Autres formulations simplifi´ ees

Il existe dans la litt´erature plusieurs autres m´ethodes simplifi´ees notamment pour le calcul de diff´erents param`etres hydrodynamiques. Malgr´e l’importance de la p´eriode fondamentale des syst`emes eau-structure, peu de techniques sont propos´ees dans la litt´erature pour l’es- timer. Hatanaka (1960) a d´evelopp´e des expressions simplifi´ees pour estimer la fr´equence fondamentale d’un barrage avec un r´eservoir vide. Pour cela, la g´eom´etrie du barrage fut approxim´ee par un triangle sym´etrique et diff´erentes formulations furent d´evelopp´ees pour traiter les cas o`u les d´eformations en flexion ou en cisaillement furent pr´edominantes dans la r´eponse dynamique du barrage. En consid´erant l’analogie avec la th´eorie des poutres, Okamoto (1984) proposa une m´ethode simplifi´ee pour estimer la p´eriode fondamentale d’un syst`eme barrage-r´eservoir.

Pour ce qui est de m´ethodes simplifi´ees pour le calcul des pressions hydrodynamiques, Bouaanani et Perrault (2010) ont propos´e une ´equation qui relie directement la pression hydrodynamique due au mouvement de corps rigide du barrage `a celle due au mouvement de flexion du barrage. Par ailleurs, dans ce mˆeme travail, une expression approximative a ´et´e d´evelopp´ee pour estimer les valeurs propres d’un r´eservoir avec un fond absorbant. Ceci offre un avantage consid´erable, car les calculer exactement ne peut se faire que par it´eration en utilisant des m´ethodes telles que Newton-Raphson.

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