recurrence equation
1.The vibration analysis of a coupled system composed of a beam and multiple degree of freedom (MDOF) subsystem is carried out, and the analytical expressions for harmonic responses as well as the natural characteristics of this kind of system are obtained with the recurrence equation method.
2.Based on the theory of stochastic finite element,the structural parameters of frame-shear structure including stiffness and mass and damping are simulated to be stochastic variables.By solving recurrence equation of stochastic finite element,the duration curve of mean value and standard deviation of seismic response can be obtained for every floor of frame-shear structure.An analysis is thus given to the effects of independent variation and simultaneous variation of structural parameters on the seismic dynamic response of frame-shear structure.As shown by the results,with regard to frame-shear structure,the effect of variation of strucural parameters on the change of mean value are chiefly the increase of standard deviation of response.Variation of stiffness will cause the response of frame-shear structure to variate greatly;variation of mass shows less effect;and variation of damping shows insignificant effect .The effects of simultaneous variation of various structral parametres on seismic response are only slightly greater than the effect of stiffness variation alone.
3.three recurrence formulae for solving increment dynamic equilibrium equation of a non-linear structure are derived by using the third order spline function as piecewise trial functions in discrete regions of time according to weighted residual method,namely:the recurrence formula of sPline function subdomain method,that of spline function Galerkin subdomain method,and that of spline function least square subdomain method.
4.and the recurrent discriminant equation was:Y(1)= -3 936 7 +2 170 6 X 1+4 289 3 X 2+0 973 5 X 3+2 831 3 X 4.Conclusion To reduce the recurrence of the stroke,we should strengthen the rehabilitation and social support as well as the active treatment on the patients.
5.The tangent of phase of phase shift function δ l(r) is expressed as a power series in wave vector k, and then substituted into the linear F. Calogero equation to get the recurrence relation of the coefficients. The phase shift and scattering length of the spherical square potential well and Yukawa potential scattering for low energy collisions were calculated, which were also compared with the numerical solutions of the different equations.
