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.
Experiments were performed to understand the complex fluid-structure interactions that occur during aircraft internal store carriage. A cylindrical store was installed in a rectangular cavity having a length-to-depth ratio of 3.33 and a length-to-width ratio of 1. The Mach number ranged from 0.6 to 2.5 and the incoming boundary layer was turbulent. Fast-response pressure measurements provided aeroacoustic loading in the cavity, while triaxial accelerometers provided simultaneous store response. Despite occupying only 6% of the cavity volume, the store significantly altered the cavity acoustics. The store responded to the cavity flow at its natural structural frequencies, and it exhibited a directionally dependent response to cavity resonance. Specifically, cavity tones excited the store in the streamwise and wall-normal directions consistently, whereas a spanwise response was observed only occasionally. The streamwise and wall-normal responses were attributed to the longitudinal pressure waves and shear layer vortices known to occur during cavity resonance. Although the spanwise response to cavity tones was limited, broadband pressure fluctuations resulted in significant spanwise accelerations at store natural frequencies. The largest vibrations occurred when a cavity tone matched a structural natural frequency, although energy was transferred more efficiently to natural frequencies having predominantly streamwise and wall-normal motions.
A collaborative research institute was organized and held at Sandia Albuquerque for a period of six weeks. This research institute brought together researchers from around the world to work collaboratively on a set of research projects. These research projects included: developing experimental guidelines for studying variability and repeatability of nonlinear structures; decoupling aleatoric and epistemic uncertainty in measurements to improve dynamic predictions; a numerical round robin to assess the performance of five different numerical codes for modeling systems with strong nonlinearities; and an assessment of experimentally derived and numerically derived reduced order models. In addition to the technical collaborations, the institute also included a series of seminars given by both Sandians and external experts, as well as a series of tours and field trips to local places of scientific and engineering importance. This report details both the technical research and the programmatic organization of the 2014 Sandia Nonlinear Mechanics and Dynamics Summer Research Institute.
Experimental dynamic substructures in both modal and frequency response domains using the transmission simulator method have been developed for several systems since 2007. The standard methodology couples the stiffness, mass and damping matrices of the experimental substructure to a finite element (FE) model of the remainder of the system through multi-point constraints. This can be somewhat awkward in the FE code. It is desirable to have an experimental substructure in the Craig-Bampton (CB) form to ease the implementation process, since many codes such as Nastran, ABAQUS, ANSYS and Sierra Structural Dynamics have CB as a substructure option. Many analysts are familiar with the CB form. A square transformation matrix is derived that produces a modified CB form that still requires multi-point constraints to couple to the rest of the FE model. Finally the multi-point constraints are imported to the modified CB matrices to produce substructure matrices that fit in the standard CB form. The physical boundary degrees-of-freedom (dof) of the experimental substructure matrices can be directly attached to physical dof in the remainder of the FE model. This paper derives the new experimental substructure that fits in the CB form, and presents results from an analytical and an industrial example utilizing the new CB form.
This work was motivated by a desire to transform an experimental dynamic substructure derived using the transmission simulator method into the Craig-Bampton substructure form which could easily be coupled with a finite element code with the Craig-Bampton option. Near the middle of that derivation, a modal Craig-Bampton form emerges. The modal Craig-Bampton (MCB) form was found to have several useful properties. The MCB matrices separate the response into convenient partitions related to (1) the fixed boundary modes of the substructure (a diagonal partition), (2) the modes of the fixture it is mounted upon, (3) the coupling terms between the two sets of modes. Advantages of the MCB are addressed. (1) The impedance of the boundary condition for component testing, which is usually unknown, is quantified with simple terms. (2) The model is useful for shaker control in both single degree of freedom and multiple degree of freedom shaker control systems. (3) MCB provides an energy based framework for component specifications to reduce over-testing but still guarantee conservatism.
Developing constitutive models of the physics in mechanical joints is currently stymied by inability to measure forces and displacements within the joint. The current state of the art estimates whole joint stiffness and energy loss per cycle from external measured force input and one or two acceleration responses. To validate constitutive models beyond this state requires a measurement of the distributed forces and displacements at the joint interface. Unfortunately, introducing measurement devices at the interface completely disrupts the desired physics. A feasibility study is presented for a non-intrusive method of solving for the interface dynamic forces from an inverse problem using full field measured responses. The responses come from the viewable surface of a beam. The noise levels associated with digital image correlation and continuous scanning laser Doppler velocimetry are evaluated from typical beam experiments. Two inverse problems are simulated. One utilizes the extended Sum of Weighted Accelerations Technique (SWAT). The second is a new approach dubbed the method of truncated orthogonal forces. These methods are much more robust if the contact patch geometry is well identified. Various approaches to identifying the contact patch are investigated, including ion marker tracking, Prussian blue and ultrasonic measurements. A typical experiment is conceived for a beam which has a lap joint at one end with a single bolt connecting it to another identical beam. In a virtual test using the beam finite element analysis, it appears that the SWAT inverse method requires evaluation of too many coefficients to adequately identify the force distribution to be viable. However, the method of truncated orthogonal forces appears viable with current digital image correlation (and probably other) imaging techniques.
Experiments were performed to understand the complex fluid-structure interactions that occur during internal store carriage. A cylindrical store was installed in a cavity having a length-to-depth ratio of 3.33 and a length-to-width ratio of 1. The Mach number ranged from 0.6 - 2.5 and the incoming turbulent boundary layer thickness was about 30-40% of the cavity depth. Fast-response pressure measurements provided aeroacoustic loading in the cavity, while triaxial accelerometers and laser Doppler vibrometry provided simultaneous store response. Despite occupying only 6% of the cavity volume, the store significantly altered the cavity acoustics. The store responded to the cavity flow at its natural structural frequencies, as previously determined with modal hammer tests, and it exhibited a directional dependence to cavity resonance. Specifically, cavity tones excited the store in the streamwise and wall-normal directions consistently, while a spanwise response was observed only occasionally. The streamwise and wall-normal responses were attributed to the known pressure gradients in these directions. Furthermore, spanwise vibrations were greater at the downstream end of the cavity, attributable to decreased levels of flow coherence near the aftwall. Collectively, the data indicate the store response to be dependent on direction of vibration and position along the length of the store.