No abstract

One of the drawbacks of classical hydraulic system models consists in the fact, that the simulation programs couple the hydraulic components by compressible joints. Since the compressibility of oil is very small, we get stiff differential equations. To avoid these difficulties stiff elastic couplings can be replaced by unilateral constraints. Examples for hydraulic components with unilateral behavior are check valves, cylinders with stop limits and fluid volumes, in which cavitation can occur. The resulting complementarity equations can be solved with a standard Lemke algorithm. Compared to conventional methods, this leads to a significant reduction of computing times.

This study investigates the vibration reduction of tall wind-excited buildings using a tuned mass damper (TMD) with an inerter (TMDI). The performance of the TMDI is computed as a function of the floor to which the inerter is grounded as this parameter strongly influences the vibration reduction of the building and for the case when the inerter is grounded to the earth whereby the absolute acceleration of the corresponding inerter terminal is zero. Simulations are made for broadband and harmonic excitations of the first three bending modes, and the conventional TMD is used as a benchmark. It is found that the inerter performs best when grounded to the earth because, then, the inerter force is in proportion to the absolute acceleration of only the pendulum mass, but not to the relative acceleration of the two inerter terminals, which is demonstrated by the mass matrix. However, if the inerter is grounded to a floor below the pendulum mass, the TMDI only outperforms the TMD if the inerter is grounded to a floor within approximately the first third of the building’s height. For the most realistic case, where the inerter is grounded to a floor in the vicinity of the pendulum mass, the TMDI performs far worse than the classical TMD.

The efficient design of hydraulic systems requires fast simulation methods. In most simulation programs, the hydraulic components are coupled by compressible joints. Since the compressibility of oil is very small, this leads to stiff differential equations. To avoid these difficulties stiff elastic couplings can be replaced by algebraic and, in some cases, unilateral constraints. Examples for hydraulic components with unilateral behavior are check valves, cylinders with stop limits and fluid volumes, in which cavitation can occur. The resulting complementarity equations can be solved with a standard Lemke algorithm. Compared to conventional methods, this leads to a significant reduction of computational effort.