Analytical investigations on free vibration response of ferrocement plates

Abstract

The present investigation aims at studying the effect of support conditions, moduli ratio and mesh orientation on free flexural vibration response of ferrocement plates. A test slab of size 838.2 × 838.2 × 24.12 mm has been considered. The finite element analysis uses a ninenoded Lagrangian element employing both consistent and lumped mass formulations. The rigidities are evaluated by using laminated plate theory incorporating Mindlin approach. The moduli ratio (E11/E22) is varied as 1,10, 40 and the orientation is varied as 0°, 15°, 30° and 45°. Four supports arrangements viz. (i) all edges clamped (C-C-C-C), (ii) three edges clamped and one edge simply supported (C-C-C-S), (iii) two opposite edges clamped and other two edges simply supported (C-S-C-S) and (iv) one edge clamped and three edges simply supported (C-S-S-S). The highest frequency is observed for C-C-C-C plate and lowest for C-S-S-S plate. Under isotropic situation (E₁₁/E₂₂=1), for C-C-C-C plate, the highest fundamental frequency is found with 0° orientation and lowest with 45° orientation. For C-C-C-S, C-S-C-S and C-S-S-S plates, highest fundamental frequency is observed at 45° orientation and lowest at 0° orientation. When moduli ratio is 10 or 40, the highest fundamental frequency is observed at 45° orientation and lowest at 0° orientation for all plates except C-S-S-S plate, which imparts highest frequency at 0° orientation and lowest at 45° orientation. The mode shapes and contours of zero lateral deflection have been drawn.