Determination of lamb wave dispersion data in lossy anisotropic plates using time domain finite element analysis. Part I: theory and experimental verification.

A theoretical and experimental approach for extraction of guided wave dispersion data in plate structures is described. Finite element modeling is used to calculate the surface displacement data (in-plane and out-of-plane) when the plate is subject to either symmetrical or antisymmetrical impulsive force stimulation at one or both of the parallel faces. Fourier transformation of the resultant space-time displacement histories is then employed to obtain phase velocity as a function of frequency. Experimental verification in the case of antisymmetrical stimulation is provided by means of a high-power Q-switched laser source that is used to excite guided waves in the plate. The subsequent out-of-plane displacement data were then obtained by means of a scanning laser vibrometer, and good agreement between theory and experiment is demonstrated. Examples of dispersion data are provided for aluminum, and excellent correlation between the data sets and conventional Rayleigh-Lamb theory for plate structures was obtained. This was then extended to lossy polymeric plates, in addition to both unpolarized and polarized piezoelectric ceramic plates, again with good agreement between the finite element modeling and optical experiments. The last set of results prepares the way for a detailed investigation of the nonhomogeneous piezoelectric composite waveguides described in a companion paper (Part II).

Determination of lamb wave dispersion data in lossy anisotropic plates using time domain finite element analysis. Part II: application to 2-2 and 1-3 piezoelectric composite transducer arrays.

The use of finite element modeling, combined with optical generation and detection of Lamb waves in plate structures, was extended to encompass periodic ceramic-polymer materials typical of those encountered in 1-3 and 2-2 piezoelectric composite array transducers. The resultant dispersion data was employed to predict the occurrence of Lamb wave-induced cross talk in composite monolithic arrays. The finite element modeling method was then used to simulate the dispersion behavior of two array structures that were subsequently manufactured: a 1-D 45% volume fraction linear array coupon and a 2-D 35% volume fraction array coupon. Excellent agreement between theory and experiment was obtained using impedance measurements and laser scans of the surface displacement profile at selected frequencies. Regions of strong inter-element cross-coupling were identified and these are shown to correlate very well with the dispersion data obtained for the dual-phase plate material. This work is considered to provide a useful basis for the design of wideband monolithic composite arrays and minimization of guided wave propagation along the array substrate.