Sentence examples for a closed form response from inspiring English sources

Then a closed form response is derived, and the characteristics of the response are analytically examined by using the real modes.

Sun [4] has proposed a solution in a closed form for the response of a beam resting on a Winkler ground under a linear dynamic load applying the two-dimensional Fourier transform and the Green function.

The joint application of this procedure and a closed form solution of the response drastically reduces the computational burden and makes these analyses operatively possible.

The purpose of this section was to develop a closed form formula for the response of the imaginary subframe throughout the loading history of the RWMF, starting from zero to first yield, from first yield to incipient frame failure, from frame failure to LB and BRB incapacitation and eventually the collapse of the structure due to wall and/or tendon failure.

When either real modal analysis or complex modal analysis is used to calculate the response, a closed form solution, in the form of an integral of the steady state response of each normal co-ordinate (in real modal analysis), or those of the generalized co-ordinates (in complex modal analysis), can be obtained directly in accordance with the periodicity conditions of the steady state response.

Proper orthogonality conditions are then derived and a closed form solution for the dynamical response for a given eigenmode is developed.

This paper derives a closed form solution for wind-induced response of actively controlled tall buildings with linear quadratic Gaussian (LQG) controllers to facilitate the real application of modern active control theory.

This framework does not require any form of transient solution (either numerical or analytical) to the governing equation, yet it provides a closed form mathematical relationship for the response time as a function of the aquifer geometry, boundary conditions, and flow parameters.

For a uniformly sampled data set of impulse response type a closed form expression can be given for the Fisher information using the solution of a Lyapunov equation.

A closed form analysis of the non-linear steady response leads to elliptic integral solutions for the equilibrium band geometry and tension.

A closed form solution for dynamic amplification factor (DAF) for steady-state response was derived by the energy balance equation.