Vibratory Characteristics of Axially-Loaded Timoshenko Beams With Arbitrary Number of Cracks

A simple and efficient analytical approach is presented to determine the vibrational frequencies and mode shape functions of axially-loaded Timoshenko beams with an arbitrary number of cracks. The local compliance induced by a crack is described by a massless rotational spring model. A set of boundary conditions are used as initial parameters to define the mode shape of the segment of the beam before the first crack. Using this, the remaining set of boundary conditions and recurrence formula developed in the study, the mode shape function of vibration of the beam containing multiple cracks can be easily determined. Four different classical boundary conditions (pinned-pinned, clamped-pinned, clamped-free, and clamped-clamped) are considered. Elastically-restrained support condition with concentrated masses is also considered. Three crack depths and five axial force levels representing the conditions under service loads are used. A parametric study is carried out for each case of support conditions to investigate the effect of crack and axial load on the vibrational properties of cracked Timoshenko beams. The influence of crack on the buckling load of the beam is also studied statically. Part of the results obtained is checked against the published values. The study concludes that the crack location, crack severity, and axial force level strongly affect the eigenfrequencies.

[1]  Qiusheng Li,et al.  Vibratory Characteristics of Timoshenko Beams with Arbitrary Number of Cracks , 2003 .

[2]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .

[3]  José Fernández-Sáez,et al.  Natural frequencies for bending vibrations of Timoshenko cracked beams , 2006 .

[4]  Ki-Hyun Kim,et al.  EFFECT OF A CRACK ON THE DYNAMIC STABILITY OF A FREE–FREE BEAM SUBJECTED TO A FOLLOWER FORCE , 2000 .

[5]  Erasmo Viola,et al.  Detection of crack location using cracked beam element method for structural analysis , 2001 .

[6]  Hai-Ping Lin,et al.  Direct and inverse methods on free vibration analysis of simply supported beams with a crack , 2004 .

[7]  Andrew D. Dimarogonas,et al.  Vibration of cracked structures: A state of the art review , 1996 .

[8]  Marc Hoit.  Computer Assisted Structural Analysis and Modeling , 1994 .

[9]  R. B. Testa,et al.  Closure Effects on Fatigue Crack Detection , 1999 .

[10]  I. Takahashi.  Vibration and stability of non-uniform cracked Timoshenko beam subjected to follower force , 1999 .

[11]  J. N. Reddy,et al.  Shear deformable beams and plates: relationships with classical solutions , 2000 .

[12]  A. Swamidas,et al.  Identification of Cracking in Beam Structures Using Timoshenko and Euler Formulations , 2004 .

[13]  C. Mei,et al.  Analytical approach to free and forced vibrations of axially loaded cracked Timoshenko beams , 2006 .

[14]  D. Y. Zheng,et al.  NATURAL FREQUENCY CHANGES OF A CRACKED TIMOSHENKO BEAM BY MODIFIED FOURIER SERIES , 2001 .

[15]  Marek Krawczuk,et al.  The dynamic analysis of a cracked Timoshenko beam by the spectral element method , 2003 .

[16]  D. Y. Zheng,et al.  Stability of a cracked Timoshenko beam column by modified Fourier series , 2003 .

[17]  S. P. Lele,et al.  Modelling of Transverse Vibration of Short Beams for Crack Detection and Measurement of Crack Extension , 2002 .

[18]  M. Kısa,et al.  Free vibration analysis of cracked beams by a combination of finite elements and component mode synthesis methods , 1998 .

[19]  Franklin Y. Cheng.  Matrix Analysis of Structural Dynamics: Applications and Earthquake Engineering , 2000 .