A new jacobian matrix calculation method to decrease computational time in periodic force response analysis of nonlinear structures

Kızılay, Hazım Sef
The contact interfaces between the components used in high speed systems such as the turbo machinery cause nonlinear vibrations. In order to understand the dynamic characteristic of nonlinear systems, it is important to perform nonlinear vibration analysis. In nonlinear vibration analysis, due to the properties of nonlinear elements used, it is not possible to calculate the Jacobian matrix analytically or it becomes very complicated and difficult, therefore, Jacobian matrix is calculated as numerically. In each iteration, obtaining the Jacobian matrix by numeric methods greatly increases the overall calculation time. In this study, a new method is proposed for numerical Jacobian calculation of nonlinear vibration analysis of multidegree-of-freedom (MDOF) systems. The aim of the work is to obtain significant reduction of computational time for Jacobian calculation compared to classical Jacobian calculation. In order to reveal the effect of the suggested method, nonlinear equation set is derived by using receptance method. The nonlinear MDOF system is analyzed in frequency domain by using harmonic balance method (HBM) which makes nonlinear algebraic equations to be solved iteratively. The validation of the method is presented by comparing the computational times and computation reduction ratios obtained with classical Jacobian calculation and proposed Jacobian calculation method.