Publications

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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.

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.

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.

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.

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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.

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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.

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.

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