SU1272139A1 - Method of determining characteristics of energy dissipaion related with oscillations of linear system - Google Patents

Abstract

The invention relates to a measurement technique and can be used to study the mechanical properties of materials and the dynamic properties of mechanical systems. The purpose of the invention is to improve the accuracy, speed and enable analysis of systems with high energy dissipation. The method is carried out in the following manner. The measurement of the ordinates of damped oscillations excited in the system under study starts at an arbitrary time, is carried out at equal times in a time shorter than the expected oscillation period, and the scattering characteristics are calculated using the formula 1 1 / 2A1n

Description

The invention relates to measuring technique and can be used in the study of the mechanical properties of materials and the dynamic properties of mechanical systems.

The purpose of the invention is to improve the accuracy, speed and the ability to analyze systems with large ^ ι__ ^x k - b ~ ^χ κ-ι ^x k-s \ big energy dissipation due to the fact that the measurement of amplitudes is carried out in the mode of free oscillations in the interval much less period, and the calculations use relative values,

The method is as follows.

For any values of A, K, Ψ for the analyzed signal x _k = A ~ ^{Kt <z5} cos (kuM + Ψ), the following recursive

When applying the proposed method, the accuracy increases due to the fact that there is no need to analyze the resonance curve, a strictly defined calibrated effect is not necessary, and the moment the measurement starts is chosen arbitrarily. The speed increases due to the fact that the total measurement time can be much shorter than the oscillation period, therefore, it is possible to analyze systems with large scattering 15 because the measurement time is much less than the oscillation period.

ratio

2е cosuM, е, where ot is the attenuation parameter of the oscillation envelope;

cj = ²⁷ T / y ~ oscillation frequency;

- period of measurements;

^x a · ^x k-1 ", ^x k-2" ^x k-s ^_ oscillation amplitude at time points kd (k-1) d (k-2) e (k-3) A, k £ 3 L “T.

The relation ^X K-1 ^L 2 ^x k-3 'is also true

From relations (I) and (2) we obtain that

Claims (3)

The claims 20 The method for determining the characteristics of energy dissipation during vibrations of a linear system, which consists in the fact that 25 damped oscillations are excited in the studied system, measure the ordinates of vibrations at four points in time and calculate the characteristics of energy dissipation, I distinguish. This is because, in order to increase accuracy, speed, and provide the possibility of analyzing systems with large energy dissipation, the measurement is started at an arbitrary instant of time, carried out through the _equation35 d ₌ —Σ_ ^χ κ ^χ ^ ά_ · „ ^{1 x} k -d ^χ κ-ι ^x -z a _β --- 2 x ² . _a - x ^, x _h _ ₃ Free damped oscillations are excited in the system under study. At an arbitrary moment, at equal intervals of time, the amplitude X of the oscillations is measured in a time shorter than the expected period T of the oscillations. The scattering characteristics are calculated by the formulas ¹ 1 ¹ ___ _ln - _t - _r arccos time points in a time shorter than the expected period of oscillations, and the scattering characteristics are calculated by the formulas ¹ ι 1 TD ~ ¹ⁿ “G” 1 to. - ₃ - arccos, d = ^x Xil-_ ^x JS-; 2._Z_ ^x J $ _ ^x ^ i -___ ¹ 'V - VV * _ ^x 4ii._Z_ ^x x_2SjsJ? _____ ^X to \ - ^x to 1 ^X k-3 parameter of attenuation of the envelope of oscillations; os =. where ci is the frequency of oscillations; Δ is the measurement period; x _k , x _k r x _k . ₅ , xc-y — ordinates of oscillations at the moments of time cd, (k-1) d, (k-2) d, (k-3) d at k 3, A “T. DECLARED Order 6328/38 Circulation 778_____ Custom polygr. ave, city of Uzhhorod, st. Subscription Project, 4