Abstract:The calculation of dynamic behaviors of a beam structure with a lumped mass of both translational and rotary inertias is 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 attachment can be calculated accurately using the higher-order beam elements. Further, numerical results show that use of the generic beam element of the cubic polynomial displacement can also achieve the frequency sensitivity satisfactorily with a dense finite element mesh.