Dynamic Environments Testing, Vol. 7: Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics 2024

This chapter presents a straightforward framework for input characterization when challenging modeling conditions hinder the use of parametric estimators for accurate source reconstruction. The study case of a Range Rover Evoque drivetrain is utilized as a testing platform to address such problems. The aim of this work is to indirectly estimate the torque generated in the prop-shaft of the Evoque while considering the full assembly and complex interactions among all the drivetrain components. To achieve this, a least squares alternative approach leveraging training data is proposed to practically deploy a virtual sensor solution in the physical asset. The study provides an overview of the technical specifications of the Evoque drivetrain and the sensor layout designed to capture the system’s dynamic response. Operational datasets obtained under various conditions are described, serving as the basis for the analysis. The performance of the data-driven estimator is assessed in both the time and frequency domains, with a particular focus on phase differences between the training data and operational data. The results highlight the effectiveness of the proposed framework in addressing the challenges posed by complex multibody systems. The data-driven approach demonstrates promising performance with relatively small errors in the order of 5% of the range of the measured torque signals, enabling reliable source reconstruction.

The comparison of single input single output (SISO) and multiple input multiple output (MIMO) testing is a critical area of research in the field of random vibration testing (RVT). SISO testing is widely used in industry and defense applications but does not realistically reproduce the loading seen in the field environment. Subsequently, SISO testing has the potential to over-test or under-test the structure. MIMO testing allows multiple axes to be controlled simultaneously, creating a more realistic representation of the field environment. Unfortunately, MIMO testing requires more design considerations adding to the complexity of the test setup. It is therefore useful to quantify the similarities and differences between MIMO and SISO testing. This can provide insight to test engineers as they seek to adhere to a test specification while balancing setup complexity.

This study analyzes the box assembly with removable component (BARC) structure under MIMO and SISO testing configurations. The BARC has been thoroughly analyzed in the literature, and its well-documented dynamic behavior makes it a viable candidate to investigate the differences between MIMO and SISO testing. Specifically, the distribution of energy, the relative motion between points, and the relative energy between points are studied via calculation of the power spectral density (PSD), transmissibility frequency response function (TFRF), and ratio of PSDs (RPSD). Additionally, the PSDs, TFRFs, and RPSDs are compared to the environment or each other using the Frequency Response Function Similarity Metric (FRFSM).

It is well known in the aerospace industry that performing shock analysis and testing on spacecraft is very difficult to do (Yunis S, ShockSat: A system to provide public data for advancing shock prediction. Spacecraft and launch vehicle dynamic environments workshop. 28–30 June 2022; Kennedy M, Blough, J, ShockSat testing and analysis results. SCLV 2023 proceedings; Sisemore C, Babuska, V, The science and engineering of mechanical shock. Springer, 2020; NASA-STD-7003A, Pyroshock test criteria, 20 Dec 2011; NASA-HDBK-7005, Dynamics environmental criteria, 13 Mar 2001; Space Engineering Mechanical Shock Design and Verification Handbook. European Cooperation for Space Standardization. ECSS-E-HB-32-25A, 14 July 2015; Kennedy M, Blough J, Guidelines for reducing uncertainty in shock analysis and testing. SAVE 2022 proceedings; MIL-STD-810G, Environmental engineering considerations and laboratory tests. Department of Defense Test Method Standard, 31 Oct 2008) (leading to significantly larger analysis and testing errors—as much as an order of magnitude shock levels at some frequencies, NASA-HDBK-7005, Dynamics environmental criteria, 13 Mar 2001), and it is the main reason why it is so far behind other types of vibration analysis and testing like sine and random vibration (with acceleration response errors perhaps 10–20% at critical frequencies). These types of large errors are mostly a result of less spacecraft-level shock testing.

To help reduce these difficulties, customers who procure spacecraft and the launch vehicle providers that put spacecraft into orbit need to improve their approach to shock loads. They typically treat shock loads the same as other loads. Shock loads are entirely different from any other loads that a spacecraft will be exposed to, and as such clearer and more consistent direction and additional information are needed than are currently being provided.

Multi-axis testing has gained popularity in the dynamic environments testing community due to its potential to recreate observed field conditions more accurately and reduce test durations. However, the increased control degrees of freedom and excitation sources necessary for testing in a multi-axis setting add complexity to planning and execution. Two important components of a successful multi-axis test are (1) the ability to run accurate virtual tests to determine the optimal shaker and sensor configuration and (2) a vibration controller that can produce the shaker forces necessary to match the test specification at control locations on the test article. This project aims to evaluate the control capabilities within virtual tests and between virtual and hardware tests for the base section of a Box Assembly with Removable Component (BARC). The Rattlesnake Vibration Controller software developed at Sandia National Laboratories is used to conduct the virtual and hardware tests in this study, and a finite element model (FEM) of the BARC base forms the model for the virtual tests. It is expected that the virtual test’s ability to predict hardware test results will depend on control law, model fidelity, control locations, boundary conditions, and the test specification characteristics. This study analyzes how control law selection influences results in the virtual-to-hardware test pipeline, facilitating the development of new vibration control strategies and test planning optimization frameworks.

Random vibration testing is one of the most frequently employed procedures to ensure the durability of a component in operational conditions. Random vibration tests are commonly performed by means of single-axis tests. In particular, it is common practice to test the component multiple times, changing the loading direction. However, real working environments present, in general, multi-axis vibration, and single-axis loads are often incapable of reproducing the response of a component subjected to multi-axis vibration. In this work, the effects of sequential single-axis and multi-axis vibration are compared in terms of fatigue damage. A test campaign has been carried out, exploiting the triaxial shaker system available at the University of Ferrara. In particular, a specifically designed specimen has been tested until failure in different configurations under sequential single-axis and multi-axis uncorrelated vibration. The objective of the test campaign is to quantify the difference in terms of time to failure of the specimen when its dynamic behavior is activated differently. The tests performed with multi-axis vibration resulted always in a significant reduction of the time to failure, compared to sequential single-axis testing. Moreover, it has been found that the S–N curve of the specimen is heavily affected by the activation of the specimen dynamics, resulting in a different fatigue damage accumulation. Finally, the time to failure and the S–N curve of the specimen are used to define a correction factor that quantify the damage inflicted to the specimen by the multi-axis vibration, compared to sequential single-axis testing. The correction factor takes into account the different activation of the specimen dynamics, and it is capable of accurately estimating the time to failure of the specimen under multi-axis loading.

Multiple-input multiple-output (MIMO) vibration testing techniques offer the ability to closely replicate field environments during ground testing in a cost-effective manner, often with significant time savings compared to single-axis methods. MIMO techniques have been successfully applied to vibration testing for aerospace applications, yet they are also useful for providing inputs for the model validation process. However, choosing appropriate sensor locations and degrees of freedom (DOF) is an important but challenging aspect of the MIMO approach. This work highlights the application of MIMO techniques to perform model validation for an example aerospace system using synthetic test data. An inverse approach is utilized to perform input estimation, with frequency response functions and simulated acceleration response data from a finite element model. To assess the quality of the input estimation, several selection techniques for MIMO are evaluated, including those based on effective independence, optimal experimental design, modal projection error, and an iterative approach based on mean-squared error. This work demonstrates the development of a workflow for model validation of an aerospace system using the application of MIMO techniques, emphasizing the importance of control DOF selection and showcasing advantages over single-axis methods.

It is well known in the aerospace industry that performing shock analysis and testing on spacecraft is very difficult (Yunis, ShockSat: a system to provide public data for advancing shock prediction, 2022; Kennedy et al., ShockSat testing and analysis results, 2023; Sisemore and Babuska, The science and engineering of mechanical shock, Springer, 2020; NASA-STD-7003A, Pyroshock test criteria, 2011; NASA-HDBK-7005, Dynamics environmental criteria, 2001; ECSS-E-HB-32-25A, Space engineering mechanical shock design and verification handbook, European Cooperation for Space Standardization, 2015; Kennedy and Blough, Guidelines for reducing uncertainty in shock analysis and testing, 2022; MIL-STD-810G, Environmental engineering considerations and laboratory tests, Department of Defense Test Method Standard, 2008) (leading to significantly larger analysis and testing errors—as much as an order of magnitude shock levels at some frequencies (NASA-HDBK-7005, Dynamics environmental criteria, 2001]), and it is the main reason why it is so far behind other types of vibration analysis and testing like sine and random vibration (with acceleration response errors perhaps 10–20% at critical frequencies). These types of large errors are mostly a result of not enough spacecraft-level shock testing being performed.

Based on the shock research conducted for the past 2 ½ years, the number one finding that will significantly improve shock analysis and testing is that shock testing at the spacecraft level needs to become routine, just like sine and random vibration testing.

Transient time history motions are environmentally induced dynamic phenomena relevant to many engineering fields, such as mechanical, civil, and aerospace engineering. Particularly in structural dynamics applications, transient time history motions are widely used to simulate specific environmental loading conditions such as earthquakes, impacts, blasts, or spacecraft launches. The presented experimental study uses a suite of transient motions to investigate the motion replication of a 20 kN electrodynamic shaker that includes payloads with variable stiffness. When shaking a rigid and flexible structure in three orthogonal directions, the measurements focus on the achieved transient time history motion amplitude. The experiments are designed to test the impact of the motion characteristics and variable loading conditions on the motion replication. Specifically, the impact of shortening/decreasing the motion time duration and increasing the transient motion amplitude is investigated to identify the limit of the shaker performance. Further, the role of the motion type, e.g., single-frequency sine beats, triangle beats, or random bursts, to alter the achievable performance range of the shaker is investigated. This will inform best practices for motion selection and modifications for future studies experiencing the limit of their shake table performance.

A typical constraint in multiple-input/multiple-output (MIMO) vibration testing is the number of available control gauges and associated MIMO-compatible specifications. This can arise due to the difficulty in obtaining field response data with high channel counts which would be used to create MIMO-compatible specifications at multiple control gauge locations. As MIMO vibration control is typically posed as an over-determined (i.e., more outputs than inputs) regression problem, having limited controls (outputs) limits the number of inputs that can be used. To allow a MIMO vibration test to be run with a sufficient number of inputs, it may be necessary to utilize fewer outputs than inputs, which switches the control to an under-determined regression problem. Under-determined regression problems have different behavior than over-determined problems, and it is not immediately clear how those differences translate to quantities of interest in MIMO vibration control. This paper aims to explore under-determined problems in the context of MIMO vibration control using examples to provide guidance to the MIMO vibration practitioner.

Mechanical shock testing utilizing different types of resonating fixtures is an aerospace environmental testing practice useful in simulating mid-field pyroshock. The resonant bar shock test method was developed in the 1980s to perform controlled single-axis resonant shock tests on aerospace components. In this method, a test article is attached to one end of a bar, and then the opposite end of the bar is struck with a projectile, resulting in a transient acceleration that rings down at the natural frequency of the longitudinal extension mode of the assembly. If the impact of the projectile occurs on the longitudinal axis of the bar, nearly all the test article acceleration is in the longitudinal direction; acceleration response in transverse directions is very low.

In recent testing, it is found that substantial transverse acceleration of the test article, on an order similar to the longitudinal acceleration, can be achieved if the projectile impact is offset from the longitudinal bar axis. This effect was investigated on a legacy resonant bar test assembly and on a new resonant bar test assembly designed to exploit the potential for transverse acceleration shock response. The controlled acceleration response achieved using these techniques has the potential to meet a shock response specification in three response directions simultaneously in a single shock test.

Shaker testing is an important step in evaluating the structural performance and fatigue of components and assemblies in many important areas like aerospace, automotive, and electronic products. In many of these tests, head expanders or slip tables are used for mounting the test specimen on the shaker. As these components may have significant impact on the overall dynamics of the system, a basic understanding of their structural properties is essential. Otherwise, depending on the positioning of the control transducers and the mounting points significant under or over testing may occur. Thus, it is important to understand the structural dynamics of the test assembly, shaker, and head expander to achieve testing in accordance with specifications. Especially, mounting the test specimen and the control accelerometers on nodes or antinodes of the head expander has significant impact on the test results and the vibration control algorithm.

In this chapter a shaker with a head expander model is analyzed using three different approaches. Initially, the head expander’s mode shapes are examined via classical modal impact hammer testing. Additionally, Operational Deflection Shape (ODS) analysis and its applicability in evaluating the dynamic behavior of the vibrating system are investigated before the concept of Operational Modal Analysis (OMA) as an alternative method is introduced.

To provide a comprehensive analysis, the results obtained from the traditional ODS analysis, impact analysis, and OMA are compared. By examining the strengths and limitations of each approach, insights into their suitability for different testing scenarios are provided. By considering the implications of these modes on structural integrity and test performance, the quality of shaker vibration test setups can be improved.

Lastly, the feasibility of conducting in situ OMA analysis during complex shaker tests is discussed.

Dynamic environmental tests play a crucial role in verifying that components will perform as expected in operational conditions. Multi-axial testing platforms have continuously grown in popularity because they are capable of more accurately replicating the in-service environment than traditional single-axis vibration control tests. In a digital twin (DT)-based approach, correlated/validated numerical models of both test rig (including shakers, fixtures, etc.) and device under test (DUT) can be coupled to encapsulate the complex dynamic interactions between test hardware and article. This DT of the testing platform can become a powerful tool for the design and preparation of multiple-input multiple-output (MIMO) test configurations and provide a virtual environment for pre-test analysis of the multi-axis vibration test, predicting the expected test results in advance. Consequently, the test engineer can optimize the campaign beforehand and ensure the integrity of the DUT. This paper describes a model-based framework used for the development of a virtual simulation environment of a vibration test rig. The latter is based on a 4-degree-of-freedom multi-axis shaker platform combining four commercial medium-sized electromagnetic exciters in a decoupled build. The resultant DT combines electromechanical shaker models and a reduced order model (ROM) of the multi-axis platform. Finally, the virtual responses from the digital twin of the multi-axis platform are validated against experimental data, and its potential application to perform highly accurate pre-test activities is discussed.

The necessity of digital engineering solutions to design and validate components and systems has greatly increased in previous years. As the dependence on digital solutions increases, it is critical that all aspects of the system are validated with experimental testing to ensure the model’s structural dynamic response is representative of what it will experience in operation. Bolted joints often cause analysts a lot of grief because they are complex and unique to their application. The complex nature of bolted joints has resulted in many methods to represent bolted joints in finite element models. In this study, multiple bolt modeling approaches are applied to the BARC system and compared to experimental tests. The mode shapes of the BARC will be compared to the experimental mode shapes using the modal assurance criterion. It is shown that including the hardware in the model improves the MAC values and decreases the percent difference between the model and the test natural frequencies. The aim of this study is to present a comparison of bolted joint methods for the linear structural dynamics of the BARC system.

This paper describes a series of ambient vibration tests conducted at a designated site in the province of British Columbia, Canada, to measure the shear wave velocity in soil in order to characterize the seismic site according to the seismic provisions in design codes.

At the designated site, the vibration recordings were conducted at multiple locations using wireless sensors: single-instrument recordings for site period estimation (single-station test), multi-instrument simultaneous circular array ambient vibration recordings (passive test), and multi-instrument simultaneous linear array recordings with an active source (active test).

The recorded data was processed and analyzed in order to characterize the soil conditions. For each location, the ratio of the horizontal to vertical Fourier spectra of ambient noise recorded (typically noted as H/V) was calculated by a three-component sensor to determine the site period. Also, shear wave velocity profile was computed using the dispersion curves obtained from passive or active array tests. The average Vs to a depth of 30 m (Vs30) was then calculated and reported in the results, as it is the current site parameter in the NBCC. This information could be then used for site response analysis and earthquake site amplification prediction.

Dynamic environmental testing is an essential part of qualifying aerospace structures and components for transportation and flight. Traditional environmental testing subjects test articles to three single-input single-output tests, orthogonally exciting test specifications to approximate a three-dimensional field input to the article. However, altered boundary conditions between the laboratory and the field result in differing environments imparted onto the article. Furthermore, uncontrolled motion out of axis from the direction of excitation still imparts energy onto the test article. The dynamic environmental testing community has begun to explore multi-axis testing to better approximate field environments and save time on testing. Challenges in single-axis tests include ignoring certain stress states and failure modes that should otherwise exist in the test. Multi-input multi-output testing has the potential to reduce over and under testing and test times as the environments are tested simultaneously.

Baseline field data is used as an input for random environmental testing in both single- and multi-axis tests. The structure analyzed in vibration tests was the Box Assembly with Removable Component (BARC) developed at Sandia National Laboratory and Kansas City National Security Campus, as a benchmark for dynamic testing [1]. Random field data was gathered by transporting the BARC structure in a vehicle across bumpy roads. Metrics must be developed to compare single-axis and multi-axis tests to quantitatively represent advantages and disadvantages seen in single axis and multi-axis for a given experimental setup. This project seeks to develop metrics that effectively and quantitatively compare the fidelity of dynamic environmental testing methods. Metrics used to compare testing methods include Fatigue Damage Spectrum (FDS) and Root Mean Square (RMS) of the acceleration power spectral densities (PSDs). These metrics encompass the success of the test at control locations and uncontrolled locations and throughout the different frequency ranges tested.