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It is shown that the direct multiple scales method yields better results for the system than the ordinary discretization multiple scales method.
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.
Then, the multiple scales method (a perturbation method) is applied to obtain the appropriate solutions.
The analysis of basic phenomena is performed using the multiple scales method.
Utilizing the Galerkin's method considering multiple scales method provides the primary mode of nanoplate oscillations.
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The obtained equations are solved through Galerkin and multiple scales methods for primary and secondary resonances.
The paper demonstrates that, despite the strong nonlinearity of the model system, one can efficiently describe the dynamics with a combination of averaging and multiple scales methods.
The multiple scale method, a perturbation technique, is used to obtain.
Accordingly, the perturbation solution by applying the multiple scale method contains three time scales.
The dynamic behaviors of system are investigated by means of the so-called multiple scale method.
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