This paper clarifies the reason why error occurs in the mass lumping procedure and presents a new approach to construct lumped mass matrices for Euler–Bernoulli beam elements, which contain both translational and rotational degrees of freedom. Lumped mass matrices provide the proper translational inertia but change the rotational inertia compared with the continuous mass representation. Therefore, the optimal lumped mass matrices are expressed through the adoption of a variable rotational inertia parameter to counterbalance the decreased or increased rotational inertia. The goal of this study is to propose lumped mass matrices to minimize the modal error for beam elements. The accuracy of the new mass matrices is validated by a number of numerical tests.
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April 2014
Research-Article
Optimal Lumped Mass Matrices by Minimization of Modal Errors for Beam Elements
Zhanxuan Zuo,
Zhanxuan Zuo
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
Ministry of Education,
School of Civil Engineering,
Harbin Institute of Technology
,Heilongjiang
,Harbin 150090
, China
Search for other works by this author on:
Shuang Li,
Shuang Li
1
Assistant Professor
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
e-mail: shuangli@hit.edu.cn
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
Harbin Institute of Technology
,Heilongjiang
,Harbin 150090
, China
e-mail: shuangli@hit.edu.cn
1Corresponding authors.
Search for other works by this author on:
Changhai Zhai,
Changhai Zhai
1
Professor
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
e-mail: zch-hit@hit.edu.cn
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
Harbin Institute of Technology
,Heilongjiang
,Harbin 150090
, China
e-mail: zch-hit@hit.edu.cn
Search for other works by this author on:
Lili Xie
Lili Xie
Professor
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
Harbin Institute of Technology
,Heilongjiang
,Harbin 150090
, China
Search for other works by this author on:
Zhanxuan Zuo
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
Ministry of Education,
School of Civil Engineering,
Harbin Institute of Technology
,Heilongjiang
,Harbin 150090
, China
Shuang Li
Assistant Professor
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
e-mail: shuangli@hit.edu.cn
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
Harbin Institute of Technology
,Heilongjiang
,Harbin 150090
, China
e-mail: shuangli@hit.edu.cn
Changhai Zhai
Professor
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
e-mail: zch-hit@hit.edu.cn
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
Harbin Institute of Technology
,Heilongjiang
,Harbin 150090
, China
e-mail: zch-hit@hit.edu.cn
Lili Xie
Professor
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
Key Lab of Structures Dynamic and Control,
Ministry of Education,
School of Civil Engineering,
Harbin Institute of Technology
,Heilongjiang
,Harbin 150090
, China
1Corresponding authors.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 26, 2013; final manuscript received November 22, 2013; published online January 16, 2014. Assoc. Editor: Dr. Corina Sandu.
J. Vib. Acoust. Apr 2014, 136(2): 021015 (7 pages)
Published Online: January 16, 2014
Article history
Received:
March 26, 2013
Revision Received:
November 22, 2013
Citation
Zuo, Z., Li, S., Zhai, C., and Xie, L. (January 16, 2014). "Optimal Lumped Mass Matrices by Minimization of Modal Errors for Beam Elements." ASME. J. Vib. Acoust. April 2014; 136(2): 021015. https://doi.org/10.1115/1.4026247
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