A Technique for Relating Vehicle Structural Modes to Stiffness as Determined in Static Determinate Tests

During the development of a new vehicle, the vehicle is usually tested to determine both its static torsional and bending stiffness, and its dynamic torsional and bending modes. This paper discusses a method for determining both static and dynamic properties from the modal analysis test. Such a connection between static stiffness and dynamic modes would be useful for three reasons: (1) the relative importance of apparent bending and torsion modes could be determined by their contribution to stiffness, (2) the stiffening effect of structural modifications could be determined from experimental modal tests (the modal frequency shift is also affected by any change in mass), (3) the total static compliance could easily be split on a modal basis into compliance due to the overall structure and local compliance due to local structural deflections. INTRODUCTION For NVH purposes vehicle structural characteristics are usually characterized either by the stiffness (or compliance) as measured in a static test, or by the structural vibration modes measured in a dynamic test. The static test is usually almost static determinate, that is the reaction forces are related to the applied forces by the test geometry. The dynamic modal tests are “freefree”, that is the dynamic forces applied by the support system can be ignored. It is well known that the static compliance is important for NVH, for example low torsional compliance leads to vehicle shake, squeaks and rattles. Also low torsional compliance degrades vehicle handling. The static compliance and the modes are connected in that as stiffness is decreased (mass being held constant) the modal frequencies are decreased. For example, if a sedan is changed into a convertible by removing the greenhouse, the torsional rigidity is drastically reduced, the main torsional mode frequency drops into the range of the main suspension hop-tramp modes, and the vehicle becomes very shaky unless countermeasures are taken. This paper shows an explicit relationship between compliance measurements and dynamic modal measurements. Conventional vehicle modal analysis is often confused by a variety of local modes. For example, seat-back fore-aft modes may also be associated with overall bending and torsion. It is not uncommon that the column bending mode is close to the body bending mode and the resultant coupling leads to difficulty in interpreting the modes. The methods described in this paper show each mode can be related to its contribution to the relevant static test, and thus how the relative importance of modes can be determined. Frequently it would be valuable to determine the relative contribution of overall and local compliance to the total compliance. This can be done on a modal basis by separating out the contributions on the basis of frequency since the overall modes are generally at low frequencies, and the local modes contributing to total compliance occur at high frequency. MAIN SECTION THEORY Given a static determinate test involving only forces and translational displacements, it can be shown (see appendix) that all the forces (Fn) can be written in terms of a single generalized force F and a set of coefficients that depend only on geometry and the scaling of the generalized force: