# The method for determination of structural elements natural frequencies of the solid-fuel rocket engine system

### Aerospace propulsion engineering

### Аuthors

^{*},

^{**}

Perm National Research Polytechnic University, PNRPU, 29, Komsomolsky Prospekt, Perm, 614990, Russia

*e-mail: I.Kashina@energos.perm.ru

**e-mail: afsal@pstu.ru

### Abstract

Frequency characteristics of solid propellant rocket engine design elements.

Methods for estimation of natural frequencies of solid propellant rocket engine design elements.

To carry out the estimation of influence of solid propellant rocket engine design elements during the resonance interaction on variation value of pressure oscillatory amplitude in combustion chamber under the origination of pitching acoustic instability.

Within the solution of the assigned task there were developed two models of solid propellant rocket engine that allow to determine frequency characteristics of solid propellant rocket engine design elements at concrete periods of time. 1. Model of discrete mass with elastic dissipative couplings. 2. Model with distributed parameters. Solid propellant rocket engine systems presented as discrete mass with elastic dissipative couplings is to be divided into six subsystems of finding partial frequencies of its elements and it is come to matrix solution with the help of the following components: joint coordinates of motion, restoring forces, inertia parameters, constraining forces, dissipative forces and quasi-elastic coefficients. Second model doesn’t require the solution of practical issue regarding determination of solid propellant rocket engine frequency characteristics. In order to form this model (with distributed parameters) the complex solid propellant rocket engine system is presented as the thin-walled shell and thick-walled massif made of another material and it contacts with the inner surface of thin-walled shell.

As the result the set task is come to joint ratio integration of shell theory and three dimensional elastic theory subjected to specific conditions at surface to contact medias and other conditions. Verification of achieved results was done according to pilot testing with application of the modal analysis.

There were developed two algorithms of solid propellant rocket engine natural frequencies estimation: with the application of the point mass method and “distributed” model. Researching of the achieved models was carried out with the purposes to analyze their precision and complexity of their realization.

Determination of natural frequencies of solid propellant rocket engine is the actual for the estimation of operability of newly developed solid propellant rocket engines. This research displays that more complex but more precision algorithm is the “distributed” method. This algorithm allows to do detailed estimation of solid propellant rocket engine system dynamic parameters. Less labour and time-consuming algorithm is the algorithm for presenting the solid propellant rocket engine system as the discrete mass with elastic dissipative couplings. This algorithm requires the concrete attitude to set up of boundary conditions. Achieved algorithms can be used for estimation of influence of geometric and physics mathematic parameters of solid propellant rocket engine elements on the whole solid propellant rocket engine system amplitude frequency characteristic. In this case algorithm using discrete mass model with elastic dissipative couplings is applied on the initial stage of solid propellant rocket engine development and “distributed” model is applied for specification of received results.

### Keywords:

own frequency of fluctuations, self-oscillatory system, solid-fuel rocket engine, discrete mass method, method with distributed parameter### References

- Frolov K.V.
*Vibratsii v tekhnike*(Vibration in technique), Moscow, Mashinostroenie, 1981,vol.6, 456 p. - Il'gamov M.A., Ivanov V.A., Gulin B.V.
*Raschet obolochek s uprugim zapolnitelem*(The calculation of shells with elastic filler), Moscow, Nauka, 1987, 260 p. - Kashina I.A., Sal'nikov A.F.
*Vestnik RGATA,*2012, no 1, vol.22, pp.17-22. - Sal'nikov A.F., Sal'nikov D.A., Petrova E.H.
*Materialy mezhdunarodnoy konferentsii «Issledovanie uslovii perekachki energii iz zony goreniya tverdogo topliva v akusticheskie kolebaniya kamery sgoraniya raketnogo dvigatelya*», Sankt-Peterburg, 2006, issue 1 pp.. 175-179. - Sal'nikov A.F., Sal'nikov D.A., Petrova E.H.
*Khimicheskaya fizika i mezoskopiya,*2006, vol. 8, no.2, pp. 169-176. - Sal'nikov A.F., Petrova E.H.
*Materialy mezhdunarodnoy konferentsii « Issledovanie uslovii perekachki energii iz zony goreniya tverdogo topliva v akusticheskie kolebaniya kamery sgoraniya raketnogo dvigatelya*», Sankt-Peterburg, 2006, Sankt-Peterburg, 2006, issue 1, pp. 120-123.

Download