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The analytical solution for fluid membrane coupling vibration has been approximated using the Galerkin and small parameter perturbation methods.

Variations of the plate deflection and angles of rotation between the unloaded edges have been approximated using the solution to the bending problem for the shear deformable beam with clamped ends.

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The fractional time delay in the sensor to controller and controller to actuator channel is approximated using the Thiran approximation technique to design the sliding surface.

The integral can be approximated using the Laplace approximation, see (31– 31).

In addition, the P d for two-dimensional systems was approximated using the non-central/central approximation and provided in [18] following the results in [30].

The derivatives are approximated using the central difference formula.

which can be approximated using the simple absolute sum: (8).

The displacement variables are approximated using the Ritz method.

The structural response is approximated using the same basis functions describing the geometry.

The joint probability density of the surge and sway responses is approximated using the Nataf transformation.

The rheology of the fluid was approximated using the Ostwald model.

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