Optimal dampers localization for a body under double load and the body behaviour for its intermediate loads

A multibody dynamics is a well-known tool used in many analyses of mechanisms. It simplifies predictions of any mechanism behaviour, even in long before of time when the final mechanism is set to any physical experiment. Some important step in a project preparation is a selection of elastic and damping coefficients for elements of the system. The process can be simplified if a combination of dynamics and optimisation tools is in a disposition of project manager. But even then, it request in a numbers of numerical calculation, so numerically effective models are necessary. The paper presents researches in an optimal configuration of damping elements. In some previous, publication [

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] we had focus on question: whether it is possible to obtain a configuration of dampers that satisfy presumed level of damping of vibrations for a structure with varying load Especially, does exist it for a single body with double sets of workload. The answer was negative, even if some important improvement of damping was obtained. Within the actual paper some deeper analyse of behaviour of the optimised system is performed, especially its behaviour for intermediate loads is analysed. Short description of rigid bodies multibody dynamics

Any multibody system consists of two kinds of elements: rigid bodies and massless joints. Any of the bodies have to be connected to at least one joint. Any of the joints can connect two bodies. To obtain the dynamics equations, we will employ methodology described in [

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]. It leads to the second order differential equations expressed in from

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$$ M\left( q \right) \cdot \ddot q + F\left( {\dot q,q} \right) + Q\left( {\dot q,q,f_e ,t_e ,t} \right) = 0 $$

The methodology is cited with lot of details in the full version of the article. Optimization

The problem is formulated as a multi objective optimization problem. The simplex algorithm is proposed as the optimization method.

Tested system A test system is a single body, planar system. The body has form of a rectangle. Position the body is fixed with the use of 4 elastic elements. It is extended with 3 dampers and optimized under double load conditions. To avoid “infinite parameters”, there are restrictions set on dampers localisation.

The test The system is tested for intermediate loads. Important deviations from presumed values are observed.