Sentence examples for modes the nonlinear from inspiring English sources

For higher modes, the nonlinear plate theory should be used even if the deflection amplitude is very small compared to plate thickness.

During tapping mode, the nonlinear tip-sample force activates the internal resonance and thereby amplifies the out-of-phase resonant mode.

Four imperfection forms are examined: the linear bifurcation mode, the nonlinear buckling mode, several post-buckling deformed shapes for the perfect shell, and a weld depression.

The influence of higher modes on the nonlinear dynamics of the considered resonator is investigated in order to retain the number of modes which will be used by the HBM+ANM procedure.

To do this, the interaction Hamiltonian between the trapped modes and the nonlinear components must be found.

It is also found that the optical wave modes in the nonlinear metamaterial are sensitive to the parameters of the nonlinear constitutive relation.

In the simulations without control, the value of the linear mode to the nonlinear deflection is quantified; and the minimum number of linear modes needed for accurate model is obtained.

To study the natural frequencies and mode-shapes, the nonlinear governing equation is linearized about the static configuration.

The control law is designed to guarantee the existence of the sliding mode around the nonlinear surface, and the damping ratio of the closed-loop system is increased as the output approaches the set-point.

The core issue here is the difficulty in determining the true cracking mode for the nonlinear crack problem, which requires the most active crack or cracks to be identified among a group of potentially active cracks during each load increment in numerical analysis.

The results show that the proposed sliding mode controller improves the nonlinear HGRS system performance with an accurate precision and a shorter time in all cases.