Mechanical Characterization of Engineering Materials by Modal Testing
Doktorsavhandling, 1997

This thesis deals with the use of modal testing for establishing elastic constants of engineering materials and for indicating material variability in terms of stiffness and damping properties. The methodology using modal testing techniques, is applied to timber beams, high strength concrete prisms, wood-based panels (oriented strand board and chipboard), an aluminium alloy panel and plastic laminate panels (high-pressure laminate). Experimental modal information, weighed masses and geometrical measures of the test objects are used together with the appropriate theories and models to determine elastic constants. Theories used are related to the following: free longitudinal, torsional and bending vibrations of beams and bars; free plate bending and in-plane vibrations of panels; and the free vibrations of confined solids. Where closed form solutions do not exist, solutions from finite element analyses (FEA, from available software) are used. Accuracy aspects of the modal test methodology for material characterisation are discussed. For most of the objects, static test results are compared with the dynamically established ones. It is concluded that the Rayleigh-Timoshenko-St. Venant beam theories apply well to the beam-formed materials tested. The results from an approximate solution, presented by Goens in 1931, for the free bending vibrations of free-free Timoshenko beams agree with the results obtained from FEAs. The use of modal testing to evaluate material variability is discussed in conjunction with the curing of concrete and the differences in elastic properties and bending strength of lumber. Two different methods for establishing the four independent elastic constants of thin orthotropic plates are presented. The first method uses plate bending modes and an in-plane mode, while the second method uses only in-plane modes. Values of the elastic moduli are first estimated by using expressions valid for beams after which the values are updated by matching experimental and FEA results. The in-plane Poisson ratio is determined by using specific mode shape values of an in-plane mode. For the in-plane method, the Goens solution was used and reformulated to obtain an initial estimate of the shear modulus. In addition, the Mindlin plate theory was applied to two relatively thin panels to establish the transverse shear moduli. Suggestions for characterizing confined solids are discussed. The results for the concrete prisms when using beam theories are compared with the results from using FEAs of solid models. A discussion of accuracy includes some suggestions for estimating the tolerances in established elastic constants when using modal tests. The divergence between theory and practice for realised boundary conditions is a source of error. A general guide is presented for choosing what theory should be used for a given test object in a rectangular parallelepipedic form. It is then assumed that the direction of the major E modulus coincides with the direction of the length of the object (L > B, L > H).

material variability

modal testing

non-destructive test methods

damping ratios

timber beams

plastic panels

aluminium panel

elastic constants

concrete curing

wood-based panels


high-strength concrete

anisotropic materials


Daniel Larsson

Chalmers, Institutionen för konstruktionsteknik





Publ. - Chalmers tekniska högskola, Institutionen för konstruktionsteknik, Konstruktionsteknisk dynamik. D: 97:4

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 1341