The main goal of this note is to discuss the applicability of approximate closed-form solutions to evaluate the natural frequencies for bending vibrations of simply supported Euler–Bernoulli cracked beams. From the well-known model, which considers the cracked beam as two beams connected by a rotational spring, different approximate solutions are revisited and compared with those found by a direct method, which has been chosen as reference.

1.
Shen
,
M. H.
, and
Taylor
,
J. E.
, 1991, “
An Identification Problem for Vibrating Cracked Beams
,”
J. Sound Vib.
0022-460X,
150
, pp.
457
484
.
2.
Narkis
,
Y.
, 1994, “
Identification of Crack Location in Vibrating Simply Supported Beams
,”
J. Sound Vib.
0022-460X,
172
, pp.
549
558
.
3.
Hasan
,
W. M.
, 1995, “
Crack Detection From the Variation of Eigenfrequencies of a Beam on Elastic Foundation
,”
Eng. Fract. Mech.
0013-7944,
52
, pp.
409
421
.
4.
Dimarogonas
,
A. D.
, 1996, “
Vibrations of Cracked Structures: A State of the Art Review
,”
Eng. Fract. Mech.
0013-7944,
55
, pp.
831
857
.
5.
Salawu
,
O.
, 1997, “
Detection of Structural Damage Through Changes in Frequencies: A Review
,”
Eng. Struct.
0141-0296,
19
, pp.
718
723
.
6.
Nandwana
,
B. P.
, and
Maiti
,
S. K.
, 1997, “
Detection of Location and Size of a Crack in Stepped Cantilever Beam Based on Measurement of Natural Frequencies
,”
J. Sound Vib.
0022-460X,
203
, pp.
435
446
.
7.
Suh
,
M. W.
,
Yu
,
J. M.
, and
Lee
,
J. H.
, 2000, “
Crack Identification Using Classical Optimization Technique
,”
Key Eng. Mater.
1013-9826,
183–187
, pp.
61
66
.
8.
Morassi
,
A.
, 2001, “
Identification of a Crack in a Rod Based on Changes in a Pair of Natural Frequencies
,”
J. Sound Vib.
0022-460X,
242
, pp.
577
596
.
9.
Morassi
,
A.
, and
Rollo
,
M.
, 2001, “
Identification of Two Cracks in a Simply Supported Beam From Minimal Frequency Measurements
,”
J. Vib. Control
1077-5463,
7
, pp.
729
739
.
10.
Shim
,
M. B.
, and
Suh
,
M. W.
, 2002, “
A Study on Multiobjective Optimization Technique for Inverse and Crack Identification Problems
,”
Inverse Probl. Eng.
1068-2767,
10
, pp.
441
465
.
11.
Shim
,
M. B.
, and
Suh
,
M. W.
, 2003, “
Crack Identification Using Evolutionary Algorithms in Parallel Computing Environment
,”
J. Sound Vib.
0022-460X,
262
, pp.
141
160
.
12.
Dilena
,
M.
, and
Morassi
,
A.
, 2004, “
The Use of Antiresonances for Crack Detection in Beams
,”
J. Sound Vib.
0022-460X,
276
, pp.
195
214
.
13.
Khiem
,
N. T.
, and
Lien
,
T. V.
, 2004, “
Multi-Crack Detection for Beam by the Natural Frequencies
,”
J. Sound Vib.
0022-460X,
273
, pp.
175
184
.
14.
Rubio
,
L.
, 2009, “
An Efficient Method for Crack Identification in Simply Supported Euler-Bernoulli Beams
,”
ASME J. Vibr. Acoust.
0739-3717
131
(
5
), p.
051001
.
15.
Kim
,
T. J.
, and
Stubbs
,
N.
, 2002, “
Improved Damage Identification Method Based on Modal Information
,”
J. Sound Vib.
0022-460X,
252
, pp.
223
238
.
16.
Kim
,
T. J.
,
Ryu
,
Y. S.
,
Cho
,
H. M.
, and
Stubbs
,
N.
, 2003, “
Damage Identification in Beam-Type Structures: Frequency-Based Method vs Mode-Shape-Based Method
,”
Eng. Struct.
0141-0296,
25
, pp.
57
67
.
17.
Karthikeyan
,
M.
,
Tiwari
,
R.
, and
Talukdar
,
S.
, 2007, “
Development of a Technique to Locate and Quantify a Crack in a Beam Based on Modal Parameters
,”
ASME J. Vibr. Acoust.
0739-3717,
129
, pp.
390
395
.
18.
Karthikeyan
,
M.
,
Tiwari
,
R.
, and
Talukdar
,
S.
, 2008, “
Development of a Novel Algorithm for Crack Detection, Localization, and Sizing in a Beam Based on Forced Response Measurements
,”
ASME J. Vibr. Acoust.
0739-3717,
130
, p.
021002
.
19.
Zhong
,
S.
, and
Oyadiji
,
S. O.
, 2008, “
Identification of Cracks in Beams With Auxiliary Mass Spatial Probing by Stationary Wavelet Transform
,”
ASME J. Vibr. Acoust.
0739-3717,
130
, p.
041001
.
20.
Freund
,
L. B.
, and
Herrmann
,
G.
, 1976, “
Dynamic Fracture of a Beam or Plate in Plane Bending
,”
ASME J. Appl. Mech.
0021-8936,
43
, pp.
112
116
.
21.
Fernández-Saez
,
J.
,
Rubio
,
L.
, and
Navarro
,
C.
, 1999, “
Approximate Calculation of the Fundamental Frequency for Bending Vibrations of Cracked Beams
,”
J. Sound Vib.
0022-460X,
225
, pp.
345
352
.
22.
Fernández-Saez
,
J.
, and
Navarro
,
C.
, 2002, “
Fundamental Frequency of Cracked Beams: An Analytical Approach
,”
J. Sound Vib.
0022-460X,
256
, pp.
17
31
.
23.
Morassi
,
A.
, 1993, “
Crack-Induced Changes in Eigenfrequencies of Beam Structures
,”
J. Eng. Mech.
0733-9399,
119
, pp.
1798
1803
.
24.
Loya
,
J. A.
,
Rubio
,
L.
, and
Fernández-Saez
,
J.
, 2006, “
Natural Frequencies for Bending Vibrations of Timoshenko Cracked Beams
,”
J. Sound Vib.
0022-460X,
290
, pp.
640
653
.
25.
Zhong
,
S.
, and
Oyadiji
,
S. O.
, 2008, “
Analytical Predictions of Natural Frequencies of Cracked Simply Supported Beams With a Stationary Roving Mass
,”
J. Sound Vib.
0022-460X,
311
, pp.
328
352
.
26.
Adams
,
R. D.
,
Cawley
,
P.
,
Pye
,
C. J.
, and
Stone
,
B. J.
, 1978, “
A Vibration Technique for Non-Destructive Assessing the Integrity of Structures
,”
J. Mech. Eng. Sci.
0022-2542,
20
, pp.
93
100
.
27.
Tada
,
H.
,
Paris
,
P.
, and
Irwin
,
G.
, 1985,
The Stress Analysis of Cracks Handbook
, 2nd ed.,
Paris Productions, Inc.
,
St. Louis, MO
.
28.
Rubio
,
L.
,
de Luna
,
S.
,
Fernández-Saez
,
J.
, and
Navarro
,
C.
, 2000, “
Cálculo de las frecuencias propias de vigas fisuradas
,”
Anales de Ingeniería Mecánica
, 0212-5072
13
, pp.
745
754
.
29.
Rao
,
S. S.
, 1990,
Mechanical Vibrations
, 2nd ed.,
Addison-Wesley
,
New York
.
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