Free vibration analysis of a thin rectangular plate with multiple circular and rectangular cut-outs

The present work is to investigate the variation in the natural frequency of a rectangular plate with the change in position of cut outs of different sizes along its diagonal and major axis line by considering different aspect ratios of plates. In this regard the free vibration analysis of an isotropic rectangular plate of various aspect ratios with different sizes of multiple circular and rectangular cut-outs is carried out by using an Independent coordinate coupling method (ICCM) under simply supported boundary condition. The ICCM utilizes independent coordinates separately for plate domain and hole domain, in which the reduced mass and stiffness matrices can be derived, by matching the deflection conditions for each hole imposed on the expressions. The resulting equation is useful for the calculation of the Eigen values. The position, size, and number of cutouts have been varied in all the possible ways to investigate their effects on the natural frequency of the rectangular plate.