An engineering interpretation of the complex modal mass in structural dynamics

In this paper the modal mass is considered in the case of general damping where it is well-known that the modal mass becomes a complex valued quantity. The aim of this paper is to present a definition of the complex modal mass, which leads to an easier physical understanding of this modal parameter. It is demonstrated that based on the structural modification theory, the complex modal mass can be expressed as a linear combination of the un-damped modal masses, where a complex coefficient matrix can be defined that depends on the general damping matrix and on the mode shapes of the damped and the un-damped system. An important finding is that an apparent mass can be defined so that the modal mass is always equal to the product between the apparent mass and the length squared. The paper includes a 2-DOF example that illustrates the influence of the amount of general damping on modal quantities that are normally considered non-sensitive to damping.