Nonlinear Forced Response Synthesis with Quasi-Static Modal Analysis.
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Ferroelectric materials based on lead zirconate titanate (PZT) are widely used as sensors and actuators because of their strong piezoelectric activity. However, their application is limited because of the high processing temperature, brittleness, lack of conformal deposition, and a limited possibility to be integrated with the microelectromechanical systems (MEMS). Recent studies on the piezoelectricity in the 2-D materials have demonstrated their potential in these applications, essentially due to their flexibility and integrability with the MEMS. In this work, we deposited a few layer graphene (FLG) on the amorphous oxidized Si 3 N 4 membranes and studied their piezoelectric response by sensitive laser interferometry and rigorous finite-element modeling (FEM) analysis. Modal analysis by FEM and comparison with the experimental results show that the driving force for the piezoelectric-like response can be a polar interface layer formed between the residual oxygen in Si 3 N 4 and the FLG. The response was about 14 nm/V at resonance and could be further enhanced by adjusting the geometry of the device. These phenomena are fully consistent with the earlier piezoresponse force microscopy (PFM) observations of the piezoelectricity of the graphene on SiO 2 and open up an avenue for using graphene-coated structures in the MEMS.
Lunar soil 15601 has been studied petrographically using grain size analysis, modal analysis, and electron probe microanalysis of monomineralic fragments in the 90-150-micron size fraction. The soil is immature; the grain size distribution is unimodal and very symmetrical, indicating that the soil is a homogeneous product of a single set of processes. It is concluded that 15601 is mostly a simple Apollo 15 mare basalt soil, and its properties can be used to approximate an end product of the array of complex soils that the lunar sample missions have returned.
The petrology of submillimeter fractions of soils from 13 levels of Apollo 15 drive tube 15007/8 have been studied through grain size analysis, modal analysis of the 90-150 micron sieve fraction, and electron probe microanalysis of monomineralic fragments of olivine, pyroxene, and plagioclase from the soils. It is shown that core 15007/8 does not contain distinct lithologic units and probably contains soils of mixed maturity in which mixing has greatly dominated in situ reworking. No petrologic layering is found in the core. Abundances of KREEP basalts correlate with mare basalts and not with anorthosite, norite, and troctolite components from the Apennine Front. Some olivine and pyroxene fragments with mare basalt affinity are found to be optically and chemically unzoned, suggesting that they may have been derived from unusual source rocks.
Modern analytical techniques have expended the ability to evaluate solid rocket motors used in launch vehicles. As more detailed models of solid rocket motors were developed, testing methods were required to verify the models. Experimental modal analysis (modal testing) of space structures and launch vehicles has been a requirement for model validation for many years. However, previous testing of solid rocket motors has not typically involved dynamic modal testing of full scale motors for verification of solid propellant or system assembly properties. Innovative approaches to the testing of solid rocket motors were developed and modal testing of a full scale, two segment Titan 34D Solid Rocket Motor (SRM) was performed to validate detailed computer modeling. Special modifications were made to convert an existing facility into a temporary modal test facility which would accommodate the test article. The assembly of conventional data acquisition equipment into a multiple channel count portable system has made modal testing in the field feasible. Special purpose hydraulic exciters were configured to apply the dynamic driving forces required. All instrumentation and data collection equipment were installed at the test site for the duration of the test program and removed upon completion. Conversion of an existing test facility into a temporary modal test facility, and use of a multiple channel count portable test data acquisition system allowed all test objectives to be met and resulted in validation of the computer model in a minimum time.
Based on previous demonstrated success at fabricating 5 and 10 kW scale magnetic gearbox (MGB) prototypes, Emrgy and its partners (the project team) proposed to design and construct a 100 kW scale MGB with a 30:1 gear ratio for the low-head hydro applications. The Statement of Project Objectives included tasks covering: 1) Market Applicability; 2) Technical Metrics; 3) Design (initial); 4) Electromagnetic (EM) Load and Structural Analysis; 5) Modal Analysis; 6) Sealing Design and 7) Final Design during Budget Period 1. Budget Period 2 included tasks covering: 1) Materials Procurement and Test Plan Development; 2) Assembly; and 3) Testing. The Market Applicability study (Task 1) led to a clear conclusion and recommendation toward “Low Head” technologies for maximum market share of both New Stream Reach development as well as powering Non-Powered Dams. The findings of this study also identified the opportunity for a larger scale magnetic gearbox-based drive train as a function of increased torque, as opposed to increased speed. The Technical Metrics Study (Task 2) concluded a horizontal orientation was preferred, examined potential loss mechanisms, concluded that a Halbach Array magnetic design was preferred, established a 30:1 gear ratio as optimal, and established a power rating of 100 kW as optimal. The subsequent initial and final detailed design process included electro-magnetic (EM) load and structural analysis (Task 4), a Modal analysis (for vibration) (Task 5), and a sealing design (Task 6) to assure water impermeability. The final design package (Task 7) included 729 individual parts, 117 unique part numbers, and 15 assemblies. In order to facilitate procurement, the full bill of materials was broken down into several sub-components: 1) custom magnetic parts; 2) custom machined parts; 3) custom casted parts; and 4) commercial off the shelf (COTS) parts. The casted parts were fabricated by Oak Ridge National Laboratory (ORNL) via a Cooperative Research and Development Agreement (CRADA) with Emrgy and funded by the Advanced Manufacturing Office (AMO). The procurement effort (Task 8) ultimately covered three time periods based on challenges encountered in meeting the budgeted cost for the prototype. Following the first effort in the early stages of Budget Period 2 in 2017, a no-cost time extension was granted to seek alternative fabrication and procurement options. The project was re-booted in 2020 based on the new ORNL CRADA that would focus on five (5) of the more difficult and expensive parts using their advanced manufacturing expertise. Procurement efforts for the other custom machined parts resulted in quotations that still exceeded the budget by more than $\$$100k. This was, in part, also due to the concurrent COVID-19 pandemic that caused both supply chain disruptions and labor shortages. As the project continued, pricing and availability degraded further. In Q2 FY’22, it was decided to not proceed with the fabrication of the prototype (Task 9) based on budgetary limitations. Outcomes included a full and detailed design of a 100 kW magnetic gearbox and associated indented bill of materials (BOM) and CAD drawings, a full assembly instruction manual with an associated BOM for materials necessary to support assembly, the fabrication of the double Halbach magnetic array for the rotor/stator system, fabrication of five (5) sand-casted/machined parts (via CRADA with ORNL) and an initial draft of a comprehensive testing plan. The most significant non-outcome was the actual fabrication and testing of the prototype gearbox based on budget limitations. Lessons learned included the need for an Application / Design / Cost trade analysis to better elucidate the cost potential of the MGB in the projected volumes anticipated for future demand. This would better establish the efficacy of the original cost target ($\$$0.80/Watt) and/or the need for reconsideration of designs and applications. Likewise, additional consideration of the prototype nature of the gearbox – single use, short lifetime, etc. - either as a separate exercise or in place of the design process completed, to reduce the cost of the demonstration prototype device. Additionally, project continuity was cited as a significant risk based on the loss of the primary design engineering firm after Budget Period 1. A design analysis exercise was conducted at the conclusion of the project to identify potential areas for cost reduction. One concept considered was the removal of the inner ring of magnets (with associated changes in the outer ring magnets) to enable a horizontal collapse of the design. It was estimated this could reduce cost by 10-25% without impacting performance.
Over the past 50 years, great advances have been achieved in both analytical modal analysis (i.e. finite element models and analysis) and experimental modal analysis (i.e. modal testing) in aerospace and other fields. With the advent of more powerful computers, higher performance instrumentation and data acquisition systems, and powerful linear modal extraction tools, analysts and test engineers have a breadth and depth of technical resources only dreamed of by our predecessors. However, some observed recent trends indicate that hard lessons learned are being forgotten or ignored, and possibly fundamental concepts are not being understood. These trends have the potential of leading to the degradation of the quality of and confidence in both analytical and test results. These trends are a making of our own doing, and directly related to having ever more powerful computers, programmatic budgetary pressures to limit analysis and testing, and technical capital loss due to the retirement of the senior component of a bimodal workforce. This paper endeavors to highlight some of the most important lessons learned, common pitfalls to hopefully avoid, and potential steps that may be taken to help reverse this trend.
Most experimental setups and environment specifications define acceleration loads on the component. However, Sierra Structural Dynamics cannot apply acceleration boundary conditions in modal transient analysis. Modal analysis of these systems and environments must be done through the application of a huge artificial force to a large fictitious point mass. Introducing a large mass into the analysis is a common source of numerical error. In this report we detail a mathematical procedure to directly apply acceleration boundary conditions in modal analyses without the requirement of adding a non-physical mass to the system. We prototype and demonstrate this procedure in Matlab and scope the work required to integrate this procedure into Sierra Structural Dynamics.
A computer program was developed for designing a low vibration gearbox. The code is based on a finite element shell analysis, a modal analysis, and a structural optimization method. In the finite element analysis, a triangular shell element with 18 degrees-of-freedom is used. In the optimization method, the overall vibration energy of the gearbox is used as the objective function and is minimized at the exciting frequency by varying the finite element thickness. Modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variable. The sensitivity is representative of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. The computer code is applied to a design problem derived from an experimental gearbox in use at the NASA Lewis Research Center. The top plate and two side plates of the gearbox are redesigned and the contribution of each surface to the total vibration is determined. Results show that optimization of the top plate alone is effective in reducing total gearbox vibration.
An optimization method is proposed to reduce the vibration of thin plate structures. The method is based on a finite element shell analysis, a modal analysis, and a structural optimization method. In the finite element analysis, a triangular shell element with 18 dof is used. In the optimization, the overall vibration energy of the structure is adopted as the objective function, and it is minimized at the given exciting frequency by varying the thickness of the elements. The technique of modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variables. The sensitivity is represented by the sensitivities of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. A computer code, based on the proposed method, is developed and is applied to design problems using a beam and a plate as test cases. It is confirmed that the vibration energy is reduced at the given exciting frequency. For the beam excited by a frequency slightly less than the fundamental natural frequency, the optimized shape is close to the beam of uniform strength.