Stability behavior of variable stiffness composite panels under periodic in-plane shear and compression

Dynamic stability characteristics of variable stiffness composite plates under periodic in-plane loads are investigated here using a shear-deformable sixteen-node plate bending element. The modal transformation technique is used to reduce the equations of motion for the flexural vibration problem of a rectangular panel into a set of Mathieu-Hill equations. The diagonal and off-diagonal dominance of the parametric coefficient matrix is studied for the representative cases of in-plane loading, i.e., periodic compression/shear in presence or absence of static compression for the isotropic and composite plates. The multi-modal response (participating and accompanying modes) of the shear panels under periodic edge traction is demonstrated through the time history analysis. Then, the method of multiple scales is used to identify the dynamic instability regions corresponding to the simple (single mode flexural vibration) or combination (two mode flexural vibrations) type of resonances in various (isotropic and laminated composite made of straight or curvilinear fibers) shear panels, for which results are not available in the literature.