Abstract
We considered a numerical modeling technique called ‘large mass method’ or large mass model, which is used for a dynamic problem of a structure that is subjected to support or ground acceleration time history. Since its analytic background has not been extensively verified yet, this paper extends the previous analysis for a single degree-of-freedom system to that for the multi-degree-of-freedom springmass system to present theoretical effectiveness or rigorous comprehension of the technique. The theorems are discussed and checked by using the concept of quasi-static decomposition with simple examples. The analysis shows that the characteristics of LM model for single DOF system are conserved consistently even in multi-DOF system and that the response of LM model for spring-mass system is also composed of quasi-static part and dynamic part like the response of an original spring-mass model. Numerical tests for multi-degree-offreedom spring-mass systems show that they match well with the present analysis.
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References
R. D. Mindlin and L. E. Goodman, Beam vibrations with time-dependent boundary conditions, Journal of Applied Mechanics, ASME, 17 (1950) 377–380.
P. Léger, I. M. Idé and P. Paultre, Multiple-support seismic analysis of large structures, Computers & Structures, 36(6) (1990) 1153–1158.
R. W. Clough and J. Penzien, Dynamics of structures, 2nd ed., McGraw-Hill, Singapore (1993).
C. C. Flanigan, Accurate enforced motion analysis using MSC/NASTRAN superelements, MSC/NASTRAN World Users Conference, Orlando, Florida, USA (1994) 1–15.
D. Haberman, CSI ANSYS Tip of the Week: “Sine-Sweep” test simulation in ANSYS using the large-mass and directdisplacement methods (2000).
MSC/NASTRAN User’s Guide, V70 Advanced Dynamic Analysis (2002).
E. A. Paraskevopoulos, C. G. Panagiotopoulos and G. D. Manolis, Imposition of time-dependent boundary conditions in FEM formulations for elastodynamics: critical assessment of penalty-type methods, Comput Mech., 45 (2010) 157–166.
J. Zhang, Z. Mu and M. Gan, Study of the analysis methods of wave-passage effect based on ABAQUS, Advanced Materials Research, 163–167 (2011) 4316–4319.
F. Bai, J. Liu and L. Li, Elasto-plastic analysis of large span reticulated shell structure under multi-support excitations, Advanced Materials Research, 446–449 (2012) 54–58.
J. T. Chen, H.-K. Hong, C. S. Yeh and S. W. Chyuan, Integral representation and regularization for a divergent series solution of a beam subjected to support motions, Earthquake Engineering and Structural Dynamics, 25 (1996) 909–925.
Y.-W. Kim and M. J. Jhung, Mathematical analysis using two modeling techniques for dynamic responses of a structure subjected to a ground acceleration time history, Nuclear Engineering and Technology, 43(4) (2011) 361–374.
L. Meirovitch, Elements of vibration analysis, McGraw-Hill, New York (1975).
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Recommended by Associate Editor Kyung-Soo Kim
Yong-Woo Kim is currently Professor at Department of Mechanical Engineering at Sunchon National University in Sunchon, Korea. Dr. Kim’s research interests include structural analysis, machine design and tire mechanics.
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Kim, YW., Jhung, M.J. A study on large mass method for dynamic problem of multiple degree-of-freedom system excited by ground acceleration time history?. J Mech Sci Technol 28, 25–41 (2014). https://doi.org/10.1007/s12206-013-0941-x
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DOI: https://doi.org/10.1007/s12206-013-0941-x