Abstract
This paper discusses the new aspects of the formulation for structural model updates presented by Larsson and Sas at the 10th International Modal Analysis Conference held in San Diego, California in February 1991. First, a closed-form representation of the reduced impedance matrix is presented. It clarifies the issues associated with the range of the excitation frequencies used in model updates. Second, the applicable range of excitation frequencies is considered through an example where low frequency local modes are present. Third, the computational aspects of this algorithm are studied. It is shown that displacement sensitivity vectors corresponding to the virtual loads are critical in the computation of the reduced impedance matrix sensitivity. Finally, applicability of this algorithm for approximate frequency responses in structural optimization is studied. Numerical results are included to illustrate the essence of this formulation.
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Abbreviations
- [B1]:
-
Viscous damping matrix (N × N)
- [B2]:
-
Structural damping matrix (N × N)
- [E]:
-
Impedance matrix (N × N) [E] = [K+i(B 1+ΩB2)−Ω2M]
- F:
-
Forcing vector used for analysis (N × 1)
- G:
-
Measured force vector (N × 1)
- [H]:
-
Receptance matrix (N × N) [H] = [E]−1
- J :
-
Number of independent loading cases
- [K]:
-
Stiffness matrix (N × N)
- K :
-
Number of degrees of freedom where frequency responses are measured
- KT :
-
Total number of responses for which measured data are available
- L :
-
Number of excitation frequencies for each loading case
- [M]:
-
Mass matrix (N × N)
- M :
-
Number of parameters modified for system identification or design optimization
- N :
-
Total number of structural system degrees of freedom in the analysis model
- R :
-
Structural response
- Q :
-
Number of vectors used in the modal analysis
- U :
-
Frequency responses computed analytically
- V :
-
Frequency responses measured in the shake tests
- 0:
-
Status prior to perturbation
- model:
-
Quantities computed by an analysis model
- red:
-
Indicates a reduced system obtained by isolating the measuredK degrees of freedom
- test:
-
Quantities measured in the vibration tests
- ~:
-
Approximate quantity
References
Larsson, P.O.; Sas, P. 1992: Model updating based on forced vibration testing using numerically stable formulations.Proc. 10th IMAC (held in San Diego, CA)
Miura, H.; Chargin, M.K. 1991: New approximations of frequency response for structural synthesis and parameter identification.Proc. 9th Int. Modal Analysis Conf. and Exhibit (held in Florence, Italy)
Thomas, H.; Shyy, Y.K.; Lieva, J. 1994: Improved approximation for frequency response of damped structures.Proc. 35th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf. (held at Hilton Head, SC)
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Miura, H., Chargin, M. Approximation of frequency responses based on Larsson's method. Structural Optimization 10, 9–15 (1995). https://doi.org/10.1007/BF01743690
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DOI: https://doi.org/10.1007/BF01743690