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SRSM is based on application of the stochastic finite-element method via the polynomial chaos expansion method or the modal perturbation method.
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The modal perturbation stochastic finite element method (SFEM) then condenses the response sensitivities to assess the response variability.
A multi-parameter perturbation method is employed to solve the modal problem of internally resonant systems.
In that regard, a modal perturbation solution is developed in the context of the asymptotic method of Krylov, Bogoliubov and Mitropolsky for a general, continuous, non-autonomous, gyroscopic system with weakly non-linear stiffness.
Perturbation method is used to analyze the relationship between modal damping ratios and control gain.
The results show that a first order and a second order perturbation method can be applied to predict free vibration frequencies and modal shapes accurately.
Based on the perturbation method, the post-buckling equilibrium path of the system is presented with the multi-modal analysis, and two bifurcation points appear on the stable equilibrium path.
Homotopy Perturbation Method.
Alternatively, a modal perturbation (MP) approach allows rapid synthesis of the random response.
The perturbation method is employed.
In particular, it is shown that the perturbation method not only reduces the computational effort but allows clear physical insight into the effect of uniform and non-uniform in-plane force on the modal parameters of an annular plate.
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