Generalization of Dunkerley's equation for the undamped linear positive semidefinite system

The Dunkerley's equation can be generalized for the undamped linear positive semidefinite system (p s-d system) based on a new concise method for making the system's matrices nonsingular, which was advanced by the authors [9]. It was found that this kind of system has similar characteristic as the positive definite system—its fundamental frequency can be estimated with its basic subsystems by a formula which is similar to Dunkerley's equation. For the undamped linear p s-d system, in which masses are connected in series with springs, the reciprocal of its fundamental frequency squared is approximately equal to the sum of the reciprocals of the natural frequencies squared as the system is divided into two groups of masses rigidized according to their connection relationship of springs.