Effects of geometric ratios and fibre orientation on the natural frequencies of laminated composite plates

Abstract

The present investigation aims to examine the influence of geometric ratios and fibre orientation on the natural frequencies of fibre-reinforced laminated composite plates using finite element method based on Yang’s theory and his collaborators. The transverse shear and rotatory inertia effects were taken into consideration in the developed Fortran computer program. It has been shown that the use of first-order displacement field provides the same accuracy as higher-order displacement field when the number of elements representing the plate structure is increased (refined mesh). However, poor precision may appear for plates with high thickness-to-side ratio h/a (thickness/side length). This discrepancy limits the application of the developed theory to thick plates (h/a<0.5). The various curves show the evolution of the dimensionless frequency (w*) versus fibre orientation angle (q) and illustrate the apparition of a “triple-point” phenomenon engendered by the increase of the plate aspect ratio a/b (length/width) for a specific value of h/a. This point defines the maximum natural frequency and the associated fibre orientation. Also, results show that for high and/or low aspect ratios, the triple-point phenomenon does not occur. This latter is rapidly reached for thick plates than thin plates when the plate aspect ratio a/b is progressively increased.

 Keywords: composite plates, dimensionless frequency, fibre orientation, finite element method, geometric ratios, triple-point.