Abstract:

The deflection of an impacted plate may be treated as a time-dependent forced vibration at the impact point. The position of the impactor head can be determined from its initial velocity and deceleration on impact. The difference between the impactor position and the plate deflection is the relative approach of the contacting surfaces (Hertz' law). This is a Volterra integral equation of the second kind which must be solved numerically. Two structures of different sizes but of the same shape will have proportional modal properties. For similar geometries, it can be shown that there are three basic variables; the fundamental frequency, the mass ratio of impactor and plate, and a contact parameter. It is of interest to determine the extent to which the distribution of the higher modes (or equivalently, the shape of the plate) governs the impact force and duration. For example, is it valid to approximate a circular plate by a rectangular one, or to use thin plate bending theory rather than thick? The benefit is the reduced precision required in the modal analysis: With a numerical modal analyzer such as finite-element method, reliable impact force levels may be determined with a low precision modal model.