During launch, a spacecraft undergoes loads ranging from quasi-static to highly transient or harmonic low frequency events, from higher frequency shock loads to acoustic excitations. In order to reproduce such a dynamic diversity, fixed base sinusoidal tests, wide band acoustic loading and different regimes of shock testing are implemented in the test facilities. In this article, the main focus is on fixed base sinusoidal tests, fundamental for a number of reasons, including demonstrating that the satellite can withstand the low frequency dynamic environment and validating the mathematical model which will then be also used for coupled load analysis purposes. For the latter, a post-test correlation process is carried out and the basic assumption is trusting the experimental results obtained from shaker testing. In reality, some of these assumptions (e.g. ?infinitely? stiff boundary and inertial properties of the shaker) are not correct, as for the kind of applications treated in this article experimental results are significantly affected by boundary flexibilities, modes of the shaker/head expander and non-perfect implementation of the control algorithm in the electronic hardware. In the last decade, there has been a growing interest in virtual testing, with the long-term view to use simulation as substitute for the majority of testing, but currently under investigation for pre-test response predictions and post-test correlation. Here, the satellite is mathematically modelled along with the shaker and the control system. In this article, in particular, a simulation capability of longitudinal closed loop control simulation of the ESA electrodynamic shaker (QUAD) flexible body coupled with a test specimen (Bepi Colombo) flexible model is developed. This shows how significant the differences are when looking at the analytical results from two different perspectives (standard Finite Element Analysis and Virtual Testing implementation). The focus of this article is specifically on post-test correlation: correlation methods are used for both procedures and results show significant improvements when the satellite Finite Element Model undergoes the virtual testing approach.
Remedia M, Aglietti G, Zhang Z, Page BL, Richardson G (2012) A general methodology to study the transmission of micro-vibrations in satellites, Proceedings of the International Astronautical Congress, IAC 8 pp. 6386-6393
In the recent years, micro-vibrations have been an issue of growing importance, due to the high-stability requirements imposed by some modern payloads. These low level mechanical disturbances, occurring at frequencies from sub hertz up to 1000 Hz, are created by different sources in the spacecraft (e.g. reaction wheels) and how to model the micro-vibration environment is currently under investigation. In this paper, a methodology is presented, involving analyses techniques such as FEA (reliable at low frequencies), Monte Carlo Simulation (precise but still computationally demanding and time consuming) and Modal Hybridization (a Stochastic Finite Element Method which involves perturbation of modes and natural frequencies and will be used to refine the general methodology). The various modelling techniques also require a particular attention when dealing with micro-vibrations. For instance, mechanical equipment typically on board a spacecraft (such as harness, thermal straps etc.) affects the response caused by low level disturbances and a FEM which models them with simple non-structural mass appears to be not accurate enough. Another important aspect of the modelling is the coupling between the sources and the tested structure. All the methods described above will be applied to a bench-work model represented by the satellite platform SSTL 300 (the relative testing campaign will be also described in this paper) and comparisons between the experimental and the computational results will be performed. Copyright © (2012) by the International Astronautical Federation.
Remedia M, Aglietti GS, Richardson G, Le Page B (2013) A general methodology for analysis of structure-borne micro-vibration, 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
Driven by the increasingly stringent stability requirement of some modern payloads (e.g. the new generations of optical instruments) the issue of accurate spacecraft micro-vibration modelling has grown of importance. This article focuses on the dynamic coupling between a source of micro-vibration (e.g. reaction wheel) and a structure, taking into account the uncertainties related to both parts. In this context, an alternative to the Monte Carlo Simulation for complex structures has been developed, consisting in sub-structural approach to perturb the natural frequencies of specific subsystem reduced with the Craig-Bampton method. In order to prove the validity of the method and its application to the theory of the coupling, benchmark examples and practical applications will be described. © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Addari D, Aglietti GS, Remedia M, Richardson G, LePage B (2014) Inspecting the characterisation of microvibration sources, Proceedings of the International Astronautical Congress, IAC 8 pp. 5616-5621
Copyright ©2014 by the International Astronautical Federation. All rights reserved.Microvibrations of a reaction wheel assembly are commonly investigated in either hard-mounted or coupled boundary conditions, although coupled wheel-structure disturbances are more representative than the hard-mounted disturbances. With the aim to reproduce the dynamics between a reaction wheel and its supporting structure, the dynamic mass (or its inverse, the accelerance) of the wheel and the driving point accelerance of the supporting structure have to be evaluated. This usually involves a series of experiments to characterise the hardware and produce exemplary models. Here a methodology is presented which has been shown to produce good estimates over a wide frequency range using a less complex test campaign. In addition, a practical example of coupling between a reaction wheel assembly and a structural panel, where the coupled loads have been estimated using the mathematical model and compared with experimental results, will be presented. Moreover, indications of the level of accuracy that can be expected from this type of analyses will be given herein.
Remedia M, Aglietti GS, Richardson G, Sweeting M (2015) Integrated Semiempirical Methodology for Microvibration Prediction, AIAA JOURNAL 53 (5) pp. 1236-1250 AMER INST AERONAUTICS ASTRONAUTICS
Driven by the increasingly stringent stability requirement of some modern payloads (e.g. the new generations of optical instruments) the issue of accurate spacecraft micro-vibration modelling has grown of importance. This article focuses on the dynamic coupling between a source of micro-vibration (e.g. reaction wheel) and a structure, taking into account the uncertainties related to both parts. In this context, an alternative to the Monte Carlo Simulation for complex structures has been developed, consisting in sub-structural approach to perturb the natural frequencies of specific subsystem reduced with the Craig-Bampton method. In order to prove the validity of the method and its application to the theory of the coupling, benchmark examples and practical applications will be described. © 2012 AIAA.
Remedia M, Aglietti GS, Richardson G (2014) A stochastic methodology for predictions of the environment created by multiple microvibration sources, Journal of Sound and Vibration
It is well documented that at frequencies beyond the first few modes of a system, the Finite Element Method is unsuitable to obtain efficient predictions. In this article, it is proposed to merge the efficiency of the Craig-Bampton reduction technique with the simplicity and reliability of Monte Carlo Simulations to produce an overall analysis methodology to evaluate the dynamic response of large structural assemblies in the mid-frequency range. The method (Craig-Bampton Stochastic Method) will be described in this article with a benchmark example shown and implemented in the theory of the dynamic coupling extended to the case when multiple sources of microvibrations act simultaneously on the same structure. The methodology will then be applied to a real practical application involving the modern satellite SSTL 300 S1.
Currently, vibroacoustic problems can be solved using a wide range of numerical techniques. In the low-frequency range, element-based deterministic methods, such as the Finite Element Method (FEM) and Boundary Element Method (BEM) are regularly employed to define the structural and acoustic domains, respectively. The fully coupled FEM-BEM is a classic, vastly popular method. In the high-frequency range probabilistic methods, such as Statistical Energy Analysis, tend to be more efficient and produce more reliable results. Although new techniques are becoming available (e.g. Hybrid FE-SEA Method), the characterisation of the mid-frequency behaviour still poses some challenges, as the computational cost of element-based techniques is often prohibitive, and the modal density is not sufficiently high for statistical approaches to be applicable. This paper discusses an approach aimed at improving the efficiency of the classic FEM-BEM method and potentially extending its usability to the mid-frequency band, specifically in the context of space-craft structural design. The iterative coupling between Craig-Bampton reduced finite element models and BEM is considered as an alternative to directly solving the FEM-BEM coupled equation, allowing the use of efficient procedures for either domain separately. A pre-process enabling the method?s computational implementation is presented, which is based on a manipulation of the reduced mass and stiffness matrices. It is used to allow the application of a distributed load to a Craig-Bampton condensed structure, while mitigating the need to retain a large number of physical degrees of free-dom. The efficiency of the aforementioned matrix modification procedure is compared to that of performing a full Craig-Bampton reduction, and its cost is expressed in terms of floating point operations. An iterative coupling scheme is used on a test-case structure for both a full physical model and a reduced one to verify the concept, and check whether convergence is susceptible to initial conditions, such as the shape of the acoustic field. Finally, the perturbation of the condensed matrices is shown to produce results consistent with those for the full physical model, while substantially reducing the computational effort required for the simulation.
© 2015 IAA. Published by Elsevier Ltd. All rights reserved.The term "microvibrations" generally refers to accelerations in the region of micro-g, occurring over a wide frequency range, up to say 500-1000 Hz. The main issues related to microvibrations are their control and minimisation, which requires their modelling and analysis. A particular challenge is posed in the mid-frequency range, where many of the micro-vibration sources on board a spacecraft tend to act. In this case, in addition to the typical issues related to predicting responses in the mid-frequency, the low amplitude of the inputs can produce further non-linear behaviour which can manifest as uncertainties. A typical example is the behaviour of cables secured onto panels; when very low forces are applied, the presence of harness can influence the characteristics of the panel in terms of stiffness and damping values. In these circumstances, the cables themselves couple with the panel, hence become paths for vibration transmission. The common practise is to model such cables as Non-Structural Mass; however, this paper illustrates that this method does not yield accurate results. In order to demonstrate this, an experimental campaign was conducted investigating a honeycomb panel, which was tested bare and with different configurations of harness secured to it. The results of this experimental campaign showed significantly different behaviour of the structure depending on the amplitude of the loads and the frequency. In particular, it was found that the effects the addition of the cables had on the panel were different depending on the frequency range considered. Based on this observation, a general methodology to deal with the whole frequency range is presented here and the basis to extend it to the case of more complex structures is also proposed.
© 2015 Elsevier Ltd. All rights reserved.It is well documented that at frequencies beyond the first few modes of a system, the Finite Element Method is unsuitable to obtain efficient predictions. In this article, it is proposed to merge the efficiency of the Craig-Bampton reduction technique with the simplicity and reliability of Monte Carlo Simulations to produce an overall analysis methodology to evaluate the dynamic response of large structural assemblies in the mid-frequency range. The method (Craig-Bampton Stochastic Method) will be described in this article with a benchmark example shown and implemented in the theory of the dynamic coupling extended to the case when multiple sources of microvibrations act simultaneously on the same structure. The methodology will then be applied to a real practical application involving the modern satellite SSTL 300 S1.
Remedia M, Aglietti GS, Richardson G, LePage B (2014) Modelling Non-Structural Elements for Microvibration Analysis, Conference on Noise and Vibration Engineering (ISMA) Proceedings
Remedia M, Aglietti GS (2011) Modeling micro-vibrations transmission in spacecraft structures, 62nd International Astronautical Congress 2011, IAC 2011 7 pp. 5682-5690
Micro-vibrations on board spacecraft are an issue of growing importance, as some modern payloads, and in particular the new generations of optical instruments require extreme platform stability. These low level mechanical disturbances are usually created by the functioning of mechanical equipment (sources) such as reaction wheels, antenna pointing mechanisms cryo-coolers etc., and cover a wide frequency range. Because of the low level of the vibrations and their wide frequency range, the modeling and analysis of micro-vibrations poses a challenge as the typical structural modeling techniques used in this sector (Finite Element Method (FEM) and Statistical Energy Analysis (SEA)) are reliable only in some areas of the frequency spectrum. The FEM is well suited for low level frequencies; whereas energy methods (e.g. SEA or Energy Finite Element Method EFEA) are suited for high-frequency problems; in the mid-frequency range, finally, other methods (e.g. Hybrid FEA-SEA) tend to be used, even if they're still not well-established such as the ones named before. However the issue is that there is no single method that can address micro-vibrations in the whole frequency range. In this paper, the methods cited above will be very briefly reviewed and their use in specific micro-vibration prediction problems will be investigated in detail and compared with experimental results. In practice the work presented here uses the Finite Element Method as base-line method to investigate the whole frequency range (say up to 1000 Hz). The FEM predictions are then compared with the experimental results, showing that at medium and high frequencies the response start to deviate significantly from the FEA predictions. The high frequency behavior of the structure will be analyzed using SEA. The mid-frequency range, finally, will be tackled from both directions: from the high frequency side using the Hybrid FE-SEA, whereas from the low frequency side the capability of the standard FEM will be extended using stochastic FEM. The tests are carried out using the structural qualification model of an SSTL satellite bus that has been used to support a high resolution camera. The computational transfer functions and those from the experimental activity will be finally compared using the Modal Assurance Criteria (MAC).
Microvibrations of a satellite reaction wheel assembly are commonly analysed in either hard-mounted or coupled boundary conditions, though coupled wheel-to-structure disturbance models are more representative of the real environment in which the wheel operates. This article investigates the coupled microvibration dynamics of a cantilever configured reaction wheel assembly mounted on either a stiff or flexible platform. Here a method is presented to cope with modern project necessities: (i) need of a model which gives accurate estimates covering a wide frequency range; (ii) reduce the personnel and time costs derived from the test campaign, (iii) reduce the computational effort without affecting the quality of the results. The method involves measurements of the disturbances induced by the reaction wheel assembly in a hard-mounted configuration and of the frequency and speed dependent dynamic mass of the reaction wheel. In addition, it corrects the approximation due to missing speed dependent dynamic mass in conventional reaction wheel assembly microvibration analysis. The former was evaluated experimentally using a previously designed and validated platform. The latter, on the other hand, was estimated analytically using a finite element model of the wheel assembly. Finally, the validation of the coupled wheel-structure disturbance model is presented, giving indication of the level of accuracy that can be achieved with this type of analyses.
Test planning and post-test correlation activity have been issues of growing importance in the last few decades and many methodologies have been developed to either quantify or improve the correlation between computational and experimental results. In this article the methodologies established so far are enhanced with the implementation of a recently developed procedure called Virtual Testing. In the context of fixed-base sinusoidal tests (commonly used in the space sector for correlation), there are several factors in the test campaign that affect the behaviour of the satellite and are not normally taken into account when performing analyses: different boundary conditions created by the shaker?s own dynamics, non-perfect control system, signal delays etc. All these factors are the core of the Virtual Testing implementation, which will be thoroughly explained in this article and applied to the specific case of Bepi-Colombo spacecraft tested on the ESA QUAD Shaker. Correlation activity will be performed in the various stages of the process, showing important improvements observed after applying the final complete methodology.
Driven by the increasingly stringent stability requirement of some modern payloads (e.g. the new generations of optical instruments) the issue of accurate spacecraft micro-vibration modeling has grown increasingly important. In this context micro-vibrations are low level mechanical disturbances occurring at frequencies from a few Hertz up to 1000 Hz. As the frequency content of these phenomena extends beyond the first few modal frequencies, FEA predictions become less accurate and alternative methods have to be considered. Other modeling and analysis techniques have been investigated and applied to vibration problems (Stochastic Finite Element Method (e.g. Monte Carlo Simulation), Statistical Energy Analysis (well-established method for high frequency ranges) and the Hybrid FE-SEA), with the aim of investigating medium and high frequency behavior. This work is part of a project whose aim is to establish appropriate procedures for the modeling and analysis of micro-vibration and validate these procedures against experimental data. All the methods cited above are implemented in this study and compared with experimental results, in order to assess the performance of the various methodologies for micro-vibration problems, covering the whole frequency range up to 1000 Hz. Some comparisons between experimental and computational results are performed using the MAC. Some other analyses, like linearity, reciprocity or effect of the harness are also described. The bench work model that has provided the experimental data is the satellite platform SSTL 300 and this paper outlines these related test campaigns.
In recent years, driven by the increasingly stringent stability requirements imposed by some satellites? payloads (e.g., the new generation of optical instruments), the issue of accurate onboard spacecraft microvibration modeling has attracted significant interest from engineers and scientists. This paper investigates the microvibration-induced phenomenon on a cantilever-configured reaction wheel assembly including sub- and higher harmonic amplifications due to modal resonances and broadband noise. A mathematical model of the reaction wheel assembly is developed and validated against experimental test results. The model is capable of representing each configuration in which the reaction wheel assembly will operate, whether it is hard mounted on a dynamometric platform or suspended free?free. The outcomes of this analysis are used to establish a novel methodology to retrieve the dynamic mass of the reaction wheel assembly in its operative range of speeds. An alternative measurement procedure has been developed for this purpose, showing to produce good estimates over a wide range of frequencies using a less complex test campaign compared with typical dynamic mass setups. Furthermore, the gyroscopic effect influence in the reaction wheel assembly response is thoroughly examined both analytically and experimentally. Finally, to what extent the noise affects the convergence of the novel approach is investigated.
Coupled Loads Analyses (CLAs), using finite element models (FEMs) of the spacecraft and launch vehicle to simulate critical flight events, are performed in order to determine the dynamic loadings that will be experienced by spacecraft during launch. A validation process is carried out on the spacecraft FEM beforehand to ensure that the dynamics of the analytical model sufficiently represent the behavior of the physical hardware. One aspect of concern is the containment of the FEM correlation and update effort to focus on the vibration modes which are most likely to be excited under test and CLA conditions. This study therefore provides new insight into the prioritization of spacecraft FEM modes for correlation to base-shake vibration test data. The work involved example application to large, unique, scientific spacecraft, with modern FEMs comprising over a million degrees of freedom. This comprehensive investigation explores: the modes inherently important to the spacecraft structures, irrespective of excitation; the particular ?critical modes? which produce peak responses to CLA level excitation; an assessment of several traditional target mode selection methods in terms of ability to predict these ?critical modes?; and an indication of the level of correlation these FEM modes achieve compared to corresponding test data. Findings indicate that, although the traditional methods of target mode selection have merit and are able to identify many of the modes of significance to the spacecraft, there are ?critical modes? which may be missed by conventional application of these methods. The use of different thresholds to select potential target modes from these parameters would enable identification of many of these missed modes. Ultimately, some consideration of the expected excitations is required to predict all modes likely to contribute to the response of the spacecraft in operation.
Mathematical finite element models (FEMs) of spacecraft are relied upon for the prediction of loads experienced during launch and flight events. It is essential that the spacecraft is able to survive the launch environment without sustaining damage which could inhibit its ability to carry out its mission. Therefore, ensuring that these FEMs give a realistic representation of the physical spacecraft structural dynamics is an important task. To achieve a high level of confidence in the FEM in question, a correlation activity is conducted. This is the process of applying various metrics to compare computational results, from analysis of the FEM, with corresponding data derived from measurements taken of the physical hardware during vibration testing. Subsequently, updates are applied to the FEM where necessary to achieve an acceptable level of correlation.
It is possible for spacecraft FEM correlation exercises to take a considerable amount of time and effort without necessarily achieving an appreciable improvement in the final FEM. As such, this project has been conducted to address the need to ensure that the procedures being applied are as effective and efficient as possible. Various aspects of the spacecraft FEM correlation process have been investigated separately, and interactions between the different stages in the process have also been considered. Two large, unique, scientific spacecraft have been used as example applications in order to carry out these studies. As well as making use of computational results from the spacecraft FEMs, this project has also included comparisons to the results from the corresponding base-shake sine-sweep test campaigns conducted on these structures.
A number of noteworthy, and industrially beneficial, findings relating to the effectiveness of the spacecraft FEM correlation process have resulted from these studies: the most appropriate techniques of modal parameter estimation for the considered spacecraft applications have been established; the potential benefits and relative merits of different pre-test sensor placement procedures have been explored; inaccuracies introduced through the use of a commonly applied FEM reduction method have been demonstrated and a superior alternative identified. In addition, the efficiency of the correlation and update process has also been addressed. This has mainly been achieved through investigations concerning the applicability of commonly used target mode selection criteria to spacecraft applications, and the potential benefits of a less widely applied method which takes into consideration the expected loading scenarios to be experienced by the considered structures.
Spacecraft overtesting is a long running problem, and the main focus of most attempts to reduce it has been to adjust the base vibration input (i.e. notching). Instead this paper examines testing alternatives for secondary structures (equipment) coupled to the main structure (satellite) when they are tested separately. Even if the vibration source is applied along one of the orthogonal axes at the base of the coupled system (satellite plus equipment), the dynamics of the system and potentially the interface configuration mean the vibration at the interface may not occur all along one axis much less the corresponding orthogonal axis of the base excitation.
This paper proposes an alternative testing methodology in which the testing of a piece of equipment occurs at an offset angle. This Angle Optimisation method may have multiple tests but each with an altered input direction allowing for the best match between all specified equipment system responses with coupled system tests. An optimisation process that compares the calculated equipment RMS values for a range of inputs with the maximum coupled system RMS values, and is used to find the optimal testing configuration for the given parameters.
A case study was performed to find the best testing angles to match the acceleration responses of the centre of mass and sum of interface forces for all three axes, as well as the von Mises stress for an element by a fastening point. The angle optimisation method resulted in RMS values and PSD responses that were much closer to the coupled system when compared with traditional testing. The optimum testing configuration resulted in an overall average error significantly smaller than the traditional method. Crucially, this case study shows that the optimum test campaign could be a single equipment level test opposed to the traditional three orthogonal direction tests.
Efficient vibroacoustic response prediction on complex structures, such as spacecraft, represents
a challenging task, even for the computers and numerical techniques of today. This is particularly
evident in the mid-frequency range, where structures begin exhibiting chaotic behaviour, rendering
element-based techniques inefficient or unreliable.
In this article, an efficient random formulation for reduced finite element method (FEM) models is
proposed, such that Monte Carlo simulations can be carried out robustly within practically acceptable
timeframes. The introduced novel non-parametric stochastic FEM is inherently compatible
with various existing component mode synthesis techniques. It is particularly well adapted to use
with popular modal reduction approaches, such as the Craig-Bampton method. The mathematical
framework for the method is outlined, enabling the deterministic reduced matrices to be robustly
perturbed at the subsystem level. Properties, such as matrix positive-(semi)definiteness, mean
system eigenvalues, and representation accuracy are preserved. This new stochastic FEM is validated
against a full parametric Monte-Carlo simulation and test data of a real spacecraft structure,
establishing its reliability and computational efficiency.
In the proposed coupled FEM-BEM approach, the acoustic domain is modelled with hierarchical
matrix accelerated collocation BEM. This alleviates the memory requirements for the large, dense
BEM matrices, and the need for spatial discretisation of acoustic FEM. The full implementation
is outlined for a simple geometry discretised with high a density mesh, showing consistent convergence
of the employed iterative solver.
In this paper, the mathematical framework for a computationally
efficient stochastic finite element method (FEM)
is outlined. It is devised for a range of applications in
structural dynamics, where uncertainties need to be reliably
dealt with in the context of reduced model formulations.
It allows random mass and stiffness matrices
to be robustly generated at the subsystem level in component
mode synthesis (CMS) applications. The technique
is validated for the particularly challenging case
of mid-frequency FEM-FEM vibroacoustic analysis of a
spacecraft structure. Results are compared against both
test data and full parametric Monte-Carlo simulation. Finally,
the method?s applicability to coupled vibroacoustic
problems utilising hierarchical matrix boundary element
method (BEM) acoustic formulations is evaluated.
This article examines the new practice of Virtual Shaker Testing (VST), starting from its motivation to its practical implementations and future possible implications. The issues currently experienced during large satellites? vibration testing are discussed, examining practical examples that highlight the coupling existing between the item under test and facility, and that are the basis for the motivation behind the new methodology (i.e. VST). VST is proposed as a way to bypass some of these issues, and here its use as a pre and post shaker test tool is discussed. In the article VST is applied to real test cases (Airbus? large spacecraft Bepi Colombo, built for the European Space Agency's first mission to Mercury), showing computations and real physical test data to illustrate the advantages of the methodology. These are mostly in terms of de-risking of the physical test campaigns (due to the capability to simulate realistically the future physical test thus reducing the probability of aborts and stops during the runs), and an improvement of the quality of the correlation process and related FEM update (resulting from the capability to separate the dynamics of the satellite from the effects of the test equipment); ultimately providing a tool to address questions arising from test response observations, which are many. This tool also offers the possibility to improve vibration testing using 6 DOF facilities. The article is concluded articulating a possible way forward to take maximum advantage of the new methodology, drawing a parallel with the current Satellite/Launch Vehicle Coupled Load Analysis cycles, and proposing a different design and validation philosophy.
The launch phase is the most demanding mechanical environment typical satellites experience. In order to verify that a payload or piece of equipment will survive the expected loads experienced during launch, it is subject to prescribed vibration environments. However, current vibration testing methods tend to overtest. This means the harshest environment a satellite and its equipment must survive is the testing, not the launch. Consequentially, design process compromises are made, moving the focus from surviving the launch to surviving the testing.
Vibration testing involves shaking the test article in each of the three standard directions (X, Y and Z) according to the provided testing specifications. These specifications are based of the single launch environment which is split into three for practical reasons, but which leads to overtesting.
One of the causes for equipment overtesting is that items are normally tested along its three orthogonal axes (i.e. X, Y and Z). However, the body axes of the equipment are not always in line with the structure it is attached to. Even if the body axes do align, the dynamics of the coupled system mean any vibration at the base of the larger structure is unlikely to be acting all on the same axis (or axes) at the interface between the satellite and equipment. Another key difference between the testing environment and launch environment is the direction of the vibrations. The launch vibration environment is a single 3D environment, while testing is usually comprised of three single axis vibrations tests.
This thesis presents two alternative testing methods that separately, or together, can create a test campaign which better matches the environment the piece of equipment would see during launch.
The first method, the Angle Optimisation Method, looks at testing the piece of equipment is mounted at an offset angle on to the shaker rather than the traditional three orthogonal mounting directions. The method optimises the testing angle for the piece of equipment such that testing responses are closer to those seen when the equipment is attached to the higher level assembly. This method focuses on covering the maximum Root Mean Square (RMS) values for each quantity (e.g. sum of interface forces, and acceleration at centre of mass) obtained from the coupled system tests - resulting in a test campaign of one to three separate tests, each with altered input directions. This results in RMS values much closer to the desired higher level testing values than the traditional testing.
The second method, the Dual Input Method, looks at adding a secondary smaller vibration source at a specific location on the test item. The method finds the best location to attach the second vibration source that produces a more representative testing of the piece of equipment when compared to the higher level testing. It also determines what the input should be at this specific point. This method looks at improving the correlation of the Operational Deflecting Shapes (ODS) of the equipment when tested in isolation and when attached to the higher level assembly. Response Vector Assurance Criterion (RVAC) is used for the correlation of the ODS.
Two case studies were undertaken to demonstrate the benefits of these methods. The first was a computational case study that both methods were applied to. In this case study the Angle Optimisation method was able to reduce the amount of over testing by up to 70% compared to the traditional testing method. While the Dual Input method was able to improve the correlation between the equipment and coupled system responses by nearly 50%.
The second case study was an experimental application of the Angle Optimisation Method. This case study successfully showed that it was possible to implement this method as a physical test. A custom angled interface plate was manufactured to the specifications determined by the Angle Optimisation method. In addition to showing the successful
This paper addresses the susceptibility of finite element models to uncertainty in frequency ranges with relatively high modal density, particularly in the con- text of vibroacoustic analysis. The principal idea is based on a stochastic fi- nite element method (FEM) technique called Craig-Bampton stochastic method (CBSM). It is a parametric Monte Carlo simulation (MCS) approach that can be performed at a fraction of the otherwise potentially impractical computational cost, due to the use of reduced rather than full system matrices. An enhanced formulation of the CBSM, significantly improving its efficiency by exploiting the block structure of the condensed model?s stiffness and mass matrices is derived. The improved method is adapted for use with distributed loads, such as diffuse sound field excitation. Its practical implementation is illustrated through a simple theoretical example followed by a high-complexity spacecraft structure case. In both cases solutions are compared to those of a classic MC simulation of the non-condensed models. Through an extensive parametric survey, recommendations are given on the ideal perturbation levels and underlying statistical distributions for the improved CBSM?s random variables. The proposed technique shows a very strong agreement with the benchmark MC results. Computational time reductions of over 1 and 3 orders of magnitude against the original CBSM and the MC simulation, respectively, are demonstrated.