Joseph J. Hollkamp

Experiments with particle damping

High cycle fatigue in jet engines is a current military concern. The vibratory stresses that cause fatigue can be reduced by adding damping. However, the high temperatures that occur in the gas turbine greatly hinder the application of mature damping technologies. One technology which may perform in the harsh environment is particle damping. Particle damping involves placing metallic or ceramic particles inside structural cavities. As the cavity vibrates, energy is dissipated through particle collisions. Performance is influenced by many parameters including the type, shape, and size of the particles; the amount of free volume for the particles to move in; density of the particles; and the level of vibration. This paper presents results from a series of experiments designed to gain an appreciation of the important parameters. The experimental setup consists of a cantilever beam with drilled holes. These holes are partially filled with particles. The types of particles, location of the particles, fill level, and other parameters are varied. Damping is estimated for each configuration. Trends in the results are studied to determine the influence of the varied parameter.

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying a series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method ...

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been develop...

Computing Nonlinear Normal Modes of Aerospace Structures Using the Multi-harmonic Balance Method

The extreme environments that hypersonic vehicles experience during flight expose the thin structural panels to high aerodynamic pressure loading and large temperature gradients, leading to a highly nonlinear structural response. Reduced order models (ROMs) provide an efficient means to compute nonlinear response, however, the accuracy of a ROM is highly dependent on how it is made: the number of modes included within the basis set and the load scaling factors used. The authors have previously proposed to validate ROMs by computing the Nonlinear Normal Modes (NNMs) of the ROMs and using them to compare ROMs of increasing order. The NNMs are a useful metric because they are independent of a specific loading scenario, yet if the NNMs are reproduced accurately then the response to various resonant inputs will also be accurate. This framework has proven challenging to apply to curved structures because they can exhibit complex softening-hardening behavior as well as many nested internal resonance branches. The numerical integration and shooting method that has been used to compute the NNMs typically tracks all the internal resonances, and so it becomes slow and tends to require manual intervention. This work seeks to address these challenges by applying a Multi-Harmonic Balance (MHB) method rather than the shooting algorithm used previously. One attractive feature of the MHB method is the fact that one can filter out internal resonance branches from the solution by limiting the number of harmonics included. This filtering property will be explored, to ascertain the extent to which it can be used to skip internal resonances and identify the primary backbone branch of the NNMs. Particular attention will be paid to balancing the number of harmonics required to obtain an accurate primary backbone branch, including modal interactions that occur along the backbone. The method is applied to a clamped-clamped flat beam, a complex aerospace panel structure and a curved beam to demonstrate the capabilities.

System Identification to Estimate the Nonlinear Modes of a Gong

Nonlinear Normal Modes (NNMs) have proven useful in a few recent works as a basis for comparing nonlinear models during model updating. In prior works the authors have used force appropriation to measure NNMs, but this is time consuming, generally requiring hand tuning of both the frequency in question and the strength of its harmonics. This paper explores the use of system identification, using a small set of broadband response data, to estimate a model from which the NNMs can be extracted. The Frequency Domain Restoring Force Surface (RFS) method will be used to perform identification, in which the nonlinearity of the system is assumed to be a polynomial function of the modal displacements, and a least squares problem is formed to solve for the nonlinear coefficients. Existing NNM calculation approaches can then be applied to the experimentally determined model in order to calculate the NNMs of the system. This approach is evaluated by applying it to full-field measurements from a traditional Gong, obtained using Stereo 3D Digital Image Correlation (3D–DIC). The results obtained using system identification are validated with measurements of the NNMs obtained using force appropriation and a scanning laser vibrometer.

Design Sensitivities of Components Using Nonlinear Reduced-Order Models and Complex Variables

This work-in-progress paper explores the use of complex variables to define the design sensitivities of high-speed aircraft components modeled by nonlinear reduced-order models (NLROMs). Extreme conditions are expected to be seen by high-speed flight vehicles and it is anticipated that portions of the structure are likely to exhibit significant nonlinearity in their response. Accurate prediction of the path-dependent response requires direct time-integration of nonlinear models. Large finite element models of the structural components would require prohibitively large amounts of computer time to properly simulate. Methodologies have been proposed that use NLROMs to model the component level, dynamic response. The nonlinear ROMs are linear modal models that have been coupled through the addition of nonlinear modal stiffness terms. The nonlinearity in these models is sensitive to the connectivity of the components with the assembly. Recent work has investigated the use of complex variables to update NLROMs based on the boundary stiffness of the adjoining structure. This paper will explore complex methods to determine component design sensitivities to the thermal expansion and stiffness of the surrounding structure.