Model reduction tools for nonlinear structural dynamics

Three mode types are proposed for reducing nonlinear dynamical system equations, resulting from finite element discretizations: tangent modes, modal derivatives, and newly added static modes. Tangent modes are obtained from an eigenvalue problem with a momentary tangent stiffness matrix. Their derivatives with respect to modal coordinates contain much beneficial reduction information. Three approaches to obtain modal derivatives are presented, including a newly introduced numerical way. Direct and reduced integration results of truss examples show that tangent modes do not describe the nonlinear system sufficiently well, whereas combining tangent modes with modal derivatives and/or static modes provides much better reduction results. [Author abstract; 7 Refs; In English]