This study considers a Lagrange direct way of modal assurance criterion (MAC) values of an undamped system. The mentioned method for the sensitivity analysis of the MAC of a sliding machine working table is more close to the exact solution and time efficient. The paper aims to discuss these issues.
Using the Lagrange multipliers to compute the first and second-order sensitivity analysis of MAC values.
Because of the Lagrange multiplier without considering the number of design parameters, one only needs to perform the calculation once. Compared with the indirect way, the direct way is more effective when the number of design parameters is greater than one. This calculation procedure is simple and accurate, which can be popularized and used.
Engineering structure often requires only some structure design, and most of the sub-structure design variables are not related to each other. In this case, this way is better and more efficient. The direct way can be applied to the dynamic optimization design of large structures, the frequency and the mode sensitivity analysis in the process of model modification.
Tian, H. and Yu, Y. (2017), "A direct way for the sensitivity analysis of modal assurance criterion of a sliding machine working table", Multidiscipline Modeling in Materials and Structures, Vol. 13 No. 1, pp. 135-146. https://doi.org/10.1108/MMMS-09-2016-0043
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