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.
Even with the advent of additive manufacturing, the vast majority of complex structures are comprised of individual components held together with bolted joints. However, bolted joints present a challenge for mechanical design as they are a source of nonlinearity and increase the uncertainty in the overall behavior of the system in a dynamic environment. While many advances have been made in the ability to accurately model and test bolted joints, it is still an open area of research. Modes of vibration that exercise bolted joints typically exhibit nonlinear behavior where, with increased excitation level, the natural frequency decreases (i.e. softens) and the damping increases. However, the system under study for this work has an axial mode which does not follow this trend; it does soften as expected, but, after an initial increase, the apparent damping decreases with excitation amplitude. At the highest excitation level, the frequency of the mode decreases to that of a nearby bending mode and the response is amplified nearly 500% above that at lower levels. It is unclear whether the decrease in damping is due to the coupling of the two modes or if it is a characteristic of the axial mode. Therefore, the objective of this project is to investigate the coupling between the axial and bending modes and the dynamics leading to the decrease in damping.
Electrical switches are often subjected to shock and vibration environments, which can result in sudden increases in the switch's electrical resistance, referred to as 'chatter'. This paper describes experimental and numerical efforts to investigate the mechanism that causes chatter in a contact pair formed between a cylindrical pin and a bifurcated receptacle. First, the contact pair was instrumented with shakers, accelerometers, laser doppler vibrometers, a high speed camera, and a 'chatter tester' that detects fluctuations in the contact's electrical resistance. Chatter tests were performed over a range of excitation amplitudes and frequencies, and high speed video from the tests suggested that 'bouncing' (i.e. loss of contact) was the primary physical mechanism causing chatter. Structural dynamics models were then developed of the pin, receptacle, and contact pair, and corresponding modal experiments were performed for comparison and model validation. Finally, a high-fidelity solid mechanics model of the contact pair was developed to study the bouncing physics observed in the high speed videos. Chatter event statistics (e.g. mean chatter event duration) were used to compare the chatter behavior recorded during testing to the behavior simulated in the high-fidelity model, and this comparison suggested that the same bouncing mechanism is the cause of chatter in both scenarios.
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.
Experimental modal analysis via shaker testing introduces errors in the measured structural response that can be attributed to the force transducer assembly fixed on the vibrating structure. Previous studies developed transducer mass-cancellation techniques for systems with translational degrees of freedom; however, studies addressing this problem when rotations cannot be neglected are sparse. In situations where rotations cannot be neglected, the apparent mass of the transducer is dependent on its geometry and is not the same in all directions. This paper investigates a method for correcting the measured system response that is contaminated with the effects of the attached force transducer mass and inertia. Experimental modal substructuring facilitated estimations of the translational and rotational mode shapes at the transducer connection point, thus enabling removal of an analytical transducer model from the measured test structure resulting in the corrected response. A numerical analysis showed the feasibility of the proposed approach in estimating the correct modal frequencies and forced response. To provide further validation, an experimental analysis showed the proposed approach applied to results obtained from a shaker test more accurately reflected results obtained from a hammer test.
Several recent studies (Mayes, R.L., Pacini, B.R., Roettgen, D.R.: A modal model to simulate typical structural dynamics nonlinearity. In: Proceedings of the 34th International Modal Analysis Conference. Orlando, FL, (2016); Pacini, B.R., Mayes, R.L., Owens, B.C., Schultz, R.: Nonlinear finite element model updating, part I: experimental techniques and nonlinear modal model parameter extraction. In: Proceedings of the 35th international modal analysis conference, Garden Grove, CA, (2017)) have investigated predicting nonlinear structural vibration responses using modified modal models. In such models, a nonlinear element is added in parallel to the traditional linear spring and damping elements. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. Previous studies have predominantly applied this method to idealistic structures. In this work, the nonlinear modal modeling technique is applied to a more realistic industrial aerospace structure which exhibits complex bilinear behavior. Linear natural frequencies, damping values, and mode shapes are first extracted from low level shaker testing. Subsequently, the structure is excited using high level tailored shaker inputs. The resulting response data are modally filtered and used to empirically derive the nonlinear elements which, together with their linear counterparts, comprise the nonlinear modal model. This model is then used in both modal and physical domain simulations. Comparisons to measured data are made and the performance of the nonlinear modal model to predict this complex bilinear behavior is discussed.