Modeling and visualization of laser-based three-dimensional experimental spatial dynamic response

Abstract

Experimental spatial dynamics modeling is a new approach to dynamics modeling using high-spatial-density experimental data from a scanning laser Doppler vibrometer (LDV). This instrument measures the surface velocity of vibrated structures. Time-signal data from the LDV is statistically modeled with multiple linear regression for harmonically excited structures. A weighted least-squares discrete finite element formulation is developed to solve for the complex-valued continuous 3-D velocity response field from sampled velocity data. The formulation is derived from the steady-state solution of the differential equation with spatial and temporal components of harmonic structural dynamic response. Linear, quadratic, cubic, and cubic B-spline basis functions are used to form isoparametric finite elements in the dynamic response model. Velocity measurements acquired from multiple positions are transformed into a single model that minimizes the least-squares error between the experimental data and the field equations in the 3-D shell element model. A multiple point nonlinear registration algorithm is developed to determine position and orientation of the LDV relative to the test structure. Polygonal shape models are successfully integrated with the experimental spatial dynamic response models via polygon ray intersection. Finite element shape models are generated from simple flat surfaces or extracted from existing finite element models of 3-D structures.

By postprocessing the model solution, many dynamic properties including rotations, full-field strains and stresses, and acoustic prediction are derived from the dynamic response representation. Visualization software was developed for animation of the 3-D spatial dynamic response models with superimposed color to represent the postprocessed results. The interactive graphics allow presentation and investigation of the experimental spatial dynamics.

To examine the method, an analytical test model is defined to simulate the surface velocity response of a structure with both in-plane and out-of-plane harmonic vibration. Random and uniformly spaced measurements of the simulated dynamic system are acquired from multiple locations. Applications of experimental spatial dynamics modeling, postprocessing, and visualization are also demonstrated with five different test structures. Through mesh refinement, increase in order of the basis functions, and additional sampling, the finite element models are converged to statistically qualified solutions.