Clearly modal vectors are orthogonal over the mass matrix, assuming proportional damping. Two identical modal vectors (mass normalized) yield a unity value, two orthogonal modal vectors yield a zero value. The modal assurance criteria (MAC) value for two orthogonal modal vectors will generally not be zero. However if the mass (or stiffness) matrix is introduced as weighting matrix when defining the modal assurance criteria the value will be zero. Very often the selected points for a set of modal vectors are evenly spread over the structure and they represent nearly the same amount of mass. Hence the diagonal elements of the mass matrix are nearly equal and the MAC value will be low for two orthogonal modal vectors. However how sensitive is the MAC value between two orthogonal modal vectors if the diagonal elements in the mass matrix are unequal. This paper will investigate the impact of a mass matrix with unequal diagonal elements on the MAC value for two orthogonal modal vectors. First for a mass-spring system and then for a beam with non-uniform property distribution. Simple rules of thumb on how to overcome the matter will be shown.
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