Calibrating a finite element model to test data is often required to accurately characterize a joint, predict its dynamic behavior, and determine fastener fatigue life. In this work, modal testing, model calibration, and fatigue analysis are performed for a bolted structure, and various joint modeling techniques are compared. The structure is designed to test a single bolt to fatigue failure by utilizing an electrodynamic modal shaker to axially force the bolted joint at resonance. Modal testing is done to obtain the dynamic properties, evaluate finite element joint modeling techniques, and assess the effectiveness of a vibration approach to fatigue testing of bolts. Results show that common joint models can be inaccurate in predicting bolt loads, and even when updated using modal test data, linear structural models alone may be insufficient in evaluating fastener fatigue.
Nonlinear force appropriation is an extension of its linear counterpart where sinusoidal excitation is applied to a structure with a modal shaker and phase quadrature is achieved between the excitation and response. While a standard practice in modal testing, modal shaker excitation has the potential to alter the dynamics of the structure under test. Previous studies have been conducted to address several concerns, but this work specifically focuses on a shaker-structure interaction phenomenon which arises during the force appropriation testing of a nonlinear structure. Under pure-tone sinusoidal forcing, a nonlinear structure may respond not only at the fundamental harmonic but also potentially at sub- or superharmonics, or it can even produce aperiodic and chaotic motion in certain cases. Shaker-structure interaction occurs when the response physically pushes back against the shaker attachment, producing non-fundamental harmonic content in the force measured by the load cell, even for pure tone voltage input to the shaker. This work develops a model to replicate these physics and investigates their influence on the response of a nonlinear normal mode of the structure. Experimental evidence is first provided that demonstrates the generation of harmonic content in the measured load cell force during a force appropriation test. This interaction is replicated by developing an electromechanical model of a modal shaker attached to a nonlinear, three-mass dynamical system. Several simulated experiments are conducted both with and without the shaker model in order to identify which effects are specifically due to the presence of the shaker. The results of these simulations are then compared to the undamped nonlinear normal modes of the structure under test to evaluate the influence of shaker-structure interaction on the identified system's dynamics.
A proper understanding of the complex physics associated with nonlinear dynamics can improve the accuracy of predictive engineering models and provide a foundation for understanding nonlinear response during environmental testing. Several researchers and studies have previously shown how localized nonlinearities can influence the global vibration modes of a system. This current work builds upon the study of a demonstration aluminum aircraft with a mock pylon with an intentionally designed, localized nonlinearity. In an effort to simplify the identification of the localized nonlinearity, previous work has developed a simplified experimental setup to collect experimental data for the isolated pylon mounted to a stiff fixture. This study builds on these test results by correlating a multi-degree-of-freedom model of the pylon to identify the appropriate model form and parameters of the nonlinear element. The experimentally measured backbone curves are correlated with a nonlinear Hurty/Craig-Bampton (HCB) reduced order model (ROM) using the calculated nonlinear normal modes (NNMs). Following the calibration, the nonlinear HCB ROM of the pylon is attached to a linear HCB ROM of the wing to predict the NNMs of the next-level wing-pylon assembly as a pre-test analysis to better understand the significance of the localized nonlinearity on the global modes of the wing structure.
One of the more crucial aspects of any mechanical design is the joining methodology of parts. During structural dynamic environments, the ability to analyze the joint and fasteners in a system for structural integrity is fundamental, especially early in a system design during design trade studies. Different modeling representations of fasteners include spring, beam, and solid elements. In this work, we compare the various methods for a linear system to help the analyst decide which method is appropriate for a design study. Ultimately, if stresses of the parts being connected are of interest, then we recommend the use of the Ring Method for modeling the joint. If the structural integrity of the fastener is of interest, then we recommend the Spring Method.
Motivation: Crucial aspect of mechanical design is joining methodology of parts. Ability to analyze joint and fasteners in system for structural integrity is fundamental. Different modeling representations of fasteners include spring, beam, and solid elements. Various methods compared for linear system to decide method appropriate for design study. New method for modeling fastener joint is explored from full system perspective. Analysis results match well with published experimental data for new method.
The industrial approach to nonlinearities in structural dynamics is still very conservative, particularly from an experimental point of view. A demo aluminum aircraft has been equipped with discrete nonlinear elements designed to replicate real-world engine pylon subassemblies to increase awareness on the effects of nonlinearities in design, and understand how these effects can be positively exploited, if properly understood. After some preliminary experiments aimed at understanding the coupled behavior of the aircraft-pylon mockup, it became clear that more in-depth numerical and experimental analyses are required on the pylon subassembly alone. For this paper, experimental data is collected to analyze the nonlinear dynamic behavior of the pylon, leading to better understanding of the subassembly once it connects to the aircraft. The pylon element has three main sources of nonlinearities: (1) geometric nonlinearities of the connecting beam, (2) contact as the beam presses into the tapered block surface and (3) friction in the bolted connections. Backbone curves are generated, which map the evolution of natural frequency and damping ratio with excitation amplitude. Using the experimental data, a low-order nonlinear model is identified to replicate the backbone characteristics and response of the pylon.
In many applications, components that are difficult or inconvenient to represent as a finite element model (FEM) are instead experimentally characterized to capture their contribution to the overall dynamics of an assembly. A recent advance in experimental substructuring, the Transmission Simulator method, has proven promising for coupling an experimentally identified model to analytical FEMs. While in typical applications all experimental and FEM data is imported into MATLAB and assembled in modal coordinates, it would be preferable to perform equivalent operations in finite element software where large models are readily handled and results are easily visualized and post-processed. This work details a process for importing experimental modal models into the Dassault Systèmes® SIMULIA™ Abaqus finite element analysis software suite through an application of the Transmission Simulator method. In this approach, after decoupling the TS from the experimental subsystem in MATLAB, the result is represented as single degree-of-freedom (DOF) spring-mass oscillators in Abaqus. These are coupled to the native Abaqus FEM by implementing the substructuring constraint equations as linear equation multipoint constraints between the necessary DOF. This approach is shown to perform very well in an analytical test case and reasonably well in an experimental test case. The limiting factors appear to be the quality of measured data and curve fitting used in defining the modal properties of the experimental subsystem, the quantity and location of constraint DOF, and the selection of modes used to represent each subsystem. These determine the quality of the decoupled experimental model, which dictates how accurate the result will be after coupling it to the FEM subsystem.
In complex structures, particularly those with jointed interfaces, the dynamic response of individual modes can behave nonlinearly. To simplify analyzing and modeling this response, it is typically assumed that modes are uncoupled, in that each responds independently of the excitation level of other modes. This assumption is derived from the belief that, while modal coupling generally exists in physical structures, its effects are relatively small and negligible. This practice is reinforced by the fact that the actual causes of modal coupling are poorly understood and difficult to model. To that end, this work attempts to isolate and fit a model to the effects of modal coupling in experimental data from a nonlinear structure. After performing a low-level test to determine the linear natural frequencies and damping ratios of several modes, sine beat testing is used to individually excite each mode and record its nonlinear dynamic response. The Restoring Force Surface (RFS) method is then implemented to fit a nonlinear model to each isolated modal response. Sine beats are then done on multiple modes simultaneously, in which the response is assumed to be a combination of the nonlinear models of each isolated mode and some coupling term between them. As the terms modeling the individual modes are known, the only unknown is the coupling term. This procedure is performed on several mode pairs and excitation levels to evaluate the effectiveness of all proposed coupling models and gauge the significance of modal coupling in the structure.
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.