Exact closed-form solution for the vibration modes of the Euler-Bernoulli beam with multiple open cracks

被引:157
作者
Caddemi, S. [1 ]
Calio, I. [1 ]
机构
[1] Univ Catania, Dipartimento Ingn Civile & Ambientale, I-95100 Catania, Italy
关键词
NATURAL FREQUENCIES; JUMP DISCONTINUITIES; DAMAGE DETECTION; EIGENFREQUENCY CHANGES; GENERALIZED SOLUTIONS; ARBITRARY NUMBER; TIMOSHENKO BEAMS; CANTILEVER BEAM; ONE-DIMENSION; IDENTIFICATION;
D O I
10.1016/j.jsv.2009.07.008
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
In this study, exact closed-form expressions for the vibration modes of the Euler-Bernoulli beam in the presence of multiple concentrated cracks are presented. The proposed expressions are provided explicitly as functions of four integration constants only, to be determined by the standard boundary conditions. The enforcement of the boundary conditions leads to explicit expressions of the natural frequency equations. Besides the evaluation of the natural frequencies, neither computational work nor recurrence expressions for the vibration modes are required. The cracks, that are not subjected to the closing phenomenon, are modelled as a sequence of Dirac's delta generalised functions in the flexural stiffness. The Eigen-mode governing equation is formulated over the entire domain of the beam without enforcement of any continuity conditions, which are already accounted for in the adopted flexural stiffness model. The vibration modes of beams with different numbers of cracks under different boundary conditions have been analysed by means of the proposed closed-form expressions in order to show their efficiency. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码:473 / 489
页数:17
相关论文
共 60 条
[1]   VIBRATION TECHNIQUE FOR NON-DESTRUCTIVELY ASSESSING INTEGRITY OF STRUCTURES [J].
ADAMS, RD ;
CAWLEY, P ;
PYE, CJ ;
STONE, BJ .
JOURNAL OF MECHANICAL ENGINEERING SCIENCE, 1978, 20 (02) :93-100
[2]   Multiplication of distributions in one dimension: Possible approaches and applications to delta-function and its derivatives [J].
Bagarello, F .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 196 (03) :885-901
[4]  
BILELLO C, 2001, THESIS U DEGLI STUDI
[5]   Vibration of beams with multiple open cracks subjected to axial force [J].
Binici, B .
JOURNAL OF SOUND AND VIBRATION, 2005, 287 (1-2) :277-295
[6]   Euler-Bernoulli beams with multiple singularities in the flexural stiffness [J].
Biondi, B. ;
Caddemi, S. .
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, 2007, 26 (05) :789-809
[7]   Closed form solutions of Euler-Bernoulli beams with singularities [J].
Biondi, B ;
Caddemi, S .
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2005, 42 (9-10) :3027-3044
[8]   ANALYTIC CONTINUATION, MULTIPLICATION, AND FOURIER TRANSFORMATIONS OF SCHWARTZ DISTRIBUTIONS [J].
BREMERMANN, H ;
DURAND, L .
JOURNAL OF MATHEMATICAL PHYSICS, 1961, 2 (02) :240-&
[9]   Identification of concentrated damages in Euler-Bernoulli beams under static loads [J].
Buda, G. ;
Caddemi, S. .
JOURNAL OF ENGINEERING MECHANICS-ASCE, 2007, 133 (08) :942-956
[10]   Exact solution of the multi-cracked Euler-Bernoulli column [J].
Caddemi, S. ;
Calio, I. .
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2008, 45 (05) :1332-1351