An exact approach for free vibration analysis of rectangular plates with line-concentrated mass and elastic line-support

An exact approach for free vibration of an isotropic rectangular plate carrying a line-concentrated mass and with a line-translational spring support or carrying a line-spring-mass system is presented in this paper. The mode shape function of vibration of such a plate is expressed in terms of the four fundamental solutions derived in this paper. The main advantage of the proposed method is that the resulted frequency equation for such a rectangular plate can be conveniently obtained from a second-order determinant. The proposed method is thus computationally efficient due to the significant decrease in the determinant order as compared with previously developed procedures which usually led to an eighth-order determinant for solving the title problem. Two numerical examples are given to illustrate the efficiency of the proposed method and to investigate the effects of the location and the magnitude of a line-concentrated mass and elastic line-support as well as the influence of the aspect ratio on the natural frequencies of a rectangular plate.