Free vibration analysis of bio-inspired helicoidal laminated composite square and annular plates having circular openings using isogeometric analysis

Abstract

Present work aims to carry out free vibration analysis of bio-inspired helicoidal laminated composite square and annular-shaped plates with circular openings. Refined plate theory, created within the context of isogeometric analysis (IGA) is used during the present study. The theory is coded in MATLAB to study the behavior of the plates and the results are validated with the frequencies obtained using ABAQUS. Recursive, semi-circular, exponential, and Fibonacci helicoidal schemes are used during the present study for studying the free vibration behavior and the frequency is compared with the conventional cross-ply and quasi-isotropic laminates. Influence of position of opening, dimensions of opening, number of plies, and end condition, on the free vibration behavior of square and annular shaped bio-inspired helicoidal plates is carried out. The plates with CCCC and CCCF ends having openings at the quarter length are found to have higher frequency by 3.518 % and 0.3897 % compared to the values of the frequency of the plate with opening at the centre with the same perimeter. Opposite trend is observed for plate with PPPP, CFCF, and CFFF end conditions, where the plate with opening at centre exhibits higher value of the frequency by 2.427 %, 0.821 %, and 1.232 %, respectively. When the opening is near to the corners, the decrease in frequency by 3.913 %, 1.576 %, 1.193 %, and 1.437 % is observed for CCCC, CCFF, CCCF, and CFCF end conditions while increase by 1.490 % and 2.717 % is observed for the CFFF and PPPP end conditions. The mode shape of the plate is found to be greatly influenced by the position and dimension of the hole and end conditions of the plate.