Sensitivity calculation of beam-mass structure using higher-order beam element

The calculation of dynamic behaviors of a beam structure with a lumped mass with both translational and rotary inertias was studied using two types of higher-order beam elements. By adding respectively independent variables of the curvature and its first-order derivative at a node, the frequency and its sensitivity with respect to the position of the lumped mass attached were calculated accurately using the higher-order beam elements. Numerical results show that the use of generic beam element of the cubic polynomial displacement can also achieve the frequency sensitivity satisfactorily with a dense finite element mesh.