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21 ·¹ÀÌ¶óÀÌ Áö¼ö¹ý(Rayleigh Quotient Method)
[211] Irons, B. and Ahmad, S., 1980, Techniques of Finite Elements, Ellis
Horwood Ltd., Chichester, England, [114]
pp. 360~361.
[212] Wang, B. P., and Pilkey, W. D., June 1986, "Eigenvalue Reanalysis
of Locally Modified Structures Using a [114]
Generalized Rayleigh's Method," AIAA Journal, Vol. 24, No. 6,
pp. 983~990.
[213] Pilkey, W. D., and Schramm, U., Jan.1995, "Reanalysis of Free
Vibrations Considering the Frequency
[114] Dependency of
the Structural Matrices," The International Journal of Analytical and
Experimental Modal
[114] Analysis, Vol.19,
No. 1, pp. 53~68.
[214] Carne, T. G. and Dohrmann, C. R., 1998, "Support Conditions,
Their Effect on Measured Modal
[114] Parameters,"
Proceedings of the 16th International Modal Analysis Conference, pp. 477~483.
[215] W. M. To and D. J. Ewins, 1990, "Structural Modification Analysis
Using Rayleigh Quotient Iteration," Int. J.
[114] Mech. Sci., Vol.
32, No. 3, pp. 169179. 





22 ¼·µ¿¹ý(Perturbation Method)
[221] Rayleigh, B., 1945, The Theory of Sound, Vol.1, Dover, New York,
pp.109118, pp. 214217.
[222] Chen, J. C. and Wada, B. K., Aug.1977, "Matrix Perturbation
for Structural Dynamic Analysis," AIAA
[114] Journal, Vol.
15, No. 8, pp. 1095~1100.
[222.5] Chon SuHuan, Liu YingLi, Huang DunPu, "A Matrix Perturbation
of Vibration Modal Analysis," IMAC
[222.6] M. S. Eldred, P. B. Lerner and W. J. Anderson, 1992, "Higher
Order Eigenpair Perturbations," AIAA
[114] Journal, Vol.
30, No 7, pp.18701875.
[223] Ravi, S. S. A., Kundra, T. K. and Nakra, B. C., 1998, "Reanalysis
of Damped Structures Using the Single
[114] Step Perturbation
Method," Journal of Sound and Vibration, Vol. 211, No. 3, pp. 355~363.
[224] Eldred, M. S., Lerner, P. B., and Anderson, W. J., July.1992, "Higher
Order Eigenpair Perturbations," AIAA
[114] Journal, Vol.
30, No. 7, pp.1870~1876.
[225] Chen, J. Y., Liu, J. K., and Zhao, L. C., 1995, "An Improved
Perturbation Method for Free Vibration
[114] Analysis,"
Journal of Sound and Vibration, Vol. 180, No. 3, pp. 519~523.
[226] Zhenhua, L. and Zhendong, F., 1988, "The Optimal Structural
Modification Principle for The Maximum
[114] Shifts of Natural
Vibration Frequencies," Proceedings of the 6th International Modal
Analysis Conference,
[114] pp.1107~1111.
[227] Kelly, W. J., and Stevens, K. K., 1989, "Application of Perturbation
Techniques to the Modal Analysis of a
[114] Shaft With Added
Viscoelastic Damping," Proceedings of the 7th International Modal Analysis
[114] Conference, pp.
45~51.
[228] Kim, K. O., Anderson, W. J. and Sandstrom, R. E., 1983, "Nonlinear
Inverse Perturbation Method in
[114] Dynamic Analysis,"
AIAA Journal, Vol. 21, No. 9, pp. 1310~1316. See [815].
[229] Paulo C. Kaminski, 1993, "Determination of Eigenvalues of Modified
Structures Using the First Order
[114] Perturbation Method
and the Rayleigh's Quotient:  A Comparative Study," IMAC 11, pp. 11811187. 





23 ¹Î°¨µµ ÇØ¼®¹ý(Sensitivity Analysis Method)
Original Formulations
[231] Fox, R. L. and Kapoor, M. P., 1968, "Rates of Change of Eigenvalues
and Eigenvectors," AIAA Journal,
[114] Vol.6, No.12,
pp. 2426~2429.
[232] Rogers, L. C., 1970, "Derivatives of Eigenvalues and Eigenvectors,"
AIAA Journal, Vol. 8, No. 5, pp.
[114] 943~944.
[233] Rudisill, C. S., 1974, "Derivatives of Eigenvalues and Eigenvectors
for a General Matrix," AIAA Journal,
[114] Vol. 12, No. 5,
pp. 721~722.
[234] Haug, E. J. and Choi, K. K., 1984, "Structural Design Sensitivity
Analysis with Generalized Global Stiffness
[114] and Mass Matrices,"
AIAA Journal, Vol. 22, No. 9, pp.1299~1303.
[235] Haug, E. J., Choi, K. K. and Komkov, V., 1986, Design Sensitivity
Analysis of Structural System, Academic
[114] Press.
[236] Yoon, B. G. and Belegundu, A. D., 1988, "Iterative Methods
for Design Sensitivity Analysis," AIAA Journal,
[114] Vol. 26, No. 11,
pp. 1413~1415. 





Higher Order Sensitivity
[237] Belle, H. V., 1982, "Higher Order Sensitivities in Structural
Systems," AIAA Journal , Vol. 20, No. 2, pp.
[114] 286~288.
[237.5] Peng Zemin, Song Jianwei, 1986, "Invariant Theorem of Relative
Sensitivity Summation and Higher
[114.5] Order Sensitivity
Analysis Applied to Structural Modification," IMAC 4, pp. 6674.
[238] Jankovic, M. S., 1988, "Analytical Solutions for the Nth Derivatives
of Eigenvalues and Eigenvectors for a
[114] Nonlinear Eigenvalue
Problem," AIAA Journal, Vol. 26, No. 2, pp. 204~205.
[239] Brandon, J. A., 1991, "SecondOrder Design Sensitivities to
Assess the Applicability of Sensitivity
[114] Analysis,"
AIAA Journal, Vol. 29, No. 1, pp. 135~139.
[2310] Zeng, X., Zhang, K., and Yang, J., 1998, "A New Dynamic Reanalysis
Method for Large Structure
[114] Modification,"
Proceedings of the 16th International Modal Analysis Conference, pp. 1598~1601.






Eigenvector Sensitivity
[2311] Nelson, R. B., 1976, "Simplified Calculation of Eigenvector
Derivatives," AIAA Journal, Vol. 14, No. 9, pp.
[1114] 1201~1205.
[2312] Lim, K. B., Juang, J. N. and Ghaemmaghami, P., 1989, "Eigenvector
Derivatives of Repeated Eigenvalues
[1114] Using Singular
Value Decomposition," Journal of Guidance, Vol. 12, No. 2, pp. 282~283.
[2313] Wang, B. P., 1991, "Improved Approximate Methods for Computing
Eigenvector Derivatives in Structural
[1114] Dynamics,"
AIAA Journal, Vol. 29, No. 6, pp.1018~1020.
[2314] Sutter, T.R., Camarda, C. J., Walsh, J. L. and Adelman, H. M.,
1988, "Comparison of Several Methods for
[1114] Calculation Vibration
Mode Shape Derivatives," AIAA Journal, Vol. 26, No. 12, pp. 1506~1511.
[2315] Alvin, K. F., 1997, "Efficient Computation of Eigenvector
Sensitivities for Structural Dynamics," AIAA
[1114] Journal, Vol.
35, No. 11, pp. 1760~1766.
[2316] Zhang, D. W. and Wei, F, S., 1997, "Efficient Computation
of Many Eigenvector Derivatives Using
[1114] Dynamic Flexibility
Method," AIAA Journal, Vol. 35, No. 4, pp.712~718.
[2317] Zhang, O. and Zerva, A., 1997, "Accelerated Iterative Procedure
for Calculating Eigenvector Derivatives,"
[1114] AIAA Journal,
Vol. 35, No. 2, pp. 340~348. 





Repeated Eigenvalue Sensitivity
[2318] Chen, T. Y., 1993, "Design Sensitivity Analysis for Repeated
Eigenvalues in Structural Design," AIAA
[1114]
Journal, Vol. 31, No.12, pp. 2347~2350.
[2818.5] KiOok Kim, 1987, "Modal Design Sensitivities for Multiple
Eigenvalues," AIAA Journal Review
[1114.5]
Manuscript.
[2818.6] Gene J. W. Hou, Sean P. Kenny, September 1992, "Eigenvalue
and Eigenvector Approximate Analysis
[1114.6]
for Repeated Eigenvalue Problems,"
AIAA Journal, Vol. 30, No. 9, pp. 23172324. 





Applications
[2319] Raju, K. K., Rao, G. V. and Venugopal, N., 1989, "Use of Design
Sensitivity Coefficients for Prediction of
[1114]
Structural Behavior after Design Modification,"
Computers & Structures, Vol. 33, No. 5, pp. 1329~1331.
[2320] Rizai, M. N. and Bernard, J. E., 1987, "An Efficient Method
to Predict the Effect of Design Modifications,"
[1114]
Journal of Mechanisms, Transmissions,
and Automation in Design, Vol. 109, pp. 373~384.
[2321] Patrick, G. B. and Wei, T. S., 1990, "Practical Sensitivity
Analysis," Proceedings of the 5th International
[1114]
Modal Analysis Conference, pp. 2125.
[2322] AiQun, L., and Debao, L., 1990, "Using Experimental Modal
Analysis to A Shell Structural Dynamic
[1114]
Modification," Proceedings of the
8th International Modal Analysis Conference, pp. 972~978.
[2323] Wang, J., Heylen, W. and Sas, P., 1987, "Accuracy of Structural
Modification Techniques," Proceedings
[1114]
of the 5th International Modal Analysis
Conference, pp. 65~71.
[2324] Heo, J. H. and Ehmann, K. F., 1991, "A Method for Substructural
Sensitivity Synthesis," Journal of
[1114]
Vibration and Acoustics, Vol. 113, pp.
201~208.
[2325] YuanFang Chou, JengShyong Chen, 1985, "Structural Dynamics
Modification Via Sensitivity Analysis,"
[1114]
IMAC 3, pp. 483489.
[2326] She Shaohua, LiuRuiyan, 1988, "Sensitivity Analysis and Optimization
for the Modal Parameters of
[1114]
Structural Vibration," IMAC 6, pp.
966972.
[2327] Ju, J. and Xu, Z., 1989, "The Multiterms Sensitivity Analysis
of Structure Modification," IMAC 7, pp. 584
[1114]
588.
[2328] Tang Xiao Bing, Zhang Kai Yin, 1993, "Sensitivity Analysis
of Structural Dynamic Behavior," IMAC 11, pp.
[1114]
913916.
[2329] ChangZhi Wu, Xia Xu and Hua Yan, 1993, "A Research for Analytical
Method of Dynamic Optimization
[1114]
Design in the Structure System of Machine
Tools," IMAC 11, pp. 12121216.
[2330] Itsurou Kajiwara, Akio Nagamatsu, 1993, "Optimum Design of
Structure by Sensitivity Analysis," IMAC 11,
[1114]
pp. 883889.
[2331] ChienHuan Chu, John A. Cafeo, 1994, "Design Modification
with Experimental Based Structural
[1114]
Models," IMAC 12, pp. 16661672.
[23misc] Miscellaneous papers on eigenvalue and eigenvector sensitivities. 





24 ¸ðµå ÇÕ¼º¹ý (Modal Synthesis Method)
Eigenvalue Upper Bound and Lower Bound
[241] Ram, Y. M., Braun, S. G. and Blech, J., 1988, "Structural Modifications
in Truncated Systems by the
[1114 RayleighRitz Method,"
Journal of Sound and Vibration, Vol. 125, No. 2, pp. 203~209.
[242] Ram, Y. M. and Braun, S. G., 1990, "Upper and Lower Bounds
for the Natural Frequencies of Modified
[1114 Structures Based
on Truncated Modal Testing Results," Journal of Sound and Vibration,
Vol. 137, No. 1,
[1114 pp. 69~81.
[242.5] Ram, Y. M., Braun, S. G. and Blech, J., 1990, "Structural
Dynamic Modifications Using Truncated Data:
[111.54 Bounds for the
Eigenvalues," Mechanical Systems and Signal Processing, Vol. 4, No.
1, pp. 39~52.
[243] Tse, C. C. and Liao, J. Y., 1993, "A Comparison of Error Bounds
for Eigenvalues in Structural Modification
[1114 Problems,"
Mechanical Systems and Signal Processing, Vol. 7, No. 3, pp. 273~279.
[244] Ram, Y. M. and Braun, S. G., 1993, "Eigenvector Error Bounds
and Their Applications to Structural
[1114 Modification,"
AIAA Journal, Vol. 31, No. 4, pp. 759~764. 





Applications
[245] Wang, B. P., 1987, "Structural Dynamic Optimization Using Reanalysis
Technique," The International
[1114
Journal of Analytical and Experimental Modal Analysis,
Vol. 2, No. 1, pp. 50~58.
[246] Wang, W., Zhang, Q., Allemang, R. J. and Brown, D. L., 1990, "Optimization
of Structural Redesign With
[1114
Dynamic Constraints," Proceedings of the 8th
International Modal Analysis Conference, pp. 946~953.
[246.5] Hiroshi Kanda, Max L. Wei, Randall J. Allemant and David L. Brown,
1986, "Structural Dynamic
[111.64
Modifications Using Mass Additive Technique,"
IMAC 4, pp. 691699.
[246.6] Lec. Zhang Jie, Chen Kechen and Xu Zhandi, 1988, "Structural
Dynamic Optimal Design Using Modal
[111.64
Model," IMAC 6, pp.
15251529.
[247] Ram, Y. M. and Braun, S., 1987, "On Structural Modifications
in Truncated System," Proceedings of the
[1114
5th International Modal
Analysis Conference, pp. 1550~1556.
[248] Xiuqing, H. and Ku, C. H., 1992, "Modal Analysis and Structural
Dynamics Modification for Vibration of
[1114
TrialProduce Vehicle,"
Proceedings of the 10th International Modal Analysis Conference, pp. 863~869.
[248.5] Y. Gallo, P. Level and Y. Ravalard, 1992, "Modal Reanalysis
with Improvement of Initial Modelization. A
[111.54
New Development in Structural
Modification," IMAC 10, pp. 11671172. 





Beam Applications
[249] John C. O'Callahan, ChaurMing Chou, 1985, "Structural Dynamics
Modification Using Generalized Beam
[1114
Mass and Stiffness
Matrices," IMAC 3, pp. 477482.
[2410] K. B. Elliott, L. D. Mitchell, 1987, "Structural Modification
Utilizing Beam Elements," IMAC 5, pp. 956965.
[2411] T. K. Kundra, B. C. Nakra, 1987, "System Modification via
Identified Dynamic Models," IMAC 5, pp. 7985.
[2412] R. R. Lin, A. B. Palazzolo, R. M. Alexander, C. H. Gerhold, 1987,
"Beam Modifications of Structural
[11124
Systems Utilizing
the Receptance Approach with Static Flexibility," IMAC 5, pp. 15571564.
[2413] K Jayaraman, Robert Reiss, 1987, "Frequency Optimization of
Repetitive Lattice BeamLike Structure
[11124
Using a Continuum Model," IMAC 5, pp. 15651572.
[2414] M. M. Tayeb, E. J. Williams, 1986, "Rib Stiffeners for Use
in Structural Dynamics Modification," IMAC 4,
[11124
pp. 10941099.
[2415] J. Zeischka, 1989, "A Modification of the Classical Beam Element
for Improved Dynamic Analysis," IMAC
[11124
7, pp. 243245.
[2416] Wallack, P., Skoog, P., and Richardson, M., 1989, "Comparison
of Analytical and Experimental Rib
[11124
Stiffener Modifications to A Structure," Proceedings of the 7th International
Modal Analysis Conference,
[11124
pp. 965~973.
[2417] Cafeo, J. A., Trethewey, M. W. and Sommer III, H. J., 1995, "Beam
Element Structural Dynamics
[11124
Modification Using Experimental Modal Rotational Data," Journal of
Vibration and Acoustics, Vol. 117,
[11124
pp. 265~271.
[2418] Brian J. Schwarz, Mark H. Richardson, 1997, "Structural Modifications
Using Higher Order Elements,"
[11124
IMAC 15, pp. 313318
[2419] Keng C. Yap, David C. Zimmerman, 1998, "A Comparison of Structural
Dynamic Modification and
[11124
Sensitivity Method Approximation," IMAC 16, pp. 14091415. 





25 Dual Modal Space Method (DMSM)
Applications
[251] Luk, Y. W. and Mitchell, L. D., 1983, "System Modeling and
Modification Via Modal Analysis," Proceedings
[1114
of the 1st International Modal Analysis Conference, pp. 423~429.
[252] Luk, Y. W. and Mitchell, L. D., 1984, "Implementation of the
Dual Modal Space Structural Modification
[1114
Method," Proceedings of the 2nd International Modal Analysis Conference,
pp. 930~936.
[253] Luk, Y. W. and Mitchell, L. D., 1984, "Analytical and Geometric
Substructuring via Dual Modal Space
[1114
Structural Modification," Proceedings of the 2nd International Modal
Analysis Conference2, pp. 50~57.
[253.5] Peter Wallack, Paul Skoog, and Mark Richafdson, 1988, "Simultaneous
Structural Dynamics
[111.54
Modification (S2DM)," IMAC 6, pp. 10331038.
[254] Deel, J, C. and Luk, Y. W., 1985, "Modal Testing Considerations
For Structural Modification Applications,"
[1114
Proceedings of the 3rd International Modal Analysis Conference, pp. 46~52.
[255] Elliot, K. B., and Mitchell, L. D., 1985, "Realistic Structural
Modification: Part I Theoretical Development,"
[1114
Proceedings of the 3rd International Modal Analysis Conference, pp. 471~476. 





Modal Truncation Error
[256] Elliott, K. B. and Mitchell, L. D., 1987, "The Effect of Modal
Truncation on Modal Modification,"
[1114
Proceedings of the 5th International Modal Analysis
Conference, pp. 72~78.
[257] Avitabile, P. and O'Callahan, J. C., 1991, "Understanding Structural
Dynamic Modification and the Effects
[1114
of Truncation," The International Journal of
Analytical and Experimental Modal Analysis, Vol. 6, No. 4, pp.
[1114
215~235.
[258] Stephan C. Ulm, 1986, "Investigations into the Effective Use
of Structural Modification," IMAC 4, pp. 1279
[1114
1286. 





26 ±¹ºÎ ±¸Á¶ º¯°æ¹ý(Localized Modification Method)
[261] Weissenburger, J. T., 1968, "Effect of Local Modifications
on the Vibration Characteristics of Linear
[1114
Systems," Journal of
Applied Mechanics, Vol. 35, pp.327~332.
[262] Pomazal, R. J. and Snyder, V. W., 1971, "Local Modifications
of Damped Linear Systems," AIAA Journal,
[1114
Vol. 9, No. 11, pp. 2216~2221.
[262.5] Moraux D., Level P. and Ravalard Y., 1993, "Efficient Methods
for Predicting the Effects of Modification
[111.54
on the Dynamic Behavior
of Structures," IMAC 11, pp. 11751180.
[263] Hallquist, J. and Snyder, V. W., 1973, "Synthesis of Two Discrete
Vibratory Systems Using Eigenvalue
[1114
Modification," AIAA
Journal, Vol. 11, No. 2, pp. 247~249.
[264] Hallquist, J. O. and Snyder, V. W., 1974, "On the Connection
of Viscously Damped Continuous Vibratory
[1114
Systems," Journal of
Sound and Vibration, Vol. 32, No. 1, pp.131~142.
[265] Hallquist, J. and Snyder, V., 1973, "Synthesis of Two Discrete
Vibratory Systems Using Eigenvalue
[1114
Modification," AIAA
Journal, Vol. 11, No. 2, pp. 247~249.
[266] Hallquist, J. O., 1976, "An Efficient Method for Determining
the Effects of Mass Modifications in Damped
[1114
Systems," Journal of
Sound and Vibration, Vol. 44, No. 3, pp. 449~459.
[267] O'Callahan, J. C. and Chou, C. M., 1984, "Study of A Structural
modification Procedure with Three
[1114
Dimensional Beam Elements
using A Local Eigenvalue Modification Procedure," Proceedings of the
2nd
[1114
International Modal Analysis
Conference, pp. 945~952.
[268] Ram, Y. M. and Blech, J. J., 1991, "The Dynamic Behavior of
a Vibratory System after Modification,"
[1114
Journal of Sound and Vibration,
Vol. 150, No. 3, pp. 357~370.
[269] Wang, B. P., 1985, "The Limitation of Local Structural Dynamic
Modification," Proceedings of the 3rd
[1114
International Modal Analysis
Conference, pp. 53~58.
[269.5] Sun Zhijian , Wang Xiaogang and Xu Xia, 1992, "An effective
Solution Method For Local Modifications of
[111.54
Damped Linear System,"
IMAC 10, pp.11081112.
[2610] Kashiwagi, M., Hirai, I., Katayama, T. and Pilkey, W. D., 1993,
"Sturm Sequence Recurrence Formula for
[11104
Eigensolution of Locally
Modified Systems," Finite Elements in Analysis and Design , Vol.12,
pp. 31~36.
[2611] Kashiwagi, M., Hirai, I., Ohwaki, S. I. and Pilkey, W. D., 1991,
"Stable Eigensolution of Locally Modified
[11104
Systems Based on the Sturm
Sequence Property," Finite Elements in Analysis and Design, Vol.9,
pp.
[11104
133~139. 





27 ¶ó±×¶ûÁö ½Â¼ö¹ý(Lagrange Multiplier Method)
[271] Dowell, E. H., 1971, "Free Vibrations of a Linear Structure
with Arbitrary Support Conditions," Journal of Applied Mechanics, pp.
595~600.
[272] Dowell, E. H., 1972, "Free Vibrations of an Arbitrary Structure
in Terms of Component Modes," Journal of Applied Mechanics, pp. 727~732.
[273] Dowell, E. H., 1979, "On Some General Properties of Combined
Dynamical Systems," Journal of Applied Mechanics, Vol. 46, pp. 206~209.
[274] Dowell, E. H., 1980, "Bounds on Modal Damping by a Component
Modes Method Using Lagrange Multipliers," Journal of Applied Mechanics,
Vol. 47, pp. 211~213.
[275] Tongue, B. H. and Dowell, E. H., 1983, "Component Mode Analysis
of Nonlinear, Nonconservative Systems," Journal of Applied Mechanics,
Vol. 50, pp. 204~209.
[275.5] Dowell, E. H., 1982, "Component Mode Analysis of a Simple
Nonlinear, Nonconservative Systems," Journal of Sound and Vibration,
Vol. 80, No.2, pp. 204~209.
[276] Dowell, E. H., 1987, "Theory and Application of Dynamic Decoupling
in Structural Analysis: Another View," Finite Elements in Analysis
and Design, Vol. 3, pp. 119~125.
[277] Hallquist, J. and Snyder, V. W., 1973, "Linear Damped Vibratory
Structures with Arbitrary Support Conditions," Journal of Applied Mechanics,
pp. 312~313.
[278] Howell, L. J., 1975, "Effects of Constraint Modification on
the Random Vibration of Damped Linear Structures," General Motors Corporation,
Warren, Mich., pp. 685~687.
[279] Hu, L. J., Smith, I., and Chui, Y. H., 1994, "Vibration Analysis
of Ribbed Plates with a Rigid Intermediate Line Support," Journal of
Sound and Vibration, Vol. 178, No. 2, pp. 163~175.
[2710] Zeng, Z., Huang, T. and Hamilton, J. F., 1990, "An Effective
Approach to Determine Natural Frequencies and Mode Shapes of Constrained
Beams Using Lagrange Multipliers," The International Journal of Analytical
and Experimental Modal Analysis, Vol. 5, No. 2, pp. 109~114.
[2710.5] Zeng Ziping, Huang Tian, James F. Hamilton, 1988, "An Effective
Approach to Determine Natural Frequencies and Mode Shapes of Constrained
Beams Using Lagrange Multipliers," IMAC 6, pp. 15091512. 






