Predication of Peak Acceleration of One Degree of Freedom Structures by Scaling Law

Acceleration responses of structures with one degree of freedom (1-DOF) under shocks are investigated based on Buckinghamʹs theorem of nondimension. The nondimensional parameters are determined based on equations of motion for the forced vibration of a mass-support system with 1-DOF. The acceleration responses of structures under possible excitations such as continuous sine wave excitations, single half-sine wave excitations, a train of half-sine wave excitations, and earthquake-like motion excitations are predicated by a numerical scheme. A model structural experiment is developed and carried out to validate the above numerical results. They agree with each other very well for all of the excitations. The scaling law is shown to be applicable for frequencies other than the resonance frequencies.