Demand-based optimal design of oscillator with parallel-layout viscous inerter damper

In this study, a demand-based optimal design method is proposed for an oscillator (a single-degree-of-freedom system) with a parallel-layout viscous inerter damper (PVID). The proposed design method overcomes some deficiencies of the existing method, which is based on the fixed-point theory and is mainly suitable for tuned mass dampers. Moreover, for the fixed-point method, the inherent damping of the primary structure is neglected, and the global optimal solution cannot be obtained. The proposed method can obtain a more rational and practical design for the actual design by minimizing both the response and the cost. The design problem of a PVID-equipped oscillator is transformed into a multi-objective optimization problem that can be solved using the epsilon-constraint approach, which is consistent with the concept of demand-based design. The dynamic response of the oscillator and the force of the PVID (i.e., the cost factor) are evaluated according to theories of random vibration to reduce the number of calculations required. A computer program is developed to perform demand-based parametric design of a PVID-equipped oscillator. Several design cases were examined under different excitation conditions using the computer program, and dynamic time history analyses were then conducted to verify the designs obtained. The results show that the proposed optimal design method identifies satisfactory designs more effectively than the existing method by obtaining PVID design parameter values that better meet the performance demand and simultaneously minimize the cost.