Lumped Parameter Beam Models Based on Mechanical Impedance

摘要

Using an impedance approach, an optimum three mass model is developed to represent a segment of a uniform Bernoulli-Euler beam. The four by four impedance matrix relating shear force, bending moment, slope, and deflection at the two ends of the element is given for the uniform beam and for the lumped parameter model. Position and size of the masses are chosen so that the impedance matrix for the optimum lumped parameter model will be the same as that for the uniform beam in the low frequency range. It is demonstrated that transient shear and bending stresses due to ground shock are represented accurately with fewer degrees of freedom using the optimum model developed. Evaluation of combinations of models is included. (Author)