A Symmetric Method for Modal Computation of Non-Classically Damped Structures Avoiding Breakdowns

Modal computation involving dampers has gained increasing attention due to the widespread use of dampers in structural dynamics. The damping matrix associated with dampers is non-classical via finite element analysis (FEA). The HR process, similar to the well-known QR process, can be used to solve that modal computation. However, the HR decomposition in HR process may be unavailable and cause breakdowns. This paper proposes a symmetric generalized HR process to solve the generalized indefinite eigenvalue problem along with a J-matrix, which is defined as a diagonal matrix with entries [Formula: see text] or [Formula: see text] on its diagonal. New breakdown criteria and corresponding solution methods in the generalized HR process are proposed, which can successfully avoid breakdowns. Meanwhile, it explicitly expresses the J-matrix in each step and provides a clearer process. Numerical examples demonstrate that the generalized HR process is effective and robust in dealing with structural dynamics and against breakdowns. Moreover, it offers valuable guidance for the solvers when considering a non-classical damping matrix in FEA.