Abstract

This work investigates the effect of elastic support stiffness on the accuracy of moving load identification of Euler–Bernoulli beams. It uses the angular velocity response in solving the ill-posed inverse vibration problem and Tikhonov regularization in the load identification process of two moving loads. The effects from moving loads' traveling direction, measurement location arrangements, number of participant measurements, and damping ratios are considered in the studies under noisy disturbance conditions. Results show that the stiffness of the translational rotational springs at the boundaries can impact the accuracy of identified moving loads considerably. Angular velocities presented much better results than accelerations under low stiffness conditions when vertical elastic supports were used. However, acceleration showed better performance when a very soft translational spring was used at one end and a much stiffer translational spring at the other end, as well as when rotational springs with large stiffness were used with simply supported beam conditions. The combination of angular velocities and accelerations provided a balanced solution for a wide range of elastic supports with different stiffnesses.

References

1.

Frýba

,

L.

,

1999

,

Vibration of Solids and Structures Under Moving Loads

,

Thomas Telford

,

London

.

2.

Yang

,

Y. B.

,

Wu

,

Y. S.

, and

Yao

,

Z.

,

2004

,

Vehicle–Bridge Interaction Dynamics With Applications to High-Speed Railways

,

World Scientific

,

London

.

3.

Law

,

S. S.

,

Chan

,

T. H.

, and

Zeng

,

Q.

,

1997

, "

Moving Force Identification: A Time Domain Method

,"

J. Sound Vib.

,

201

(

1

), pp.

1

22

. 10.1006/jsvi.1996.0774

5.

Law

,

S. S.

,

Chan

,

T. H.

, and

Zeng

,

Q.

,

1999

, "

Moving Force Identification—A Frequency and Time Domains Analysis

,"

J. Dyn. Syst. Meas. Control

,

121

(

3

), pp.

394

402

. 10.1115/1.2802487

6.

Law

,

S. S.

, and

Zhu

,

X.-Q.

,

2011

,

Moving Loads-Dynamic Analysis and Identification Techniques (Structures and Infrastructures Book Series, Vol. 8)

,

CRC Press

,

London

.

7.

Karbhari

,

V. M.

, and

Ansari

,

F.

,

2009

,

Structural Health Monitoring of Civil Infrastructure Systems

,

Woodhead Publishing

,

Cambridge

.

8.

Rao

,

S. S.

,

2019

,

Vibration of Continuous Systems

,

John Wiley & Sons

,

New York

.

9.

Qiao

,

G.

, and

Rahmatalla

,

S.

,

2019

, "

Identification of the Viscoelastic Boundary Conditions of Euler–Bernoulli Beams Using Transmissibility

,"

Eng. Rep.

,

1

(

5

), p.

e12074

. 10.1002/eng2.12074

10.

Qiao

,

G.

, and

Rahmatalla

,

S.

,

2020

, "

Dynamics of Euler–Bernoulli Beams With Unknown Viscoelastic Boundary Conditions Under a Moving Load

,"

J. Sound Vib.

, p.

115771

. 10.1016/j.jsv.2020.115771

11.

Froio

,

D.

,

Rizzi

,

E.

,

Simões

,

F. M.

, and

Da Costa

,

A. P.

,

2018

, "

Dynamics of a Beam on a Bilinear Elastic Foundation Under Harmonic Moving Load

,"

Acta Mech.

,

229

(

10

), pp.

4141

4165

. 10.1007/s00707-018-2213-4

12.

Froio

,

D.

,

Rizzi

,

E.

,

Simões

,

F. M.

, and

Da Costa

,

A. P.

,

2018

, "

Universal Analytical Solution of the Steady-State Response of an Infinite Beam on a Pasternak Elastic Foundation Under Moving Load

,"

Int. J. Solids Struct.

,

132

, pp.

245

263

. 10.1016/j.ijsolstr.2017.10.005

13.

Dimitrovová

,

Z.

,

2016

, "

Critical Velocity of a Uniformly Moving Load on a Beam Supported by a Finite Depth Foundation

,"

J. Sound Vib.

,

366

, pp.

325

342

. 10.1016/j.jsv.2015.12.023

14.

Mazilu

,

T.

,

2017

, "

The Dynamics of an Infinite Uniform Euler–Bernoulli Beam on Bilinear Viscoelastic Foundation Under Moving Loads

,"

Procedia Eng.

,

199

, pp.

2561

2566

. 10.1016/j.proeng.2017.09.327

15.

Chan

,

T. H.

, and

Ashebo

,

D. B.

,

2006

, "

Theoretical Study of Moving Force Identification on Continuous Bridges

,"

J. Sound Vib.

,

295

(

3–5

), pp.

870

883

. 10.1016/j.jsv.2006.01.059

16.

Zhu

,

X.

, and

Law

,

S.

,

2006

, "

Moving Load Identification on Multi-Span Continuous Bridges With Elastic Bearings

,"

Mech. Syst. Sig. Process.

,

20

(

7

), pp.

1759

1782

. 10.1016/j.ymssp.2005.06.004

17.

Qiao

,

G.

, and

Rahmatalla

,

S.

,

2020

, "

Moving Load Identification on Euler–Bernoulli Beams With Viscoelastic Boundary Conditions by Tikhonov Regularization

,"

Inverse Probl. Sci. Eng.

, pp.

1

38

. 10.1080/17415977.2020.1817916

18.

Chen

,

J.

, and

Li

,

J.

,

2004

, "

Simultaneous Identification of Structural Parameters and Input Time History From Output-Only Measurements

,"

Comput. Mech.

,

33

(

5

), pp.

365

374

. 10.1007/s00466-003-0538-9

19.

Pioldi

,

F.

, and

Rizzi

,

E.

,

2016

, "

A Full Dynamic Compound Inverse Method for Output-Only Element-Level System Identification and Input Estimation From Earthquake Response Signals

,"

Comput. Mech.

,

58

(

2

), pp.

307

327

. 10.1007/s00466-016-1292-0

20.

Froio

,

D.

,

Rizzi

,

E.

,

Simões

,

F. M.

, and

da Costa

,

A. P.

,

2020

, "

A True PML Approach for Steady-State Vibration Analysis of an Elastically Supported Beam Under Moving Load by a DLSFEM Formulation

,"

Comput. Struct.

,

239

, p.

106295

. 10.1016/j.compstruc.2020.106295

21.

Inoue

,

H.

,

Kishimoto

,

K.

,

Shibuya

,

T.

, and

Harada

,

K.

,

1998

, "

Regularization of Numerical Inversion of the Laplace Transform for the Inverse Analysis of Impact Force

,"

JSME Int. J. Ser. A Solid Mech. Mater. Eng.

,

41

(

4

), pp.

473

480

. 10.1299/jsmea.41.473

22.

Jacquelin

,

E.

,

Bennani

,

A.

, and

Hamelin

,

P.

,

2003

, "

Force Reconstruction: Analysis and Regularization of a Deconvolution Problem

,"

J. Sound Vib.

,

265

(

1

), pp.

81

107

. 10.1016/S0022-460X(02)01441-4

23.

Choi

,

H.

,

Thite

,

A. N.

, and

Thompson

,

D. J.

,

2006

, "

A Threshold for the Use of Tikhonov Regularization in Inverse Force Determination

,"

Appl. Acoust.

,

67

(

7

), pp.

700

719

. 10.1016/j.apacoust.2005.11.003

24.

Choi

,

H. G.

,

Thite

,

A. N.

, and

Thompson

,

D. J.

,

2007

, "

Comparison of Methods for Parameter Selection in Tikhonov Regularization With Application to Inverse Force Determination

,"

J. Sound Vib.

,

304

(

3–5

), pp.

894

917

. 10.1016/j.jsv.2007.03.040

25.

Mao

,

Y.

,

Guo

,

X.

, and

Zhao

,

Y.

,

2010

, "

A State Space Force Identification Method Based on Markov Parameters Precise Computation and Regularization Technique

,"

J. Sound Vib.

,

329

(

15

), pp.

3008

3019

. 10.1016/j.jsv.2010.02.012

26.

Ding

,

Y.

,

Law

,

S. S.

,

Wu

,

B.

,

Xu

,

G. S.

,

Lin

,

Q.

,

Jiang

,

H. B.

, and

Miao

,

Q. S.

,

2013

, "

Average Acceleration Discrete Algorithm for Force Identification in State Space

,"

Eng. Struct.

,

56

, pp.

1880

1892

. 10.1016/j.engstruct.2013.08.004

27.

González

,

A.

,

Rowley

,

C.

, and

O'Brien

,

E. J.

,

2008

, "

A General Solution to the Identification of Moving Vehicle Forces on a Bridge

,"

Int. J. Numer. Methods Eng.

,

75

(

3

), pp.

335

354

. 10.1002/nme.2262

28.

Asnachinda

,

P.

,

Pinkaew

,

T.

, and

Laman

,

J. A.

,

2008

, "

Multiple Vehicle Axle Load Identification From Continuous Bridge Bending Moment Response

,"

Eng. Struct.

,

30

(

10

), pp.

2800

2817

. 10.1016/j.engstruct.2008.02.018

29.

Clough

,

R. W.

, and

Penzien

,

J.

,

1993

,

Dynamics of Structures

,

McGraw-Hill

,

New York

.

30.

Hansen

,

P. C.

,

2007

, "

Regularization Tools Version 4.0 for Matlab 7.3

,"

Numer. Algorithms

,

46

(

2

), pp.

189

194

. 10.1007/s11075-007-9136-9

31.

Phillips

,

D. L.

,

1962

, "

A Technique for the Numerical Solution of Certain Integral Equations of the First Kind

,"

J. ACM

,

9

(

1

), pp.

84

97

. 10.1145/321105.321114

32.

Tikhonov

,

A. N.

, and

Arsenin

,

V. I. A.

,

1977

,

Solutions of Ill-Posed Problems

,

Winston & Sons

,

New York

.

33.

Wahba

,

G.

,

1990

,

Spline Models for Observational Data (CBMS-NSF Regional Conference Series in Applied Mathematics, 59)

,

SIAM

,

Philadelphia, PA

.

34.

ISO

,

2016

,

8608: 2016 Mechanical Vibration—Road Surface Profiles—Reporting of Measured Data

,

BSI Standards Publication

,

London

.

35.

Van Loan

,

C. F.

,

1976

, "

Generalizing the Singular Value Decomposition

,"

SIAM J. Numer. Anal.

,

13

(

1

), pp.

76

83

. 10.1137/0713009

36.

Hansen

,

P. C.

,

1989

, "

Regularization, GSVD and Truncated GSVD

,"

BIT Numer. Math.

,

29

(

3

), pp.

491

504

. 10.1007/BF02219234

37.

Rao

,

C. K.

, and

Mirza

,

S.

,

1989

, "

A Note on Vibrations of Generally Restrained Beams

,"

J. Sound Vib.

,

130

(

3

), pp.

453

465

. 10.1016/0022-460X(89)90069-2

38.

Register

,

A.

,

1994

, "

A Note on the Vibrations of Generally Restrained, End-Loaded Beams

,"

J. Sound Vib.

,

172

(

4

), pp.

561

571

. 10.1006/jsvi.1994.1198

39.

Kang

,

K.

, and

Kim

,

K.-J.

,

1996

, "

Modal Properties of Beams and Plates on Resilient Supports With Rotational and Translational Complex Stiffness

,"

J. Sound Vib.

,

190

(

2

), pp.

207

220

. 10.1006/jsvi.1996.0057

40.

Li

,

W. L.

,

2000

, "

Free Vibrations of Beams With General Boundary Conditions

,"

J. Sound Vib.

,

237

(

4

), pp.

709

725

. 10.1006/jsvi.2000.3150

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