Synthesis of Reactive Mechanical Circuits for Impact Loading

Abstract

High-speed operation of modern machines has emphasized the effects of high loading rates and impacts. With wide-frequency-band excitation, it becomes necessary to consider an extended range of structural resonances to determine dynamic response and to improve the effectiveness of structural damping. In this paper, synthesis techniques are applied to the design of simple undamped (i.e., reactive) structural elements. Synthesis of mechanical circuits is complicated by the characteristically large numbers of degrees of freedom, and by difficulties of response measurement over a wide frequency range. However, Cauer's method of ladder network synthesis is readily applied for more than 20 alternating zeros and poles arrayed in a wide variety of frequency patterns. Of particular interest for dissipative purposes is the equal frequency spacing of zeros and poles for the reactive structure. Examples are given of circuit synthesis for this zero-pole spacing in the derivation of dimensions for simple circuits, including 15 degree-of-freedom ladders, cantilever beams, and circular disks. Computed circuit characteristics are then verified by mechanical driving-point impedance measurements over a frequency range extending to 50 kc/sec.