Determination of Material Constants Using Experimental Free Vibration Analysis on Anisotropic Plates

Abstract

In this paper, a method is presented which determines anisotropic plate rigidities Dij using vibration data (eigenfreauencies, modeshapes).

The vibration data are experimentally obtained from rectangular testplates with 4 free boundaries. The measured data are compared with the results of an analytical model of the same test plates.

The parameters of this analytical model are the unknown plate rigidities Dij. An eigenvalue problem [Kij]-λ[Mij], in which [Kij] is the stiffness matrix and [Mij] the mass matrix (both based on the mathematical model) can be formulated. The solution of this eigenvalue problem yields eigen- frequencies and modeshapes.

The basic idea of the method is to tune the parameters DJJ until the eigendata, produced by the mathematical model, fit the experimentally obtained eigendata. Although the method works iteratively, no preliminary knowledge of the plate rigidities is required. For orthotropic or isotropic materials, only the resonance frequencies must be measured. The measurement can be carried out fast and accurately with an accelerometer and a spectrum analyzer. For anisotropic materials, also the modeshapes must be measured.

The obtained plate rigidities can be used directly as input data for finite element models, or can be used to calculate engineering elasticity parameters. For layered composite materials with a known stacking sequences it is possible to calculate the dynamic elasticity moduli E₁, E₂, v ₁₂ and G₁₂ of a single lamina from the measured D_ij.