A WEIGHTED LEAST-SQUARES DISCRETE FINITE ELEMENT FORMULATION FOR MODELING THREE-DIMENSIONAL VELOCITY RESPONSE FIELDS MEASURED BY A LASER DOPPLER VIBROMETER
✍ Scribed by David E. Montgomery; Robert L. West
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 604 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0888-3270
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✦ Synopsis
This paper reports initial results on the development of spatial dynamic response models derived from scanning laser Doppler vibrometer (LDV) velocity measurements. A weighted least squares discrete non-parametric finite element formulation is developed to reconstruct the magnitude and phase of the three-dimensional (3-D) complex dynamic response field. A fundamental concept in the formulation is that the steady-state solution for the structural dynamic response contains separable spatial and temporal components of the structure's dynamics. Therefore, the steady-state dynamic response is modeled as a spatially continuous 3-D complex velocity field. The least-squares formulation minimises the difference between the measured velocity and the dynamic response field equations. Linear, quadratic, and cubic basis functions are used to define finite elements to model the continuous 3-D dynamic response fields. The 'effective' dynamic stiffness (or mechanical impedance) matrices are developed for each element as well as the 'effective' nodal forces.
To examine the method, analytical test models are defined to simulate the surface velocity response of structures with both in-plane and out-of-plane harmonic vibration. Random and uniformly spaced measurements of the simulated dynamic systems are acquired from four locations relative to the structure. In one case, 'noise' is added to the test data set. Application of the weighted least-squares discrete finite element formulation is demonstrated with experimental data acquired by scanning a vibrating composite plate with a LDV. Although the single frequency excitation force on the plate is primarily out-of-plane, evidence of in-plane response is demonstrated by the modal solution.