The Use of Passive Element Electrical Analogs in Numerically Calculating the Response Characteristics of Beams

This discussion has two major objectives: 1) To present a derivation of passive element electrical circuits for the Bernoulli-Euler Beam, the Timoshenko Beam and a beam on an elastic foundation. 2) To formulate the dynamics for two arbitrarily selected beam systems by direct use of the analog circuits. The analog circuits are force-current, velocity voltage electrical analogies which allow the study of transient, static and steady-state conditions. The beam systems considered are the cantilever beam and a beam with both ends clamped. Moreover, the numerical formulation requires only elementary circuit theory and is expressed in a format such that conventional iteration procedures can be used in calculating the resonant frequencies and mode shapes. The concepts presented here can be extended to efficiently analyze more complex structures such as plates, shells and conic sections.