Publications

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This work extends recent methods to calculate dynamic substructuring predictions of a weakly nonlinear structure using nonlinear pseudo-modal models. In previous works, constitutive joint models (such as the modal Iwan element) were used to capture the nonlinearity of each subcomponent on a mode-by-mode basis. This work uses simpler polynomial stiffness and damping elements to capture nonlinear dynamics from more diverse jointed connections including large continuous interfaces. The proposed method requires that the modes of the system remain distinct and uncoupled in the amplitude range of interest. A windowed sinusoidal loading is used to excite each experimental subcomponent mode in order to identify the nonlinear pseudo-modal models. This allows for a higher modal amplitude to be achieved when fitting these models and extends the applicable amplitude range of this method. Once subcomponent modal models have been experimentally extracted for each mode, the Transmission Simulator method is implemented to assemble the subcomponent models into a nonlinear assembled prediction. Numerical integration methods are used to evaluate this prediction compared to a truth test of the nonlinear assembly.

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Linear structural dynamic models are often used to support system design and qualification. Overall, linear models provide an efficient means for conducting design studies and augmenting test data by recovering un-instrumented or unmeasurable quantities (e.g. stress). Nevertheless, the use of linear models often adds significant conservatism in design and qualification programs by failing to capture critical mechanisms for energy dissipation. Unfortunately, the use of explicit nonlinear models can require unacceptably large efforts in model development and experimental characterization to account for common nonlinearities such as frictional interfaces, macro-slip, and other complex material behavior. The computational requirements are also greater by orders of magnitude. Conversely, modal models are much more computationally efficient and experimentally have shown the ability to capture typical structural nonlinearity. Thus, this work will seek to use modal nonlinear identification techniques to improve the predictive capability of a finite element structural dynamics model. Part I of this paper discusses the experimental aspects of this work. Linear natural frequencies, damping values, and mode shapes are extracted from low excitation level testing. Subsequently, the structure is excited with high level user-defined shaker inputs. The corresponding response data are modally filtered and fit with nonlinear elements to create the nonlinear pseudo-modal model. This is then used to simulate the measured response from a high level excitation experiment which utilized a different type of input. The nonlinear model is then employed in a reduced order, generalized structural dynamics model as discussed in Part II.

Linear structural dynamic models are often used to support system design and qualification. Overall, linear models provide an efficient means for conducting design studies and augmenting test data by recovering un-instrumented or unmeasurable quantities (e.g. stress). Nevertheless, the use of linear models often adds significant conservatism in design and qualification programs by failing to capture critical mechanisms for energy dissipation. Unfortunately, the use of explicit nonlinear models can require unacceptably large efforts in model development and experimental characterization to account for common nonlinearities such as frictional interfaces, macro-slip, and other complex material behavior. The computational requirements are also greater by orders of magnitude. Conversely, modal models are much more computationally efficient and experimentally have shown the ability to capture typical structural nonlinearity. Thus, this work will seek to use modal nonlinear identification techniques to improve the predictive capability of a finite element structural dynamics model. Part I of this paper discussed experimental aspects of this work. Part II will consider use of nonlinear modal models in finite element modeling. First, the basic theory and numerical implementation is discussed. Next, the linear structural dynamic model of a configuration of interest is presented and model updating procedures are discussed. Finally, verification exercises are presented for a high level excitation using test data and simulated predictions from a structural dynamics model augmented with models obtained in nonlinear identification efforts.

One of the more common forms of passive vibration isolation in mechanical systems has been the use of elastomeric or foam pads. Cellular silicone foam is one such example which has been used for vibration isolation and mitigating the effects of mechanical shock. There are many desirable properties of cellular silicone, including its resilience and relative insensitivity to environmental extremes. However, there is very little test data that is useful for understanding its dynamic characteristics or for the development of a predictive finite element model. The problem becomes increasingly difficult since foam materials typically exhibit nonlinear damping and stiffness characteristics. In this paper we present a test fixture design and method for extraction of a few dynamic properties of one type of cellular silicone foam pad. The nonlinear damping characteristics derived from the experimental testing are then used to attempt to improve the predictive capability of a linear finite element model of the system. Difficulties and lessons learned are also presented.

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Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.

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Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.