Development of hencky bar-net for vibration analysis of plates

This paper is concerned with the development of the Hencky bar-net model (HBM) for free vibration analyses of rectangular plates. The HBM is a two dimensional discrete net system composed of rigid segments connected by frictionless hinges and rotational springs. In the model, bending of the plate is accommodated by rotational springs at joints while twisting by diagonal spring systems in each grid cell. The total mass of the plate is distributed as lumped masses at joints and the continuous boundary stiffness of plate is simulated by calibrated springs located at the edge joints. By resorting to the energy approach, one is able to derive the governing equation of motion for the HBM which has a mathematically equivalency to the governing equation for the first order central finite difference model (FDM) provided that the segmental length of HBM is made equal to the nodal spacing of the FDM. Based on the equivalence between HBM and FDM, HBM can be fully developed with the appropriate boundary spring stiffness from comparing the edge spring stiffness of the FDM. Owing to the discrete property of HBM, it is able to readily handle plates with complicated boundary conditions. The developed HBM is used to solve some vibration problems of rectangular plates to demonstrate its accuracy and convenience for plate analyses.