Static Torsional Stiffness From Dynamic Measurements Using Impedance Modeling Technique Hasan G. Pasha, Randall J. Allemang, David L. Brown and Allyn W. Phillips University of Cincinnati – Structural Dynamics Research Lab (UC-SDRL), Cincinnati, Ohio, USA Abstract. Static torsional stiffness of a structure is the measure of the resistance it offers to twisting. It is an important design parameter for structures subjected to torsion loading. Estimating the static torsional and bending stiffness values of a structure from test rigs is resource intensive. In order to obtain reasonable estimates of static torsional stiffness at a minimal cost and less time, diagnostic procedures that are efficient and accurate are needed. A method that utilizes the impedance modeling technique to extract the static stiffness from free-free modal test is discussed in this paper. The results of applying this technique on a rectangular plate structure are compared with analytical estimates for static torsional stiffness. The merits and limitations of this technique are also discussed. Keywords. Impedance Modeling, Dynamic Stiffness method, Compliance method, Hybrid Impedance method, Static Torsional Stiffness Notation Symbol Description [·] -1 Inverse of matrix [·] [·] +1 Pseudo-Inverse of matrix [·] Δ Vertical deflection (in) θ Angular deflection (rad) ω Frequency (rad/s) F Applied force (lb f ) [H(ω)] Free boundary FRFs ( X F ) [H mod ] Modified compliance/FRF matrix [ΔK dyn ] Modification dynamic stiffness matrix [K mod ] Modified dynamic stiffness matrix K SS Driving-point stiffness K T Static torsional stiffness L f Distance between front DOFs (in) L r Distance between rear DOFs (in) T Applied Torque (lb f in) DOF Degree of freedom DOF 1 Left front DOF, z–direction DOF 2 Right front DOF, z–direction DOF 3 Left rear DOF, z–direction DOF 4 Right rear DOF, z–direction 1. Introduction The performance of an automobile with respect to vehicle dynamics and passenger ride comfort is characterized by the auto-body’s global static and dynamic stiffnesses [2]. Currently, special test rigs are used to estimate static stiffnesses. A method based utilizing dynamic measurements (usually taken from a free-free modal test) together with modeling techniques to estimate the static stiffnesses has been developed. Both existing approaches take considerable resources to arrive at a reasonable estimate of the global torsion and bending stiffnesses. In order to obtain reasonable estimates of static global stiffnesses at a minimal cost and less time, diagnostic procedures that