Abstract
In the previous chapters we have applied the wavelet approach for solving problems of mathematical calculus. In the subsequent chapters we will demonstrate that the Haar wavelet method is also a valuable tool in structural mechanics. To begin with, the buckling of elastic beams is discussed. The material in this Chapter has been published by Lepik [18].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bilello, E.: Theoretical and experimental investigation of damaged beam under moving system. Dissertation, Universita degli Studi di Palermo (2001)
Bovsunovski, A., Matveev, V.: Analytical approach to the determination of dynamic characteristics of a beam with a closing crack. J. Sound Vib. 235, 415–434 (2000)
Caddemi, S., Calio, I., Marietta, M.: The non-linear dynamic response of the Euler-Bernoulli beams with an arbitrary number of switching cracks. Int. J. Non-Linear Mech. 45, 714–726 (2010)
Chen, C.: Vibrations of prismatic beams on an elastic foundation by the differential quadrature element method. J. Comput. Struct. 77, 1–9 (2000)
Chen, X., Xiang, J., Li, B., He, Z.: A study of multiscale wavelet-based elements for adaptive finite elements analysis. Adv. Eng. Softw. 41, 196–205 (2010)
Christides, S., Barr, A.: One dimensional theory of cracked Bernoulli-Euler beams. Int. J. Non-Linear Mech. 26, 639–648 (1984)
Deng, X., Wang, Q.: Crack detection using spatial measurements and wavelet. Int. J. Fract. 91, L23–L28 (2008)
Díaz, L., Martín, M., Vampa, V.: Daubechies wavelet beam and plate finite elements. Finite Elem. Anal. Des. 45, 200–209 (2009)
Dimarogonas, A.: Vibration of cracked structures: a state of the art review. Eng. Fract. Mech. 55, 831–857 (1996)
Doebling, S., Farrar, C., Prime, M.: A summary review of vibration-based damage identification methods. Shock Vib. Dig. 30, 91–105 (1998)
Douka, E., Loutridis, S., Trochidis, A.: Crack identification in beams using wavelet analysis. Int. J. Solids Struct. 40, 3557–3569 (2003)
Fan, W., Qiao, P.: A 2-D continuous wavelet transform of mode shape data for damage detection of plate structures. Int. J. Solids Struct. 46, 4379–4395 (2009)
Gentile, A., Messina, A.: On the continuous wavelet transforms applied to discrete vibrational data for detecting open cracks in damaged beams. Int. J. Solids Struct. 40, 295–315 (2003)
Glabisz, W.: The use of Walsh-wavelet packets in linear boundary value problems. Comput. Struct. 82, 131–141 (2004)
He, W., Ren, W.: Finite element analysis of beam structures based on trigonometric wavelet. Finite Elem. Anal. Des. 51, 59–66 (2012)
Karaagac, C., Örtürk, H., Sabuncu, M.: Free vibrations and lateral buckling of a cantilever slender beam with an edge crack: experimental and numerical studies. J. Sound Vib. 326, 235–250 (2009)
Kim, B., Kim, H., Park, T.: Nondestructive damage evaluation of plates using the multi-resolution analysis of two-dimensional Haar wavelet. J. Sound Vib. 292, 82–104 (2006)
Lepik, Ü.: Buckling of elastic beams by the Haar wavelet method. Est. J. Eng. 17, 271–284 (2011)
Lin, H., Chang, S.: Free vibration analysis of multi-span beams with intermediate flexible constraints. J. Sound Vib. 281, 155–169 (2005)
Quek, S., Wang, Q., Zhang, L., Ang, K.: Sensitivity analysis of crack detection in beams by wavelet technique. Int. J. Mech. Sci. 43, 2899–2910 (2001)
Shen, M., Pierre, C.: Natural modes of Bernoulli-Euler beams with symmetric cracks. J. Sound Vib. 138, 115–134 (1990)
Sinha, J., Friswell, M., Edwards, S.: Simplified models for the location of cracks in beam structures using measured vibration data. J. Sound Vib. 251, 13–38 (2002)
Skrinar, M.: On the application of a simply computational model for slender transversely cracked beams in buckling problems. Comput. Mater. Sci. 39, 242–249 (2009)
Timoshenko, S.: Theory of Elastic Stability. McGraw-Hill Book Company, New York (1936)
Wang, Q., Deng, X.: Damage detection with spacial wavelets. Int. J. Solids Struct. 36, 3443–3468 (1999)
Zhong, S., Oyadiji, S.O.: Crack detection in simply supported beams without baseline modal parameters by stationary wavelet transform. Mech. Syst. Sign. Process. 21, 1853–1884 (2007)
Zhong, Y., Xiang, J.: Construction of wavelet-based elements for static and stability analysis of elastic problems. Acta Mech. Solida Sin. 24, 355–364 (2011)
Zhou, Y., Zhou, J.: A modified wavelet approximation of deflections for solving PDEs of beams and square thin plates. Finite Elem. Anal. Des. 44, 773–783 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Lepik, Ü., Hein, H. (2014). Buckling of Elastic Beams. In: Haar Wavelets. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-04295-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-04295-4_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04294-7
Online ISBN: 978-3-319-04295-4
eBook Packages: EngineeringEngineering (R0)