Abstract
The literature about the mass associated with a certain mode, usually denoted as the modal mass, is sparse. Moreover, the units of the modal mass depend on the technique used to normalize the mode shapes, and its magnitude depends on the number of degrees of freedom (DOFs) used to discretize the model. This has led to a situation where the meaning of the modal mass and the length of the associated mode shape is not well understood. As a result, normally, both the modal mass and the length measure have no meaning as individual quantities, but only when they are combined in the frequency response function. In this paper, the problems of defining the modal mass and mode shape length are discussed, and solutions are found to define the quantities in such a way that they have individual physical meaning and can be estimated in an objective way.
Highlights
Where mr, cr, kr, and pr(t) ψTr p(t) are the modal mass, the modal damping, the modal stiffness, and the modal load, respectively, corresponding to the r-th mode
From equations (3) and (5), it is seen that the modal mass is needed in all applications where the frequency response function (FRF) (or the impulse response function (IRF)) has to be constructed from the modal parameters, such as structural modification, health-monitoring applications, and damage detection [1,2,3,4, 10]
For practical applications, it is important that the ways to estimate modal mass and mode shape length are objective so that different people will arrive at the same number for a given mode and a given structure
Summary
In order to achieve a better understanding of modal mass, one would expect that a new definition would lead to a better physical meaning of the modal mass. For practical applications (and for the physical meaning), it is important that the ways to estimate modal mass and mode shape length are objective so that different people will arrive at the same number for a given mode and a given structure At least they should be able to agree on some simple rules for obtaining these quantities so that independently, they would arrive at the same estimates. (i) e modal mass must be physically meaningful, having the unit of [kg] and being a measure of the amount of mass moving in a given mode (ii) e length of the mode shape must be a pure geometrical quantity, describing the average movement of the considered mode (iii) Estimation of modal mass and mode shape length must be objective so that estimates obtained by different people are equal
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