The use of reduced models in the reliability analysis of deformable systems with dynamic vibration dampers

The transformations of the initial design models of complex constructions and structures as the multi-degrees of freedom (DOF) systems is advantageous to use in order to reduce the amount of computational procedures in their dynamic analysis. This becomes particularly relevant in the reliability analysis requiring multiple recalculations for taking into account the stochastic properties of system parameters and impacts. The paper presents a technique based on known approaches of reduction the original multi-DOF system to an equivalent generalized design model with one degree of freedom. Various combinations of the equivalence conditions for the original system and the generalized model, including equalities of their natural frequencies, characteristic displacements or kinetic energies, were used to determine the modelling lumped mass and the corresponding rigidity of the design model. An algorithm for the probabilistic properties evaluation of the design model characteristics has been developed. The verification of the correctness of the proposed model in the area of tuning in to the workload frequency is performed. The quantitative results of solving the model problems in reliability calculations of multi-DOF structures with dynamic vibration dampers (DVD) are presented. The proposed approach allows us to simplify the process of selecting a single-mass DVD taking into account reliability requirements. (paper)