Various Values Of Frequency Research Articles

Displacements and stresses caused by forces acting on the lateral surfaces of a crack in infinite elastic medium

Considering the fault as a crack in the infinite elastic space, the field of displacement and stress due to forces acting on the lateral surfaces of the crack are obtained. The use of Fourier and Laplace transform methods yield dual integral equations. The solution to these dual integral equations and the formal expressions for the displacements and stresses in terms of integrals are obtained. The forces acting on the lateral surfaces of the crack are assumed to have the following three forms: (a) compressive stress perpendicular to the surfaces of the crack; (b) shear stress along the dip-direction of the crack; (c) shear stress along the strike-direction of the crack. Numerical results are calculated for various values of frequency and Poisson's ratios.

On the possible instabilities in the ferromagnetic resonance due to non-linear relaxation

The case of ferromagnetic resonance with effective frequency shift and effective linewidth dependent on excitation will be dealt with. The stability of steady state solutions will be proved and the general instability conditions will be deduced for the case considered. Afterwards, the transverse resonance relaxation caused by a system of two-level ions will be investigated. The steady solutions and their stability will be discussed for ions with identical doublet splitting as well as for a system with fluctuating value of splitting frequency. The general considerations will be illustrated by numerical calculations for various values of frequency and h.f. field intensity parameters.

Complex-curve fitting

The mathematical analysis of linear dynamic systems, based on experimental test results, often requires that the frequency response of the system be fitted by an algebraic expression. The form in which this expression is usually desired is that of a ratio of two frequency-dependent polynomials. In this paper, a method of evaluation of the polynomial coefficients is presented. It is based on the minimization of the weighted sum of the squares of the errors between the absolute magnitudes of the actual function and the polynomial ratio, taken at various values of frequency (the independent variable). The problem of the evaluation of the unknown coefficients is reduced to that of the numerical solution of certain determinants. The elements of these determinants are functions of the amplitude ratio and phase shift, taken at various values of frequency. This form of solution is particularly adaptable to digital computing methods, be-because of the simplicity in the required programming. The treatment is restricted to systems which have no poles on the imaginary axis; i.e., to systems having a finite, steady-state (zero frequency) magnitude.