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This method is based on the substructure synthesis formulation and a multiple scales procedure, which is applied to the analysis of non-linear responses.
A new method of multiple scales procedure is used to analyze the forced responses of multiple degrees of freedom systems with cubic non-linearity, in which the internal resonance takes place simultaneously together with the forced resonances.
While retaining generality of expression, the multiple-scale procedure is carried out until a closed-form solution for the velocity field is obtained for an arbitrary mean-flow function.
In the first approach, time and space domains are discretized using the method of multiple scale (MMS) and Galerkin procedure respectively, and in the second one differential quadrature method (DQM) is utilized to space discretization.
Based on the method of multiple scales, the proposed procedure reduces the size of large-degree-of-freedom problem in solving the non-linear equations.
For second and third sub-procedures, we dealt with multiple scale factors using a two-dimension GPU thread block assigning method for exploiting time-frequency-scale data parallelism.
This novel procedure is compared to solutions obtained by directly applying the classical multiple scale analysis to the gyroscopically coupled system without decoupling.
Such multiple scale spatial dynamics is potentially reflected in multiple time scales of temporal dynamics.
An approximate solution for this model is obtained via Galérkin procedure and multiple scales method.
An approximate solution for this model is found via Galérkin procedure and the multiple scales method.
The governing displacement equations of motion are established and solved on the basis of the Galerkin procedure and the method of multiple scales.
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