Abstract: A vibration analysis of a structure with joints is performed. The
simulation is conducted with finite element software capable of performing a
numeric modal analysis with hysteretic damping assumption. The joints are
modeled with thin layer elements, representing dissipation and stiffness of the
joints. The matrices describing the system consist of the mass, as well as real
and complex-valued stiffness matrices. If the eigenvalues of this system are
found in one step, due to the mode crossing occurring for the closely spaced
modes, it is difficult and time consuming to assign calculated modal damping
factors to the corresponding undamped eigenvalues. In order to avoid this
problem, an eigenvalue following method is used. The outcome of the solution is
the graphical presentation of continuous eigenvalue paths, showing the change
in the eigenvalues from the undamped to the fully damped case. For every
undamped eigenvalue exists its equivalent eigenfrequency and damping factor
that can be used for further numerical analysis. In scope of this article a
Predictor-Corrector and a Rayleigh-Quotient Iteration algorithms are applied to
the problem. The algorithms are tested specifically on the type of matrices
resulting from the weakly damped hysteretic formulation arising from the
simulation of metallic structures with joints.
