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The Stability of an Irrigation Canal System

Bounit H.

International Journal of Applied Mathematics and Computer Science

2003

Vol. 13, no 4

453-468

In this paper we examine the stability of an irrigation canal system. The system considered is a single reach of an irrigation canal which is derived from Saint-Venant's equations. It is modelled as a system of nonlinear partial differential equations which is then linearized. The linearized system consists of hyperbolic partial differential equations. Both the control and observation operators are unbounded but admissible. From the theory of symmetric hyperbolic systems, we derive the exponential (or internal) stability of the semigroup underlying the system. Next, we compute explicitly the transfer functions of the system and we show that the input-output (or external) stability holds. Finally, we prove that the system is regular in the sense of (Weiss, 1994) and give various properties related to its transfer functions.

Wpływ wymuszeń eksploatacyjnych na stabilność złącz śrubowych

Kisiel S., Broniec Z.

Zagadnienia Eksploatacji Maszyn

2002

Vol. 37, nr 2

117-129

W publikacji zamieszczono: - metodykę badań złącz śrubowych znajdujących się pod wpływem drgań, - wyniki badań doświadczalnych przeprowadzonych dla weryfikacji wyników badań analitycznych samohamowności złącz śrubowych w warunkach drgań, - sposób przystosowania stanowiska K-3 do badań eksploatacyjnych niezawodności złącz śrubowych oraz wyniki badań wstępnych.

The lack of standardized information and tests in the stage of assembly and operational use of bolt connections leads to the scatter of values of parameters deciding on proper work of the connection. Thus the unification of methods, test stands and information data have been proposed and finally development of standards being the base of reliability tests. The paper contains description of methodology of bolt connections tests being under influence of vibration. Within the proposed methods is given description of the test method and the test stand. Developed method demand measurement recording of acceleration values of connected elements and the value of initial tension Pw for load parameters given for the test programme. The knowledge on values of virtual accelerations of masses of the fixed element xm and the body xk allows for determination of the relative acceleration delta xi=xk-xm and makes possible determination of the dynamic force P(t)=delta x x m exerted on the bolt when known is the mass of the element. Obtained values P(t) give the possibility to determine the value of the coefficient of dynamic intensity k=P(t)H whose level determine the limit value of relaxation of bolt connection for analytical consideration. Described method has been proven in tests on the stand K-3 whose structure and measurement-recording lines are described in this paper. In the paper are also included results of experiments of self-lock of bolt connections in conditions of programmed loads. In tests it was stated that bolt connections made with bolts M6-M10 the loss of self-lock is when k>1,5 and WSH>1.7. Presented results describe the zone of stability of bolt connection with the use of dimensionless criteria and determine boundary states in estimation of reliability of those connections. In own investigations has been also observed the effect of the lenght of the bolt thread on the disturbance of friction surfaces of connection. Then the bolt is under the cyclic bending and fails as the result of fatigue (e.g. crack under the bolt head). Thus there is demand for tests which show the bending flexibility on the capacity and reliability of bolt connections.