Inverse eigenvalue problems for discrete gyroscopic systems

References

• Meirovitch L. A modal analysis for the response of linear gyroscopic systems. ASME J Appl Mech. 1975;42:446–450.
   Google Scholar
• Meirovitch L. A new method of solution of the eigenvalue problem for gyroscopic systems. AIAA J. 1974;12:1337–1342.
   Google Scholar
• Yuan Y, Dai H. An inverse problem for undamped gyroscopic systems. J Comput Appl Math. 2012;236:2574–2581.
   Google Scholar
• Yuan Y, Guo Y. A direct updating method for damped gyroscopic systems using measured modal data. Appl Math Model. 2010;34:1450–1457.
   Google Scholar
• Mao X, Dai H. Structure preserving eigenvalue embedding for undamped gyroscopic systems. Appl Math Model. 2014;38:4333–4344.
   Google Scholar
• Lancaster P. Stability of linear gyroscopic systems: a review. Linear Algebra Appl. 2013;439:686–706.
   Google Scholar
• Ouyang H, Zhang J. Passive modifications for partial assignment of natural frequencies of mass-spring systems. Mech Syst Signal Process. 2015;50–51:214–226.
   Google Scholar
• Tresser S, Bucher I. Balancing fast flexible gyroscopic systems at low speed using parametric excitation. Mech Syst Signal Process. 2019;130:452–469.
   Google Scholar
• Cooley CG, Parker RG. Eigenvalue sensitivity and veering in gyroscopic systems with application to high-speed planetary gears. European J Mech – A/Solids. 2018;67:123–136.
   Google Scholar
• Lancaster P, Maroulas J. Inverse eigenvalue problems for damped vibrating systems. J Math Anal Appl. 1987;123:238–261.
   Google Scholar
• Lancaster P, Ye Q. Inverse spectral problems for linear and quadratic matrix pencils. Linear Algebra Appl. 1988;107:293–309.
   Google Scholar
• Starek L, Inman DJ, Kress A. A symmetric inverse vibration problem. ASME J Vib Acoust. 1992;114:564–568.
   Google Scholar
• Starek L, Inman DJ. A symmetric inverse vibration problem with over-damped modes. J Sound Vib. 1995;181:893–903.
   Google Scholar
• Starek L, Inman DJ. A symmetric inverse vibration problem for non-proportional underdamped system. ASME J Appl Mech. 1997;64:601–605.
   Google Scholar
• Starek L, Inman DJ. Design of nonproportional damped systems via symmetric positive inverse problems. ASME J Vib Acoust. 2004;126:212–219.
   Google Scholar
• Friswell MI, Inman DJ, Pilkey DF. The direct updating of damping and stiffness matrices. AIAA J. 1998;36:491–493.
   Google Scholar
• Kuo Y-C, Lin W-W, Xu S-F. New methods for finite element model updating problems. AIAA J. 2006;44:1310–1316.
   Google Scholar
• Chu D, Chu MT, Lin W-W. Quadratic model updating with symmetry, positive definiteness, and no spill-over. SIAM J Matrix Anal Appl. 2009;31:546–564.
   Google Scholar
• Yuan Y, Dai H. On a class of inverse quadratic eigenvalue problem. J Comput Appl Math. 2011;235:2662–2669.
   Google Scholar
• Yuan Y, Liu H. A gradient based iterative algorithm for solving structural dynamics model updating problems. Meccanica. 2013;48:2245–2253.
   Google Scholar
• Rogers GS. Matrix derivatives. New York: Marcel Dekker, Inc.; 1980. (Lecture Notes in Statistics; 2).
   Google Scholar
• Wei Y, Zhang N, Ng MK, et al. Tikhonov regularization for weighted total least squares problems. Appl Math Lett. 2007;20:82–87.
   Google Scholar
• Aubin JP. Applied functional analysis. John Wiley & Sons: New York; 1979.
   Google Scholar
• Bai Z-Z. On Hermitian and skew-Hermitian splitting iteration methods for continuous Sylvester equations. J Comput Math. 2011;29:185–198.
   Google Scholar
• Zhou R, Wang X, Zhou P. A modified HSS iteration method for solving the complex linear matrix equation AXB = C. J Comput Math. 2016;34:437–450.
   Google Scholar
• Wang X, Li Y, Dai L. On Hermitian and skew-Hermitian splitting iteration methods for the linear matrix equation AXB = C. Computers and Math Appl. 2013;65:657–664.
   Google Scholar
• Zhou R, Wang X, Tang X-B. Preconditioned positive-definite and skew-Hermitian splitting iteration methods for continuous Sylvester equations AX + XB = C. East Asian J Appl Math. 2017;7:55–69.
   Google Scholar
• Wang X, Li W-W, Mao L-Z. On positive-definite and skew-Hermitian splitting iteration methods for continuous Sylvester equation AX + XB = C. Comput Math Appl. 2013;66:2352–2361.
   Google Scholar
• Albert A. Condition for positive and nonnegative definite in terms of pseudoinverse. SIAM J Appl Math. 1969;17:434–440.
   Google Scholar