Relative sensitivity analysis of responses using transmissibility

To identify the most effective position for solving vibrational problems, it is necessary to analyze the system sensitivities. In this study, new sensitivity indices based on the concept of transmissibility are proposed for analyzing the relative sensitivities of the responses with respect to the design variables that are used to indicate the sensitive positions where small design modifications can be applied, and analyze the effect of these modifications on the responses. The transmissibility concept is applied after differentiating the equation of motion to consider the crosstalk effects. More important information regarding the relative sensitivity characteristics of a system with easily measured response data to reduce unintended responses can be acquired by using the proposed indices. Further, the proposed indices are applicable to the variables of mass, stiffness, and damping. The indices are validated analytically and numerically, and the results demonstrate the effectiveness of the proposed indices.