Engineers are interested in the ability to compare dynamic environments for many reasons. Current methods of comparing environments compare the measured acceleration at the same physical point via a direct measurement during the two environments. Comparing the acceleration at a defined point only provides a comparison of response at that location. However, the stress and strain of the structure are defined by the global response of all the points in a structure. This chapter uses modal filtering to transform a set of measurements at physical degrees of freedom into modal degrees of freedom that quantify the global response of the structure. Once the global response of the structure is quantified, two environments can be more reliably and accurately compared. This chapter compares the response of an aerospace component in a service environment to the response of the same component in a laboratory test environment. The comparison first compares the mode shapes between the two environments. Once it is determined that the same mode shapes are present in both configurations, the modal accelerations are compared in order to determine the similarity of the global response of the component.
Resonant plate shock testing techniques have been used for mechanical shock testing at Sandia for several decades. A mechanical shock qualification test is often done by performing three separate uniaxial tests on a resonant plate to simulate one shock event. Multi-axis mechanical shock activities, in which shock specifications are simultaneously met in different directions during a single shock test event performed in the lab, are not always repeatable and greatly depend on the fixture used during testing. This chapter provides insights into various designs of a concept fixture that includes both resonant plate and angle bracket used for multi-axis shock testing from a modeling and simulation point of view based on the results of finite element modal analysis. Initial model validation and testing performed show substantial excitation of the system under test as the fundamental modes drive the response in all three directions. The response also shows that higher order modes are influencing the system, the axial and transverse response are highly coupled, and tunability is difficult to achieve. By varying the material properties, changing thicknesses, adding masses, and moving the location of the fixture on the resonant plate, the response can be changed significantly. The goal of this work is to identify the parameters that have the greatest influence on the response of the system when using the angle bracket fixture for a mechanical shock test for the intent of tunability of the system.
Calibrating a finite element model to test data is often required to accurately characterize a joint, predict its dynamic behavior, and determine fastener fatigue life. In this work, modal testing, model calibration, and fatigue analysis are performed for a bolted structure, and various joint modeling techniques are compared. The structure is designed to test a single bolt to fatigue failure by utilizing an electrodynamic modal shaker to axially force the bolted joint at resonance. Modal testing is done to obtain the dynamic properties, evaluate finite element joint modeling techniques, and assess the effectiveness of a vibration approach to fatigue testing of bolts. Results show that common joint models can be inaccurate in predicting bolt loads, and even when updated using modal test data, linear structural models alone may be insufficient in evaluating fastener fatigue.
The resonant plate shock test is a dynamic test of a mid-field pyroshock environment where a projectile is struck against a plate. The structure undergoing the simulated field shock is mounted to the plate. The plate resonates when struck and provides a two sided shock that is representative of the shock observed in the field. This test environment shock simulates a shock in a single coordinate direction for components looking to provide evidence that they will survive a similar or less shock when deployed in their operating environment. However, testing in one axis at a time provides many challenges. The true environment is a multi-axis environment. The test environment exhibits strong off-axis motion when only motion in one axis is desired. Multiple fixtures are needed for a single test series. It would be advantageous if a single test could be developed that tests the multi-axis environment simultaneously. In order to design such a test, a model must be developed and validated. The model can be iterated in design and configuration until the specified multi-axis environment is met. The test can then execute the model driven test design. This report discusses the resonant plate model needed to design future tests and the steps and methods used to obtain the model. This report also details aspects of the resonant plate test discovered during the process of model development that aids in our understanding of the test.
In recent years, the Boundary Condition Challenge has gained acceptance in the structural dynamics community. In this challenge problem, an example dynamic system known as the Box and Removable Component, or BARC, is subjected to a single point shock load. The BARC consists of a Removable Component mounted to a box-shaped fixture. The challenge problem specifies a shock load applied to the Box fixture. Here, an additional environment for the challenge problem is proposed. This new environment will be stationary random vibration due to multiple exciters on the Box fixture. In this work, the response of the BARC to this environment will be explored with mod/sim. The goal is to provide the structural dynamics community with all the pieces necessary to examine the various facets of the challenge problem in the context of random vibration and enable researchers to more easily explore problems in random vibration. A data set including input and output degrees of freedom, model modes, model frequency response functions, and input and output time histories and power spectral densities will be created and placed on the challenge problem shared site for others to download and use.
Calibrating a finite element model to test data is often required to accurately characterize a joint, predict its dynamic behavior, and determine fastener fatigue life. In this work, modal testing, model calibration, and fatigue analysis are performed for a bolted structure, and various joint modeling techniques are compared. The structure is designed to test a single bolt to fatigue failure by utilizing an electrodynamic modal shaker to axially force the bolted joint at resonance. Modal testing is done to obtain the dynamic properties, evaluate finite element joint modeling techniques, and assess the effectiveness of a vibration approach to fatigue testing of bolts. Results show that common joint models can be inaccurate in predicting bolt loads, and even when updated using modal test data, linear structural models alone may be insufficient in evaluating fastener fatigue.
Expansion techniques are powerful tools that can take a limited measurement set and provide information on responses at unmeasured locations. Expansion techniques are used in dynamic environments specifications, full field stress measurements, model calibration, and other calculations that require response at locations not measured. However, the process of modal expansion techniques such as SEREP (System Equivalent Reduction Expansion Process) has error with the projection of the measurement set of degrees of freedom to the expanded degrees of freedom. Empirical evidence has been used in the past to qualitatively determine the error. In recent years, the modal projection error was developed to quantify the error through a projection between different domains. The modal projection error is used in this paper to demonstrate the use of the metric in quantifying the error of the expansion process and to quantify which modes of the expansion process are the most important.
In a typical optical test, a stereo camera pair is required to measure the three-dimensional motion of a test article; one camera typically only measures motions in the image plane of the camera, and measurements in the out-of-plane direction are missing. Finite element expansion techniques provide a path to estimate responses from a test at unmeasured degrees of freedom. Treating the case of a single camera as a measurement with unmeasured degrees of freedom, a finite element model is used to expand to the missing third dimension of the image data, allowing a full-field, three-dimensional measurement to be obtained from a set of images from a single camera. The key to this technique relies on the mapping of finite element deformations to image deformations, creating a set of mode shape images that are used to filter the response in the image into modal responses. These modal responses are then applied to the finite element model to estimate physical responses at all finite element model degrees of freedom. The mapping from finite element model to image is achieved using synthetic images produced by a rendering software. The technique is applied first to a synthetic deformation image, and then is validated using an experimental set of images.
Six degree of freedom shaker tests are becoming more popular as they save testing time because they test a component in multiple directions in one test rather than executing multiple tests in one direction at a time. However, there are several difficulties in conducting a component six degree of freedom shaker test in a way that adequately replicates the component field stress. One difficulty is knowing if a classical rigid test fixture will produce component modes that span the displacement space of the component in the field environment. If the modes of the component while attached to a rigid fixture do not span the space of the component in the field environment, then the test will be unable to replicate that motion and corresponding stresses. This paper will examine the motion of the Removable Component of the BARC hardware in an field assembly and calculate the modal projection error expected by executing a six degree of freedom shaker test on a rigid fixture. The paper will conclude by examining the data and comparing it to the pre-test predictions of error calculated by the modal projection error.
Drop shock machines are commonly used to create a single sided shock pulse that is characterized by an amplitude and a pulse length. While the amplitude of the pulse input is critical in determining a majority of the stresses found in a test article, the pulse length determines the frequency content excited by the shock and can also have an effect on stress. Current simulation methods to model the drop shock machine environment typically use an experimentally measured acceleration on the surface of the drop tower carriage as the input. This measurement assumes that the surface of the drop table is rigid through the shock event, due to a lack of knowledge about the true input force on the drop table during the shock event. The purpose of this work is to test this rigid assumption and reconstruct the input force to better characterize the shock event seen by a test article. Results from laboratory modal and drop tests, force reconstruction using SWAT, and FEM analysis are presented along with a brief background into the drop shock machine environment and the SWAT method.