A summary of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations in presented. First, a review of the recent studies on the free-vibration analysis of symmetrically laminated plates is given. These studies have been conducted for various geometric shapes and edge conditions. Both analytical (closed-form, Galerkin, Rayleigh-Ritz) and numerical methods have been used. Because of the importance of unsymmetrically laminated structural components in many applications, a detailed review of the various developments in the analysis of unsymmetrical ly laminated beams and plates also is given. A survey of the nonlinear vibrations of the perfect and geometrically laminated plates is presented next. It is seen that due to the bending-stretching coupling, the nonlinear behavior of the unsymmetrically laminated perfect and imperfect plates, depending upon the boundary conditions, may be hardening or softening type. Similar behavior also is observed for imperfect isotropic and laminated plates. Lastly, the developments in studying the wave propagation in laminated materials are reviewed. It is seen that a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials. Some recent studies on the linear and nonlinear transient response of laminated materials also are described.

Recent Advances in Analysis of Laminated Beams and Plates, Part II: Vibrations and Wave Propagation

The propagation of Lamb waves in plates has been the subject of numerous investigations since their postulation by Lamb in 1916 [1,2]. Most of the work in existence deals with various aspects of these guided waves in plates of isotropic materials. Comparatively speaking a limited number of results has appeared in which Lamb or horizontaly polarized SH wave propagation in anisotropic plates has been considered in any detail. For Lamb waves, theoretical analyses have been reported in plates of cubic [3,4], transversely isotropic [5,6], and orthotropic [7,9] media.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1899&context=qnde

Free Wave Propagation in Plates of General Anisotropic Media

In this article, we review the present authors' own approach to elastic wave modeling and experimental measurements in fibrous composites. The materials and structural problem addressed here concerns the propagation of guided elastic leaky waves in continuous-fiber composite plates. The guided wavevector may be oriented along the fibers or in an arbitrary azimuthal direction. These plates can be structured as single-layer or multilayer media, where each successive layer contains fibers in different directions. Further, the multiaxial plates are loaded by a fluid or by different fluids on each boundary. Each of these cases has been investigated both experimentally and theoretically. It is found that some reasonable approximations lead to significant simplifications in treating these complicated structures and yet preserve the accuracy needed to make useful predictions of realistic sound wave behavior. Comparisons of the results of model calculations and experimental measurements of ultrasonic reflection show very good agreement over a wide range of experimental parameters and types of composites. Suggestions are offered at the end of the article for extensions of the modeling to account for non-ideal behavior of the materials and the chosen means of interrogation.

Ultrasonic Reflection and Guided Waves in Fluid-Coupled Composite Laminates

The boundary conditions at free surface of an incompressible, transversely isotropic elastic half-space are satisfied to obtain the reflection coefficients for the case when outer slowness section is re-entrant. Two quasi-shear waves will be reflected for an angular range of direction of incident wave. The numerical illustrations of reflection coefficients are presented graphically for three arbitrary materials.

Wave propagation in an incompressible transversely isotropic fibre-reinforced elastic media

Owing to the dispersive nature and complexity of the Lamb waves generated in a composite plate, the measurement of the phase velocities by using classical methods is complicated. This paper describes a measurement method based upon the spectrum-analysis technique, which allows one to overcome these problems. The technique consists of using the fast Fourier transform to compute the spatial power-density spectrum. Additionally, weighted functions are used to increase the probability of detecting the various propagation modes. Experimental Lamb-wave dispersion curves of multilayered plates are successfully compared with the analytical ones. This technique is expected to be a useful way to design composite parts integrating ultrasonic transducers in the field of health monitoring. Indeed, Lamb waves and particularly their velocities are very sensitive to defects.

http://iopscience.iop.org/article/10.1088/0957-0233/10/5/002/pdf

W.A. Green

Papers

Flexural waves in fibre-reinforced laminated plates