid procedure to identify the optimal stiffness coefficients of elastically restrained beams

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The formulation of a bending vibration problem of an elastically restrained Bernoulli–Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli–Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams, taking into account the effect of attached concentrated masses and rotational inertias, followed by a reconciliation step between the theoretical model results and the experimental ones. The proposed optimal identification of the elastic support parameters is computationally demanding if the exact eigenproblem solving is considered. Hence, the use of a Gaussian process regression as a meta-model is addressed. An experimental application is used in order to assess the accuracy of the estimated parameters throughout the comparison of the experimentally obtained natural frequency, from impact tests, and the correspondent computed eigenfrequency.
Rocznik
Strony
245--257
Opis fizyczny
Bibliogr. 43 poz., rys., tab., wykr.
Twórcy
autor
  • Research Group on Modelling and Optimization of Multifunctional Systems (GI-MOSM), Mechanical Engineering Department, Instituto Superior de Engenharia de Lisboa (ADEM/ISEL), Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisboa, Portugal; LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal
autor
  • Research Group on Modelling and Optimization of Multifunctional Systems (GI-MOSM), Mechanical Engineering Department, Instituto Superior de Engenharia de Lisboa (ADEM/ISEL), Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisboa, Portugal; LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal
autor
  • LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal
autor
  • Research Group on Modelling and Optimization of Multifunctional Systems (GI-MOSM), Mechanical Engineering Department, Instituto Superior de Engenharia de Lisboa (ADEM/ISEL), Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisboa, Portugal; LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal
Bibliografia
  • [1] Ahmadian, H., Mottershead, J.E. and Friswell, M.I. (2001). Boundary conditions identification by solving characteristic equations, Journal of Sound and Vibration 247(5): 755–763.
  • [2] Albarracín, C., Zannier, L. and Grossi, R. (2004). Some observations in the dynamics of beams with intermediate supports, Journal of Sound and Vibration 271(1–2): 475–480.
  • [3] Auciello, N. (1996). Transverse vibrations of a linearly tapered cantilever beam with tip mass of rotary inertia and eccentricity, Journal of Sound and Vibration 194(1): 25–34.
  • [4] Babu, B. and Jehan, M. (2003). Differential evolution for multi-objective optimization, Proceedings of the 2003 Congress on Evolutionary Computation, CEC 2003, Canberra, Australia, pp. 2696–2703.
  • [5] Babu, B. and Munawar, S. (2007). Differential evolution strategies for optimal design of shell-and-tube heat exchangers, Chemical Engineering Science 62(14): 3720–3739.
  • [6] Bashash, S., Salehi-Khojin, A. and Jalili, N. (2008). Forced vibration analysis of flexible Euler–Bernoulli beams with geometrical discontinuities, Proceedings of the American Control Conference, ACC 2008, Seattle WA, USA, pp. 4029–4034.
  • [7] Biondi, B. and Caddemi, S. (2005). Closed form solutions of Euler–Bernoulli beams with singularities, International Journal of Solids and Structures 42(9–10): 3027–3044.
  • [8] Biondi, B. and Caddemi, S. (2007). Euler–Bernoulli beams with multiple singularities in the flexural stiffness, European Journal of Mechanics, A: Solids 26(7): 789–809.
  • [9] Chakraborty, U.K. (2008). Advances in Differential Evolution, 1st Edition, Springer, New York, NY.
  • [10] Chesne, S. (2012 ). Identification of beam boundary conditions using displacement derivatives estimations, Proceedings of the 16th IFAC Symposium on System Identification, Brussels, Belgium, pp. 416–421.
  • [11] Das, S. and Suganthan, P.N. (2011). Differential evolution: A survey of the state-of-the-art, IEEE Transactions on Evolutionary Computation 15(1): 4–31.
  • [12] De Munck, M., Moens, D., Desmet, W. and Vandepitte, D. (2009). An efficient response surface based optimisation method for non-deterministic harmonic and transient dynamic analysis, Computer Modeling in Engineering & Sciences 47(2): 119–166.
  • [13] De Rosa, M. and Auciello, N. (1996). Free vibrations of tapered beams with flexible ends, Computers & Structures 60(2): 197–202.
  • [14] De Rosa, M., Franciosi, C. and Maurizi, M. (1996). On the dynamic behaviour of slender beams with elastic ends carrying a concentrated mass, Computers & Structures 58(6): 1145–1159.
  • [15] Eiben, A.E. and Smith, J.E. (2013). Introduction to Evolutionary Computing, Natural Computing Series, Springer-Verlag, Heidelberg.
  • [16] Elishakoff, I. and Pentaras, D. (2006). Apparently the first closed-form solution of inhomogeneous elastically restrained vibrating beams, Journal of Sound and Vibration 298(1–2): 439–445.
  • [17] Grossi, R. and Albarracín, C. (2003). Eigenfrequencies of generally restrained beams, Journal of Applied Mathematics 2003(10): 503–516.
  • [18] Kitayama, S., Arakawa, M. and Yamazaki, K. (2011). Differential evolution as the global optimization technique and its application to structural optimization, Applied Soft Computing 11(4): 3792–3803.
  • [19] Lin, S.C. and Hsiao, K.M. (2001). Vibration analysis of a rotating Timoshenko beam, Journal of Sound and Vibration 240(2): 303–322.
  • [20] Loja, M.A.R., Barbosa, J.I. and Mota Soares, C.M. (2010). Optimal design of piezolaminated structures using b-spline strip finite element models models and genetic algorithms, International Journal for Computational Engineering Science and Mechanics 11(4): 185–195.
  • [21] Loja, M.A.R., Silva, T.A.N., Barbosa, I.J.C. and Simes, C.N.F. (2013). Analysis and optimization of agro-waste composite beam structures, Usak University Journal of Material Sciences 2(1): 45–60.
  • [22] Loja, M.A.R., Mota Soares, C.M. and Barbosa, J.I. (2014). Optimization of magneto-electro-elastic composite structures using differential evolution, Composite Structures 107: 276–287.
  • [23] Loja, M.A.R. (2014). On the use of particle swarm optimization to maximize bending stiffness of functionally graded structures, Journal of Symbolic Computation 61–62: 12–30.
  • [24] Maiz, S., Bambill, D.V., Rossit, C.A. and Laura, P. (2007). Transverse vibration of Bernoulli–Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution, Journal of Sound and Vibration 303(3–5): 895–908.
  • [25] Majkut, L. (2006). Identification of beams boundary conditions in ill-posed problem, Journal of Theoretical and Applied Mechanics 44(1): 91–105.
  • [26] Maplesoft (2010). Maple 14.
  • [27] Martinović, G., Bajer, D. and Zorić, B. (2014). A differential evolution approach to dimensionality reduction for classification needs, International Journal of Applied Mathematics and Computer Science 24(1): 111–122, DOI: 10.2478/amcs-2014-0009.
  • [28] Mboup, M., Join, C. and Fliess, M. (2009). Numerical differentiation with annihilators in noisy environment, Numerical Algorithm 50(4): 439–467.
  • [29] Meirovitch, L. (2001). Fundamentals of Vibrations, McGraw-Hill, Boston, MA.
  • [30] Nallim, L.G. and Grossi, R.O. (1999). A general algorithm for the study of the dynamical behaviour of beams, Applied Acoustics 57(4): 345–356.
  • [31] Posiadała (1997). Free vibrations of uniform Timoshenko beams with attachments, Journal of Sound and Vibration 204(2): 359–369.
  • [32] Price, K., Storn, R. and Lampinen, J. (2005). Differential Evolution: A Practical Approach to Global Optimization, Natural Computing Series, Springer, New York, NY.
  • [33] Rasmussen, C.E. and Williams, C.K.I. (2005). Gaussian Processes for Machine Learning, The MIT Press, Cambridge, MA.
  • [34] Reed, H.M., Nichols, J.M. and Earls, C.J. (2013). A modified differential evolution algorithm for damage identification in submerged shell structures, Mechanical Systems and Signal Processing 39(1–2): 396–408.
  • [35] Savoia, M. and Vincenzi, L. (2008). Differential evolution algorithm for dynamic structural identification, Journal of Earthquake Engineering 12(5): 800–821.
  • [36] Silva, T.A.N. and Loja, M.A.R. (2013). Differential evolution on the minimization of thermal residual stresses in functionally graded structures, in A. Madureira, C. Reis and V. Marques (Eds.), Computational Intelligence and Decision Making—Trends and Applications, Springer-Verlag, Dordrecht, pp. 289–299.
  • [37] Silva, T.A.N. and Maia, N.M.M. (2011). Elastically restrained Bernoulli–Euler beams applied to rotary machinery modelling, Acta Mechanica Sinica 27(1): 56–62.
  • [38] Silva, T.A.N. and Maia, N.M.M. (2013). Modelling a rotating shaft as an elastically restrained Bernoulli–Euler beam, Experimental Techniques 37(5): 6–13.
  • [39] Storn, R. and Price, K. (1997). Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization 11(4): 341–359.
  • [40] Vaz, J.C. (2008). Análise do comportamento dinâmico de uma viga de Euler–Bernoulli escalonada com apoios elasticamente variáveis, Master’s thesis, Universidade Federal de Itajubá, Itajubá, MG.
  • [41] Wang, L. and Yang, Z. (2011). Identification of boundary conditions of tapered beam-like structures using static flexibility measurements, Mechanical Systems and Signal Processing 25(7): 2484–2500.
  • [42] Wu, J.S. and Chen, D.W. (2003). Bending vibrations of wedge beams with any number of point masses, Journal of Sound and Vibration 262(5): 1073–1090.
  • [43] Yoneyama, S. and Arikawa, S. (2012). Identification of boundary condition from measured displacements for linear elastic deformation fields, Procedia IUTAM 4: 215–226.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-84b7ddfc-cc74-4142-9e4b-b1d41408e8b8
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