Figure 15: Strain response comparison at an interior location of box-beam by reference and predicted solutions using first six modes for expansion, (a) with 14 sensors, (b) with 24 sensors. CONCLUSION Using a limited set of measured responses, full field displacement can be obtained using an expansion procedure. The measured response can then be used in the finite element recovery process to obtain full field dynamic stress-strain due to any measured loading condition. Several cases were investigated to show the accuracy and robustness of the expansion procedure. The expansion procedure will produce accurate results provided that there are a sufficient set of orthogonal mode shapes to span the space for the solution; this requires that a sufficient number of modes that participate in the response be included in the expansion process. Noise presents variation in the results but from the cases studied, significant noise did not seriously contaminate the results obtained. In terms of the limited set of measurement points, there must be sufficient number of measurement locations available for proper expansion. Use of redundant sensors can be an advantage from a practical perspective; however, use of more sensors does not satisfy the requirement for use of proper number of modes in expansion process. REFERENCES [1] Pingle, P., Avitabile, P., “Prediction of Full Field Dynamic Stress/Strain from Limited Sets of Measured Data”, Proceedings of the Twenty-Eight International Modal Analysis Conference, Jacksonville, FL, Feb 2010 [2] Chipman,C., “Expansion of Real Time Operating Data”, Master’s Thesis, University of Massachusetts Lowell, May 2009 [3] C.Chipman, P.Avitabile, “Expansion of Real Time Operating Data for Improved Visualization”, Proceedings of the Twenty-Sixth International Modal Analysis Conference, Orlando, FL, Feb 2008 [4] C.Chipman, P.Avitabile, “Expansion of Transient Operating Data”, Proceedings of the Twenty-Seventh International Modal Analysis Conference, Orlando, FL, Feb 2009 [5] Guyan, R.J., "Reduction of Stiffness and Mass Matrices", AIAA Journal, Vol. 3, No 2, 1965 [6] Paz, M, "Dynamic Condensation", AIAA Journal, Vol22, No 5, May 1984 [7] O'Callahan,J.C., Avitabile,P., Riemer,R., "System Equivalent Reduction Expansion Process", Seventh International Modal Analysis Conference, Las Vegas, Nevada, February 1989 [8] Kammer, DC, "A Hybrid Approach to Test Analysis Model Development for Large Space Structures", Journal of Vibration and Acoustics, Vol 113, July 1991 [9] Allemang,R.J. and Brown,D.L., "A Correlation Coefficient for Modal Vector Analysis", First International Modal Analysis Conference, Orlando, Florida, November 1982, pp. 110-116 [10] Van Zandt, T., “Development of Efficient Reduced Models for Multi-Body Dynamics Simulations of Helicopter Wing Missile Configurations,” Master’s Thesis, University of Massachusetts Lowell, April 2006. 199
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