SU1295254A1 - Method of determining energy dissipation and natural frequency of linear vibratory mechanical system - Google Patents

Abstract

The invention relates to a test technique, specifically to the determination of parameters of linear mechanical oscillatory systems, in particular, energy dissipation and natural frequency. The purpose of the invention is to increase accuracy and speed. These parameters are determined by the damping method. At the moment t of passing the equilibrium position, the velocity y (t p and acceleration y (t) of oscillations is measured, then at time t, if the oscillation velocity y (tj) is equal to zero, the displacement y of vt is measured) and the acceleration y (t) of oscillations . The parameter of energy dissipation and the frequency and natural oscillations of the system are found from (t) / 2y (t); (tj) / y (t,). The method allows, within one oscillation period, the parameters fjL and u) can be determined twice. consequently, during one process of damped oscillations, the number of measurements is obtained twice as large as in the known methods. To determine and and) it is sufficient to measure during one half period of oscillation. sl with to SL to SL 4

Description

The invention relates to a testing technique, and specifically to methods for determining the parameters of linear mechanical oscillatory systems: energy dissipation and natural frequency.

The aim of the invention is to improve the accuracy and speed of determining the energy dissipation and natural frequency of the parameters of an oscillating system.

.

The method consists in that, by measuring the speed and acceleration of damped oscillations at the moment of passing the equilibrium position, displacement and acceleration of oscillations at the moment that the oscillation velocity vanishes, it is possible to determine the energy dissipation and

natural frequency of the system under study during one half period of oscillations.

The method is carried out as follows.

The investigated linear mechanical oscillatory system is excited by some dynamic action, for example by a calibrated shock. By this, the moment t of the passage of the equilibrium position is recorded and the oscillation velocity y (t) is measured, which at this time has an amplitude, within a given oscillation period, value. At the same time, the oscillation acceleration y (c) is measured. According to the measured y (t,) and y (c), the parameter oi is calculated for dissipating the mechanical energy in the oscillatory system under study using the relation:

. ii (lil;

2y (t)

(one)

u):

at the moment t of zero velocity v (t) of oscillations, measure the displacement y (t.) and acceleration y (t) of oscillations and determine the natural oscillation frequency of the system under investigation by the relation

l), (2)

Ct 2 /

The written method is based on the following.

The damped oscillations of a linear mechanical oscillatory system with one degree of freedom are described by the equation.

y (t) A-l sinCcOt + g-), (3) where is the frequency of damp oscillations

five

ten

. P

Wire differentiation and subsequent transformations, we get the expression

y (t) otyW) (uJt + 4); (4)

y (t) oty-2ot (y + dly) -u) v .. (5)

Exodus from the above

with: y (t,) 0; (6)

,, y (t.) o

(7)

From expressions (4) and (5) subject to conditions (6) and (7), we obtain

y (t) -2ciy (t); (eight)

U.CH) 5 where and) about (. + "L).

From equations (8) and (9), we obtain the desired relations for determining the parameters of the system under study

ri (iil.

  2J (t,)

"}

- -y (t.) ..

y (tj

The proposed method provides. possibility of determining d- and i) „within one half-period of oscillations of the system.

Within one oscillation period, it is possible to determine the parameters a- and cJ twice, which makes it possible to obtain twice the number of measurements in one damped oscillation process, as compared to the known methods, which reduces the errors and improves the accuracy of determining o and

The increase in the measurement accuracy of the proposed method is estimated at 15-20% relative to the known method.

Oq

Claims (1)

40 Formula Isob.teni The method for determining the dissipation of energy and the natural frequency of a linear oscillating mechanical system, according to which damped oscillations of the system under study is excited, measures the speed of oscillations at the moment of passing the equilibrium position, which differs from the fact that, in order to increase the accuracy and speed, the acceleration of oscillations is also measured, then at the moment when the oscillation speed is equal to zero, the displacement and acceleration of oscillations are measured, and the parameter oi dissipates the mechanical energy and frequency c J natural oscillations of the system are determined by the ratio m: 312952544 -y (t) 7) instant of zero velocity y (t) of oscillations; j nb), y (t,); S Sy (tj) - displacement acceleration where t is the moment of passing the position of oscillations, equilibrium;