Rates of Change of Eigenvalues, With Reference to Buckling and Vibration Problems

There are many problems in practice, particularly in the fields of buckling and vibration, where the required end result is a curve showing the relation between the eigenvalue and one or more of the basic parameters of the physical system. For example, the curve relating the buckling stress and side ratio of a rectangular plate, with some specified set of edge conditions, under uni-axial compression may be required. Or the problem may be the buckling of a rectangular plate of given proportions, under combined compression and shear, and the determination of the relation between the two types of load at buckling. Alternatively, the effect on the frequency of vibration of varying a concentrated mass, or the stiffness of an elastic constraint at a given point in an elastic system may be required.