Investigating Nonlinearity in a Bolted Structure Using Force Appropriation Techniques

Abstract

Understanding the dynamic response of a structure is critical to design. This is of extreme importance in high-consequence systems on which human life can depend. Historically, these structures have been modeled as linear, where response scales proportionally with excitation amplitude. However, most structures are nonlinear to the extent that linear models are no longer sufficient to adequately capture important dynamics. Sources of nonlinearity include, but are not limited to: large deflections (so called geometric nonlinearities), complex materials, and frictional interfaces/joints in assemblies between subcomponents. Joint nonlinearities usually cause the natural frequency to decrease and the effective damping ratio to increase with response amplitude due to microslip effects. These characteristics can drastically alter the dynamics of a structure and, if not well understood, could lead to unforeseen failure or unnecessarily over-designed features.

Nonlinear structural dynamics has been a subject of study for many years, and provide a summary of recent developments and discoveries in this field. One topic discussed in these papers are nonlinear normal modes (NNMs) which are periodic solutions of the underlying conservative system. They provide a theoretical framework for describing the energy-dependence of natural frequencies and mode shapes of nonlinear systems, and lead to a promising method to validate nonlinear models. In and, a force appropriation testing technique was developed which allowed for the experimental tracking of undamped NNMs by achieving phase quadrature between the excitation and response. These studies considered damping to be small to moderate, and constant. Nonlinear damping of an NNM was studied in using power-based quantities for a structure with a discrete, single-bolt interface. In this work, the force appropriation technique where phase quadrature is achieved between force and response as described in is applied to a target mode of a structure with two bolted joints, one of which comprised a large, continuous interface. This is a preliminary investigation which includes a study of nonlinear natural frequency, mode shape, and damping trends extracted from the measured data.