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4 Reliability of Chaotic Vibrations of Euler-Bernoulli Beams with Clearance
23. Euler, L.: Sur la force des colones. Memories de L’Academie de Berlin 13, 252–282 (1757)
24. Krysko, A.V., Awrejcewicz, J., Kutepov, I.E., Zagniboroda, N.A., Dobriyan, V., Krysko, V.A.:
Chaotic dynamics of flexible Euler-Bernoulli beams. Chaos 23(4) 043130-1 – 043130-25
(2013)
25. Krysko, A.V., Awrejcewicz, J., Saltykova, O.A., Zhigalov, M.V., Krysko, V.A.: Investigations
of chaotic dynamics of multi-layer beams using taking into account rotational inertial effects.
Commun. Nonlinear. Sci. Num. Simul. 19(8), 2568–2589 (2014)
26. Alijani, F., Amabili, M.: Non-linear vibrations of shells: a literature review from 2003 to 2013.
Int. J. Non-Linear. Mech. 58(2014), 233–257 (2003)
27. Sedighi, H.M., Shirazi, K.H., Zare, J.: Novel equivalent function for deadzone nonlinearity:
applied to analytical solution of beam vibration using He’s parameter expanding method. Lat.
Am. J. Sol. Struct. 9(4), 443–452 (2012)
28. Kármán, T.: Festigkeitsprobleme in Maschinenbau. Encykle D Math. Wiss. 4(4), 311–385
(1910)
29. Sylvester, J.J.: On the reduction of a bilinear quantic of the nth order to the form of a sum of n
products by a double orthogonal substitution. Mess. Math. 19, 42–46 (1889)
30. Liang, Y.C., Lee, H.P., Lim, S.P., Lin, W.Z., Lee, K.H., Wu, C.G.: Proper orthogonal decomposition and its applications. Part I: Theory. J. Sound. Vib. 252, 527–544 (2002)
31. Hotelling, H.: Analysis of a complex of statistical variables into principal components. J. Educ.
Phychol. 24, 417–441 (1933)
32. Krysko, A.V., Awrejcewicz, J., Papkova, I.V., Szymanowska, O., Krysko, V.A.: Principal component analysis in the nonlinear dynamics of beams: purification of the signal from noise
induced by the nonlinearity of beam vibrations. Adv. Math. Phys. 2017, 1–9 (2017)
4 Reliability of Chaotic Vibrations of Euler-Bernoulli Beams with Clearance
23. Euler, L.: Sur la force des colones. Memories de L’Academie de Berlin 13, 252–282 (1757)
24. Krysko, A.V., Awrejcewicz, J., Kutepov, I.E., Zagniboroda, N.A., Dobriyan, V., Krysko, V.A.:
Chaotic dynamics of flexible Euler-Bernoulli beams. Chaos 23(4) 043130-1 – 043130-25
(2013)
25. Krysko, A.V., Awrejcewicz, J., Saltykova, O.A., Zhigalov, M.V., Krysko, V.A.: Investigations
of chaotic dynamics of multi-layer beams using taking into account rotational inertial effects.
Commun. Nonlinear. Sci. Num. Simul. 19(8), 2568–2589 (2014)
26. Alijani, F., Amabili, M.: Non-linear vibrations of shells: a literature review from 2003 to 2013.
Int. J. Non-Linear. Mech. 58(2014), 233–257 (2003)
27. Sedighi, H.M., Shirazi, K.H., Zare, J.: Novel equivalent function for deadzone nonlinearity:
applied to analytical solution of beam vibration using He’s parameter expanding method. Lat.
Am. J. Sol. Struct. 9(4), 443–452 (2012)
28. Kármán, T.: Festigkeitsprobleme in Maschinenbau. Encykle D Math. Wiss. 4(4), 311–385
(1910)
29. Sylvester, J.J.: On the reduction of a bilinear quantic of the nth order to the form of a sum of n
products by a double orthogonal substitution. Mess. Math. 19, 42–46 (1889)
30. Liang, Y.C., Lee, H.P., Lim, S.P., Lin, W.Z., Lee, K.H., Wu, C.G.: Proper orthogonal decomposition and its applications. Part I: Theory. J. Sound. Vib. 252, 527–544 (2002)
31. Hotelling, H.: Analysis of a complex of statistical variables into principal components. J. Educ.
Phychol. 24, 417–441 (1933)
32. Krysko, A.V., Awrejcewicz, J., Papkova, I.V., Szymanowska, O., Krysko, V.A.: Principal component analysis in the nonlinear dynamics of beams: purification of the signal from noise
induced by the nonlinearity of beam vibrations. Adv. Math. Phys. 2017, 1–9 (2017)