Sentence examples for the complex eigenvalues of from inspiring English sources

The modal frequencies and damping are directly calculated from the complex eigenvalues of the damped plate.

And, the natural frequencies and loss factors of the system are obtained by solving the complex eigenvalues of the system.

In this paper, a new closed-form expression for the complex eigenvalues of non-proportionally damped system is proposed.

This can be further confirmed by examining the complex eigenvalues of the transformed linear first-order state space equations of motion.

The complex eigenvalues of the coupled system are parametrically analyzed to determine the potential benefits realized by different combinations of the coupling stiffness and damping coefficient.

The stability analysis is performed by calculating the complex eigenvalues of the linearised system and by using the Routh–Hurwitz criterion.

Because the effects of the complex eigenvalues on the mode incident field have been considered, the results are more accurate than those in previous former normal mode theories of reverberation.

Taking advantage of the assumed infinite extension of the domain in the x-direction we expand the unknowns in Fourier modes as follows: (C.5) ψ − i = e i α (x − Ω t ) ψ i (y, τ ) + c. c., where α is the dimensionless wavenumber and Ω denotes the complex eigenvalue of the system, whose real part represents the phase speed of perturbations and whose imaginary part represents the growth rate.

Both approaches are formulated by means of a first-order perturbation technique, whereby the real modes of vibration of the undamped system are used to derive approximate expressions for the complex eigenvalues and eigenvectors of a nearly proportionally damped system.

The work is concentrated particularly upon modal truncation and how this affects the distribution of matrix terms and the ability of the identified damping (together with known mass and stiffness terms) to reproduce the complex eigenvalues and eigenvectors of the full-order system.

Then, the variance and pseudo-variance of the complex eigenvalues are used for determining the statistics of the real and imaginary parts.