Synthesis of a nonlinear dynamic vibration absorber

Abstract

We consider a linear undamped vibrating system with one degree of freedom, excited by a sinusoidal force of constant amplitude. To this is attached a secondary system by means of a spring whose load-deflection characteristic is the sum of a linear and cubic term. It is desired to find optimum coefficients λ and ν for this coupling spring, such that one obtains as large a band of exciting frequencies as possible within which the vibration amplitude of the primary system is kept below unity. This choice is subject to the condition that the fundamental of the primary system response have zero amplitude at a preassigned expected excitation frequency Ω 0 . The first approximation by the Duffing Iteration Method is used to obtain the response in terms of the system parameters. Optimum values of λ 2 and ν are expressed in terms of Ω 2 . Using the optimum values corresponding to a particular value of Ω 0 , the results of the synthesis are compared with those obtained by a more exact analysis and by an electronic differential analyzer.It is found that by the synthesis criterion used, the nonlinear absorber offers a significant advantage over the corresponding linear absorber.