Sentence examples for using the multiple scale from inspiring English sources

The closed form approximate solution of nonlinear equations is solved by using the multiple scale method, a perturbation technique.

Stability diagrams of the first and the second order approximate solutions are obtained by using the multiple scale perturbation method.

To disclose the detailed intercoupling characteristics of the high order and low order modals of the system, a truncated shallow shell is studied and the internal response properties of the system are investigated by using the Multiple Scale Method.

For systems with a large support/cable mass ratio, using the multiple scale method and asymptotic approximations, a cable-support coupled reduced model, with both cable׳s geometric nonlinearity and cable-support coupling nonlinearity included, is established asymptotically and validated numerically in this paper.

In this section, numerical results can be achieved using the multiple scale method explained in Section 3.

The single component two-dimensional long wave short wave resonance interaction (LSRI) equation for a two-layer fluid model has been derived in [28] using the multiple scale perturbation method and bright and dark type one and two-soliton solutions have been reported.

Using the multiple scales (MS) method [A.

The analysis of basic phenomena is performed using the multiple scales method.

Then, in the absence of the primary and internal resonances, the frequency response equations are obtained by using the multiple scales method.

First of all, the frequency response of the controlled HSLDS vibration isolator is obtained by using the multiple scales method and further verified by numerical simulation.

Accordingly, the natural frequency is determined both exactly and approximately from the numerical calculation of the natural period and using the multiple scales method on the approximate equation, respectively.