Sentence examples for modal coordinates and from inspiring English sources

Differential equations for the modal coordinates and internal states are integrated together.

The state space equation is transformed into modal coordinates and modal feedback gains are obtained by application of the optimal control theory.

The discretized dynamic equations of motion are transformed into a nonlinear coupled-modal equation by using the proper modal coordinates and the nonlinear coupled-modal equations are then transformed into a state space model in order to design controller.

The discretized dynamic equations of motion are transformed into a nonlinear coupled-modal equation by using the proper modal coordinates and then the equation is transformed into a state space model in order to design controller.

This work develops equations of motion for a jointed structure in terms of the structural modal coordinates and implements a reduced-order description of the microslip that occurs at the interface between components.

The authors, in particular, have theoretically demonstrated that the exact statistical properties (spectral moments) of the PSD functions matrix of stress tensor of the model are obtainable only from PSD functions matrix of its modal coordinates and from PSD functions matrix of inputs.

The governing equation of the structural system is derived in the modal coordinate and is rewritten as a state-space control model.

According to the modal superposition theory [16], its dynamic characteristics can be described by the product of the shape function and the generalized coordinate, as follows: X_{1} = sumlimits_{i = 1}^{n} {Updelta_{i} (x q_{i} (t)}, (4 where q i and ∆ i are respectively the ith modal coordinate and the order shape function of the simply supported beam.

From the complex modes and modal coordinates, frequencies, wavelengths, and characteristic wave speeds can be obtained.

The chatter stability is solved in modal coordinate system, and the forced vibration marks left on the finish surface are predicted in discrete time domain.

The formulation is in modal coordinates of the elastic structure, and yields a reduced-order model of the aeroelastic feedback loop that is parametrized by airspeed.