Abstract

In many structural applications like bridges, arches, etc., frames are used, and it is important to study their dynamic behavior. Finite element method (FEM) is usually used for computational simulation of vibration for such frame structures. However, FEM simulations for high frequency are computationally intensive and lack accuracy. This paper proposes a wave propagation-based approach for the vibration analysis of a frame having angular and curved joints. The reflection and transmission matrices for the joints are derived using the kinematic compatibility and equilibrium conditions. Reflection, transmission, and propagation matrices are assembled leading to matrix equation terms of the wave amplitudes. Modal analysis and harmonic analysis of frames having curved and angular joints are performed using the present formulation. The frequency response function for point harmonic forcing acting on such structures is also presented. The formulation and the results are non-dimensionalized for wider applicability. The results obtained using the present formulation are compared with those obtained through FEM simulation in a commercial package. It is found that the results obtained using the two methods are in excellent correlation. The computational efficiency of the present method over FEM simulation is also reported.

References

References
1.
Cook
,
R. D.
,
Malkus
,
D. S.
,
Plesha
,
M. E.
, and
Witt
,
R. J.
,
1989
,
Concepts and Applications of Finite Element Analysis
,
John Wiley and Sons
,
New York
.
2.
Doyle
,
J. F.
,
1989
,
Wave Propagation in Structures
,
Springer
,
New York
, pp.
126
156
.
3.
Mace
,
B. R.
,
1984
, “
Wave Reflection and Transmission in Beams
,”
J. Sound Vib.
,
97
(
2
), pp.
237
246
. 10.1016/0022-460X(84)90320-1
4.
Mei
,
C.
, and
Sha
,
H.
,
2015
, “
An Exact Analytical Approach for Free Vibration Analysis of Built-Up Space Frames
,”
ASME J. Vib. Acoust.
,
137
(
3
), p.
031005
. 10.1115/1.4029380
5.
Gopalakrishnan
,
S.
,
2016
,
Wave Propagation in Materials and Structures
,
CRC Press
,
Boca Raton, FL
.
6.
Beale
,
L. S.
, and
Accorsi
,
M. L.
,
1995
, “
Power Flow in Two- and Three-Dimensional Frame Structures
,”
J. Sound Vib.
,
185
(
4
), pp.
685
702
. 10.1006/jsvi.1995.0409
7.
Duhamel
,
D.
,
Mace
,
B. R.
, and
Brennan
,
M. J.
,
2006
, “
Finite Element Analysis of the Vibrations of Waveguides and Periodic Structures
,”
J. Sound Vib.
,
294
(
1–2
), pp.
205
220
. 10.1016/j.jsv.2005.11.014
8.
Renno
,
J. M.
, and
Mace
,
B. R.
,
2013
, “
Calculation of Reflection and Transmission Coefficients of Joints Using a Hybrid Finite Element/Wave and Finite Element Approach
,”
J. Sound Vib.
,
332
(
9
), pp.
2149
2164
. 10.1016/j.jsv.2012.04.029
9.
Chouvion
,
B.
,
Popov
,
A. A.
,
Mcwilliam
,
S.
, and
Fox
,
C. H. J.
,
2011
, “
Vibration Modelling of Complex Waveguide Structures
,”
Comput. Struct.
,
89
(
11–12
), pp.
1253
1263
. 10.1016/j.compstruc.2010.08.010
10.
Cai
,
G. Q.
, and
Lin
,
Y. K.
,
1991
, “
Wave Propagation and Scattering in Structural Networks
,”
J. Eng. Mech.
,
117
(
7
), pp.
1555
1574
. 10.1061/(ASCE)0733-9399(1991)117:7(1555)
11.
Mei
,
C.
,
2012
, “
Wave Analysis of In-Plane Vibrations of L-Shaped and Portal Planar Frame Structures
,”
ASME J. Vib. Acoust.
,
134
(
2
), p.
021011
. 10.1115/1.4005014
12.
Mei
,
C.
,
2008
, “
Wave Analysis of In-Plane Vibrations of H- and T-Shaped Planar Frame Structures
,”
ASME J. Vib. Acoust.
,
130
(
6
), p.
061004
. 10.1115/1.2980373
13.
Mei
,
C.
,
2014
, “
An Analytical Study of Dynamic Characteristics of Multi-Story Timoshenko Planar Frame Structures
,”
ASME J. Dyn. Syst. Meas. Control
,
136
(
5
), p.
051004
. 10.1115/1.4027087
14.
Mei
,
C.
,
2011
, “
Wave Control of Vibrations in Multi-Story Planar Frame Structures Based on Classical Vibration Theories
,”
J. Sound Vib.
,
330
(
23
), pp.
5530
5544
. 10.1016/j.jsv.2011.06.022
15.
Mei
,
C.
,
2019
, “
Analysis of In- and Out-of Plane Vibrations in a Rectangular Frame Based on Two- and Three-Dimensional Structural Models
,”
J. Sound Vib.
,
440
(
1
), pp.
412
438
. 10.1016/j.jsv.2017.07.019
16.
Ouisse
,
M.
, and
Guyader
,
J.-L.
,
2003
, “
Vibration Sensitive Behaviour of a Connecting Angle. Case of Coupled Beams and Plates
,”
J. Sound Vib.
,
267
(
4
), pp.
809
850
. 10.1016/S0022-460X(03)00179-2
17.
Tomita
,
S.
,
Nakano
,
S.
,
Sugiura
,
H.
, and
Matsumura
,
Y.
,
2020
, “
Numerical Estimation of the Influence of Joint Stiffness on Free Vibrations of Frame Structures Via the Scattering of Waves at Elastic Joints
,”
Wave Motion
,
96
(
1
), p.
102575
. 10.1016/j.wavemoti.2020.102575
18.
Takiuti
,
B. E.
,
Manconi
,
E.
,
Brennan
,
M. J.
, and
Lopes
,
V.
,
2020
, “
Wave Scattering From Discontinuities Related to Corrosion-Like Damage in One-Dimensional Waveguides
,”
J. Braz. Soc. Mech. Sci. Eng.
,
42
(
10
), pp.
1
17
. 10.1007/s40430-020-02574-1
19.
Chidamparam
,
P.
, and
Leissa
,
A. W.
,
1993
, “
Vibrations of Planar Curved Beams, Rings, and Arches
,”
ASME Appl. Mech. Rev.
,
46
(
9
), pp.
467
483
. 10.1115/1.3120374
20.
Kang
,
B.
,
Riedel
,
C. H.
, and
Tan
,
C. A.
,
2003
, “
Free Vibration Analysis of Planar Curved Beams by Wave Propagation
,”
J. Sound Vib.
,
260
(
1
), pp.
19
44
. 10.1016/S0022-460X(02)00898-2
21.
Lee
,
S.-K.
,
Mace
,
B. R.
, and
Brennan
,
M. J.
,
2007
, “
Wave Propagation, Reflection and Transmission in Curved Beams
,”
J. Sound Vib.
,
306
(
3–5
), pp.
636
656
. 10.1016/j.jsv.2007.06.001
22.
Renno
,
J.
,
Søndergaard
,
N.
,
Sassi
,
S.
, and
Paurobally
,
M. R.
,
2019
, “
Wave Scattering and Power Flow in Straight-Helical-Straight Waveguide Structure
,”
Int. J. Appl. Mech.
,
11
(
8
), p.
1950075
. 10.1142/S1758825119500753
23.
Uckan
,
Y.
, and
Ang
,
A. H.-S.
,
1971
, “
Numerical Stability in Wave Propagation Problems
,”
Comput. Struct.
,
1
(
4
), pp.
495
510
. 10.1016/0045-7949(71)90027-7
24.
Yong
,
Y.
, and
Lin
,
Y. K.
,
1992
, “
Dynamic Response Analysis of Truss-Type Structural Networks: A Wave Propagation Approach
,”
J. Sound Vib.
,
156
(
1
), pp.
27
45
. 10.1016/0022-460X(92)90810-K
25.
Luongo
,
A.
, and
Romeo
,
F.
,
2005
, “
Real Wave Vectors for Dynamic Analysis of Periodic Structures
,”
J. Sound Vib.
,
279
(
1–2
), pp.
309
325
. 10.1016/j.jsv.2003.11.011
You do not currently have access to this content.