CALCULATING THE DYNAMIC STRAIN TENSOR FIELD USING MODAL ANALYSIS AND NUMERICAL DIFFERENTIATION

Based on vibration response measured at a limited number of points and continuous Hilbert space basis functions combined with spatial differentiation, a new method for strain tensor field assessment, in the frequency domain, is proposed. Essentially, results from hybrid modal analysis (HMA), are transformed from the displacement space to the strain space by use of finite difference schemes. This approach will produce a continuous strain (second order) tensor, except on a number of surfaces where material discontinuities are present. strain analysis (HSA), interpreted as dynamic strain analysis based on HMA, may be done in several ways. The method proposed here is the first realization of HSA and it has been verified by an experimental test case. The predicted results correspond well with measured strain responses. thod is applicable to a vibrating structure, regardless of the material properties of the body. Hence, any possible damping, e.g., material damping, damping in joints between structural parts, etc., need not be known a priori. Moreover, the zero frequency elastic properties and mass distribution of the structure need not be the true ones; any (meaningful) arbitrary values of the elastic properties and mass distribution can be assumed in order to obtain the Hilbert space basis functions. Material inhomogeneities present, i.e., in a piecewise continuous structure, will cause the method (when applied with unknown material properties) to be somewhat inaccurate in the vicinity around the discontinuity. The derived model is valid for a specific excitation, not necessarily known.