Modeling Nonlinearities and Predicting Contact Nonlinearity Behavior in the Vibration Problems using FE Analysis

The accurate prediction of system behavior and the stress response for vibration loads depends on how well the boundary conditions, joints, interfaces, mass, and stiffness are defined. Often, in vibration analysis several assumptions would be made due to the lack of the analytical tool capabilities, the state of art Finite Element Analysis (FEA) software still cannot handle nonlinear modal analysis. This paper attempts to develop methodology to deal with the nonlinear vibration analysis using the existing Finite Element (FE) tools. Two different aspects of nonlinearities are considered, one is impact of nonlinearities at global level in terms of predicting natural frequency & mode shapes and the other aspect is consideration of nonlinearities local to the contacts, enabling prediction of realistic stresses in the vicinity of the contacts. Linearization of nonlinearities based on regression analysis of correlating FE models with test data is proposed for estimating the linear stiffness to capture the realistic nature of mode shapes and natural frequencies as function of input excitation. For predicting stresses local to the contact, a nonlinear static submodel approach derived out of the global model is proposed based on the understanding that the global mode represent the system behavior well or correlates with test. Components such as linear hydraulic actuators especially would have several clearance joints and with the proposed methodology these interfaces can be modeled with linear approximation to capture the global modes, for instance using coupled joints in radial direction with stiffness as a function of input excitation. The realistic stresses at the interfaces can then be predicted using the proposed nonlinear static submodel analysis. This methodology of capturing nonlinearities in vibration environment using FE is found quite useful in system characterization, design decisions, test correlation & further redesign or optimization of the products.