Removing uncertainty in the boundary condition of five degree of freedom spring mass vibratory system using direct updating method

Abstract

Abstract In this paper, direct updating algorithm is used to update or correct the analytical mass and stiffness matrix of the five degree of freedom spring mass system. In the analytical model, there are assumed values of the material properties, dimensions and most importantly the boundary conditions. The material properties of any system can be approximately measured by doing experiment on the same material and treated it as a free-free beam. The dimensions of the simple structures can be measured by using mechanical equipment’s such as scales or vernier calipers. However, it is very difficult to estimate the correct boundary condition in the analytical model. In this work, the analytical mass and stiffness matrices are updated by using the Eigen values and the Eigen vectors of the experimental model. The experimental model is named as ‘simulated-experimental model’ in this study. The direct updating method is used to update the mass and the stiffness matrices of the analytical five degree of freedom model from the simulated-experimental model. It is assumed that the error is in the boundary condition of the analytical model. For analytical model the assumed boundary condition is cantilever type. However, for the simulated-experimental model the boundary condition is clamped-clamped type. The experimental modal model is always correct and it is our duty to modify the analytical model accordingly. It is found that the application direct updating method on the five degree of freedom system has updated the modal-model of the analytical model. The maximum percentage error in the natural frequencies of the analytical model is 45% that reduces to 0% after applying the updating algorithm on the analytical model. The frequency response function curve is also plotted to validate the results.