Dynamic stiffness for structures with distributed deterministic or random loads

The dynamic stiffness method applies mainly to excitations of harmonic noda l forces. For distributed loads, modal analysis is generally required. In t he case of a clamped-clamped beam, the modal decomposition of a uniformly d istributed load by the eigen beam functions inherits slow convergence becau se the finite loads at the beam-ends cannot be represented efficiently by t he zero deflection and zero slope of the clamped-clamped beam functions. Th e computed reactions at the supports do not converge at all. The problem is eliminated in this paper by using the finite element interpolation functio ns for the distributed load. If the distributed load is adequately represen ted, explicit exact solutions are found. Otherwise, the residual load is ex panded in the modal space. As the residual modal force is much smaller and agrees well with the clamped-clamped conditions, fast convergence is achiev ed. By means of the principle of superposition, a structure with members ha ving distributed loads can be analyzed by two systems: one is associated wi th the individual members having distributed loads and the other is associa ted with resulting equivalent nodal forces. The required frequency function s are given for all possible cases. The results presented are exact if the load is interpolated adequately by finite element shape functions. Both det erministic and random loads are considered. Closed-form solutions are obtai ned for the first time. (C) 2001 Academic Press.