Development of Analytical Theory of Stress-strain State of Structures during Polyharmonic Vibrations

   The paper presents a solution to the vibration protection problem for building elements subjected polyharmonic dynamic vibrations.

   Purpose: The objective of this work is to develop a calculation method of the system parameters of multi-mass dynamic vibration dampers, which is refined compared to the previously developed method.

   Methodology/approach: The approach is based on the improved formulation of the problem and computational model. The vibration suppression is a task of regulating the stress-strain parameters of a linearly deformable system protected by a set of single tuned mass dampers.

   Research findings: The parameters of dampers are determined by specified requirements for displacement vibrations at reference points of the structure. The previously proposed decomposition method is refined to improve the accuracy. Its effectiveness method and capabilities of computations are  demonstrated by the model and test problems. It is shown that analytically derived parameters fully satisfy the specified conditions for the vibration control. 

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