Lumping of Mass in Calculating Vibration Response

Analytical results are presented in which the vibration response of a uniform Bernoulli-Euler cantilever beam carrying a tip mass is compared with that of a weightless beam supporting sixteen concentrated masses. Natural frequencies and effective masses are presented for the impedance or steady-state behavior. For the shock problem, effective modal masses, as well as modal bending moment factors, are examined. Results show that the lumped mass beam depicts the shock response parameters more accurately than those associated with steady velocity at a driven point. For both shock and steady loading, the lumped mass model becomes more accurate as the ratio of tip mass to beam mass increases.