Monte Carlo model of the uncertainty of SEA loss factors

Finite Element Methods are widely used to model vibro-acoustic systems, but as the modal density becomes higher this type of model becomes inaccurate and impractical. This is why in the high modal density region the use of Statistical Energy Analysis (SEA) models has become increasingly popular. SEA has some obvious advantages such as its simple formal expression, being based on linear equation systems or the reduced number of variables involved. But SEA has drawbacks as well, such as the absence of local information or the necessity of frequency averaging. A key quantity in SEA models is the loss factor. This takes into account the energy dissipated within a given subsystem or when power flows from one subsystem to another. Even though analytical expressions exist for a number of subsystems of differing nature, the measurement of the loss factor is still advisable and a necessity for a large number of cases. The most commonly used method of measuring loss factors is the Power Injection Method. This method is based on the injection of power into every single subsystem in sequence while the energy in each subsystem is measured. In spite of its simplicity, there remain a number of problems where the accuracy of the results is influenced by various practical issues. In this paper, a Monte Carlo model is used to describe the uncertainty of a two subsystemproblem consisting of two planar elements connected along one side. The influence of the input variables is studied and the conditioning of the coefficient matrix that model the system is also taken into accoun

Trade-off aproaches for the vibroacoustic analysis of trains

Passengers’ comfort in terms of acoustic noise levels is a key design driver for train design. The problem is especially relevant for high speed trains, where the aerodynamic induced noise is dominant, but it is also important for medium speed trains where the mechanical sources of noise may have more influence. The numerical interior noise prediction inside the train is a very comp lex problem, involving many different parameters: complex geometries and materials, different noise sources, com- plex interactions among those sources, broad range of frequencies where the phenomenon is important, etc. In this paper, the main findings of this work developed at IDR/UPM (Instituto de Microgravedad “Ignacio Da Riva”, Universidad Politécnica de Madrid) are presented, concentrat ing on the different modelling methodologies used for the different frequency ranges of interest, from FEM-BEM models, hybrid FEM-SEA to pure SEA models. The advantages and disadvantages of the different approaches are summarized. Different modelling techniques have also been evaluated and compared, taking into account the various and specific geometrical configurations typical in this type of structures, and the material properties used in the models. The critical configuration of the train inside a tunnel is studied in order to evaluate the external loads due to noise sources of the train. In this work, a SEA-model composed by periodic characteristic sections of a high spee d train is analysed inside a tunnel

Air gap influence on the vibro-acoustic response of Solar Arrays during launch

One of the primary elements on the space missions is the electrical power subsystem, for which the critical component is the solar array. The behaviour of these elements during the ascent phase of the launch is critical for avoiding damages on the solar panels, which are the primary source of energy for the satellite in its final configuration. The vibro-acoustic response to the sound pressure depends on the solar array size, mass, stiffness and gap thickness. The stowed configuration of the solar array consists of a multiple system composed of structural elements and the air layers between panels. The effect of the air between panels on the behaviour of the system affects the frequency response of the system not only modifying the natural frequencies of the wings but also as interaction path between the wings of the array. The usual methods to analyze the vibro-acoustic response of structures are the FE and BE methods for the low frequency range and the SEA formulation for the high frequency range. The main issue in the latter method is, on one hand, selecting the appropriate subsystems, and, on the other, identifying the parameters of the energetic system: the internal and coupling loss factors. From the experimental point of view, the subsystems parameters can be identified by exciting each subsystem and measuring the energy of all the subsystems composing the Solar Array. Although theoretically possible, in practice it is difficult to apply loads on the air gaps. To analyse this situation, two different approaches can be studied depending on whether the air gaps between the panels are included explicitly in the problem or not. For a particular case of a solar array of three wings in stowed configuration both modelling philosophies are compared. This stowed configuration of a three wing solar arrays in stowed configuration has been tested in an acoustic chamber. The measured data on the solar wings allows, in general, determining the loss factors of the configuration. The paper presents a test description and measurements on the structure, in terms of the acceleration power spectral density. Finally, the performance of each modelling technique has been evaluated by comparison between simulations with experimental results on a spacecraft solar array and the influence on the apparent properties of the system in terms of the SEA loss factors has been analyse

Comparison of numerical models for vibro-acoustic analysis of structural panels in low modal density range engaging air layers

During launch, satellite and their equipment are subjected to loads of random nature and with a wide frequency range. Their vibro-acoustic response is an important issue to be analysed, for example for folded solar arrays and antennas. The main issue at low modal density is the modelling combinations engaging air layers, structures and external fluid. Depending on the modal density different methodologies, as FEM, BEM and SEA should be considered. This work focuses on the analysis of different combinations of the methodologies previously stated used in order to characterise the vibro-acoustic response of two rectangular sandwich structure panels isolated and engaging an air layer between them under a diffuse acoustic field. Focusing on the modelling of air layers, different models are proposed. To illustrate the phenomenology described and studied, experimental results from an acoustic test on an ARA-MKIII solar array in folded configuration are presented along with numerical results

Criteria for mathematical model selection for satellite vibro-acoustic analysis depending on frequency range

Satellites and space equipment are exposed to diffuse acoustic fields during the launch process. The use of adequate techniques to model the response to the acoustic loads is a fundamental task during the design and verification phases. Considering the modal density of each element is necessary to identify the correct methodology. In this report selection criteria are presented in order to choose the correct modelling technique depending on the frequency ranges. A model satellite’s response to acoustic loads is presented, determining the modal densities of each component in different frequency ranges. The paper proposes to select the mathematical method in each modal density range and the differences in the response estimation due to the different used techniques. In addition, the methodologies to analyse the intermediate range of the system are discussed. The results are compared with experimental testing data obtained in an experimental modal test

Development of FEM/BEM and SEA models from experimental results for structural elements with attached equipment

This work focuses on the analysis of a structural element of MetOP-A satellite. Given the special interest in the influence of equipment installed on structural elements, the paper studies one of the lateral faces on which the Advanced SCATterometer (ASCAT) is installed. The work is oriented towards the modal characterization of the specimen, describing the experimental set-up and the application of results to the development of a Finite Element Method (FEM) model to study the vibro-acoustic response. For the high frequency range, characterized by a high modal density, a Statistical Energy Analysis (SEA) model is considered, and the FEM model is used when modal density is low. The methodology for developing the SEA model and a compound FEM and Boundary Element Method (BEM) model to provide continuity in the medium frequency range is presented, as well as the necessary updating, characterization and coupling between models required to achieve numerical models that match experimental results

UPMSat-2 Micro-Satellite: In-orbit Technological Demonstration for Education and Science

The UPMSat-2 micro-satellite was launched on September the 3rd 2020 at 01:51:10 UTC from Kourou spaceport in French Guyana. The VV16 Vega Flight has been the first low Earth orbit rideshare commercial flight with a total of 53 satellites (7 of them micro-satellites) to be released by the launch vehicle, arranged in the modular SSMS (Small Spacecraft Mission Service) dispenser. UPMSat-2 is an educational, scientific and in-orbit technological demonstration microsatellite project led by the IDR/UPM research institute from Universidad Politécnica de Madrid (UPM), Spain. This mission can be considered as a logical extension of the IDR/UPM Institute activities focused on designing small satellites to be used as educational platforms of first level. Thereby, UPMSat-2 (as well as its precursor, the UPMSat-1) has the main objective to give students the competences for designing, analyzing, manufacturing, integrating, testing and operating the platform. UPMSat-2 also includes a set of scientific payloads and equipment to be tested in space, provided by research institutions and private companies. The UPMSat-2 is a 50 kg-class microsatellite developed for a 2-year LEO mission with a geometrical envelope of 0.5 x 0.5 x 0.6 m. Since launch, the satellite is orbiting the Earth in a sun-synchronous orbit of 500 km of altitude, passing over the IDR/UPM ground station four times a day. The satellite operation is being carried out by students and professors of the Master in Space Systems (MUSE), an official Master’s program of UPM organized by IDR/UPM. This work describes the most relevant characteristics of UPMSat-2, its payloads, technological contributions, and the main activities performed up to the launch, including participation in the launch campaign in French Guyana. The lessons learned during the mission are also summarized. Finally, the importance and benefits of incorporating actual space systems design and development within academic programs is also emphasized, as it improves these programs with constant and direct feedback

Vibro-acoustic analysis of spacecraft structures with thin air layers

Esta Tesis presenta un estudio sobre el comportamiento vibroacústico de estructuras espaciales que incluyen capas de aire delgadas, así como sobre su modelización numérica. Las capas de aire pueden constituir un elemento fundamental en estos sistemas, como paneles solares plegados, que se consideran el caso de estudio en este trabajo. Para evaluar la influencia de las capas de aire en la respuesta dinámica del sistema se presenta el uso de modelos unidimensionales. La modelización de estos sistemas se estudia para los rangos de baja y alta frecuencia. En el rango de baja frecuencia se propone un conjunto de estrategias de simulación basadas en técnicas numéricas que se utilizan habitualmente en la industria aeroespacial para facilitar la aplicación de los resultados de la Tesis en los modelos numéricos actuales. Los resultados muestran el importante papel de las capas de aire en la respuesta del sistema. El uso de modelos basados en elementos finitos o de contorno para estos elementos proporciona resultados equivalentes aunque la aplicabilidad de estos últimos puede estar condicionada por la geometría del problema. Se estudia asimismo el uso del Análisis Estadístico de la Energía (SEA) para estos elementos. Una de las estrategias de simulación propuestas, que incluye una formulación energética para el aire que rodea a la estructura, se propone como estimador preliminar de la respuesta del sistema y sus frecuencias propias. Para el rango de alta frecuencia, se estudia la influencia de la definición del propio modelo SEA. Se presenta el uso de técnicas de reducción para determinar una matriz de pérdidas SEA reducida para definiciones incompletas del sistema (si algún elemento que interactúa con el resto no se incluye en el modelo). Esta nueva matriz tiene en cuenta la contribución de las subestructuras que no se consideran parte del modelo y que suelen ignorarse en el procedimiento habitual para reducir el tamaño del mismo. Esta matriz permite también analizar sistemas que incluyen algún componente con problemas de accesibilidad para medir su respuesta. Respecto a la determinación de los factores de pérdidas del sistema, se presenta una metodología que permite abordar casos en los que el método usual, el Método de Inyección de Potencia (PIM), no puede usarse. Se presenta un conjunto de métodos basados en la técnicas de optimización y de actualización de modelos para casos en los que no se puede medir la respuesta de todos los elementos del sistema y también para casos en los que no todos los elementos pueden ser excitados, abarcando un conjunto de casos más amplio que el abordable con el PIM. Para ambos rangos de frecuencia se presentan diferentes casos de análisis: modelos numéricos para validar los métodos propuestos y un panel solar plegado como caso experimental que pone de manifiesto la aplicación práctica de los métodos presentados en la Tesis. ABSTRACT This Thesis presents an study on the vibro-acoustic behaviour of spacecraft structures with thin air layers and their numerical modelling. The air layers can play a key role in these systems as solar wings in folded configuration that constitute the study case for this Thesis. A method based on one-dimensional models is presented to assess the influence of the air layers in the dynamic response of the system. The modelling of such systems is studied for low and high frequency ranges. In the low frequency range a set of modelling strategies are proposed based on numerical techniques used in the industry to facilitate the application of the results in the current numerical models. Results show the active role of the air layers in the system response and their great level of influence. The modelling of these elements by means of Finite Elements (FE) and Boundary Elements (BE) provide equivalent results although the applicability of BE models can be conditioned by the geometry of the problem. The use of Statistical Energy Analysis (SEA) for these systems is also presented. Good results on the system response are found for models involving SEA beyond the usual applicability limit. A simulation strategy, involving energetic formulation for the surrounding fluid is proposed as fast preliminary approach for the system response and the coupled eigenfrequencies. For the high frequency range, the influence of the definition of the SEA model is presented. Reduction techniques are used to determine a Reduced SEA Loss Matrix if the system definition is not complete and some elements, which interact with the rest, are not included. This new matrix takes into account the contribution of the subsystems not considered that are neglected in the usual approach for decreasing the size of the model. It also allows the analysis of systems with accessibility restrictions on some element in order to measure its response. Regarding the determination of the loss factors of a system, a methodology is presented for cases in which the usual Power Injection Method (PIM) can not be applied. A set of methods are presented for cases in which not all the subsystem responses can be measured or not all the subsystems can be excited, as solar wings in folded configuration. These methods, based on error minimising and model updating techniques can be used to calculate the system loss factors in a set of cases wider than the PIM’s. For both frequency ranges, different test problems are analysed: Numerical models are studied to validate the methods proposed; an experimental case consisting in an actual solar wing is studied on both frequency ranges to highlight the industrial application of the new methods presented in the Thesis

Dynamic coupling on the design of space structures

For the design of space structures, the dynamic coupling between equipment and the satellite (or between a satellite and the launcher) is usually avoided due to negative effects like high stresses produced by structural resonance. The usual procedure to assure the dynamic decoupling is by limiting the minimum value of natural frequency of the secondary structure to a value high enough above the main natural frequencies of the main structure. However, in some spacecraft configurations, it is unavoidable that some parts or equipment present natural frequencies close to the main natural frequencies of the spacecraft because these parts may be massive or may have a special interface design with low stiffness. This dynamic coupling provokes modifications on the modal behavior of the satellite, which can lead to a significant decrease in the first natural frequency of the entire satellite. To analyze this phenomenon, a representative but simple mathematical model is studied to evaluate the influence of the design parameters of space structures. Analytical expressions are obtained that can help to highlight the influence of the parameters. The results are demonstrated with the example of the UPMSat-2 satellite design

Three-Dimensional Digital Image Correlation Based on Speckle Pattern Projection for Non-Invasive Vibrational Analysis

Non-contact vibration measurements are relevant for non-invasively characterizing the mechanical behavior of structures. This paper presents a novel methodology for full-field vibrational analysis at high frequencies using the three-dimensional digital image correlation technique combined with the projection of a speckle pattern. The method includes stereo calibration and image processing routines for accurate three-dimensional data acquisition. Quantitative analysis allows the extraction of several deformation parameters, such as the cross-correlation coefficients, shape and intensity, as well as the out-of-plane displacement fields and mode shapes. The potential of the methodology is demonstrated on an Unmanned Aerial Vehicle wing made of composite material, followed by experimental validation with reference accelerometers. The results obtained with the projected three-dimensional digital image correlation show a percentage of error below 5% compared with the measures of accelerometers, achieving, therefore, high sensitivity to detect the dynamic modes in structures made of composite material.</jats:p