Resonant plate and other resonant fixture shock techniques were developed in the 1980s at Sandia National Laboratories as flexible methods to simulate mid-field pyroshock for component qualification. Since that time, many high severity shocks have been specified that take considerable time and expertise to setup and validate. To aid in test setup and to verify the shock test is providing the intended shock loading, it is useful to visualize the resonant motion of the test hardware. Experimental modal analysis is a valuable tool for structural dynamics visualization and model validation. This chapter describes a method to perform experimental modal testing at pyroshock excitation levels, utilizing input forces calculated via the SWAT-TEEM (Sum of Weighted Accelerations Technique—Time Eliminated Elastic Motion) method and the measured acceleration responses. The calculated input force and the measured acceleration data are processed to estimate natural frequencies, damping, and scaled mode shapes of a resonant plate test system. The modal properties estimated from the pyroshock-level test environment are compared to a traditional low-level modal test. The differences between the two modal tests are examined to determine the nonlinearity of the resonant plate test 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.
Many different structures are tested in laboratory environments to replicate the operational or field environment. Structures subjected to vibration environments are typically affixed to an electrodynamic shaker table via a test fixture. The fixture with the shaker table system provides the boundary condition and dynamic impedance to the structure under test. Because the shaker system coupled with the test fixture defines the impedance to the structure under test, it is important to be able to model the shaker table system. This is a difficult task due to the complicated interface between the shaker table, oil film, bearings, and seismic mass on which the table rests. This paper uses optimization analysis with a modal projection error objective function to develop a representative shaker table model. This technique uses data to update and provide confidence in the realization of the shaker table model.
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 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.
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 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.
Engineering designers are responsible for designing parts, components, and systems that perform required functions in their intended field environment. To determine if their design will meet its requirements, the engineer must run a qualification test. For shock and vibration environments, the component or unit under test is connected to a shaker table or shock apparatus and is imparted with a load to simulate the mechanical stress from vibration. A difficulty in this approach is when the stresses in the unit under test cannot be generated by a fixed base boundary condition. A fixed base boundary condition is the approximate boundary condition when the unit under test is affixed to a stiff test fixture and shaker table. To aid in correcting for this error, a flexible fixture needs to be designed to account for the stresses that the unit under test will experience in the field. This paper will use topology optimization to design a test fixture that will minimize the difference between the mechanical impedance of the next level of assembly and the test fixture. The optimized fixture will be compared to the rigid fixture with respect to the test’s ability to produce the field stresses.
The Box Assembly with Removable Component (BARC) structure was developed as a challenge problem for those investigating boundary conditions and their effect on structural dynamic tests. To investigate the effects of boundary conditions on the dynamic response of the Removable Component, it was tested in three configurations, each with a different fixture and thus a different boundary condition. A “truth” configuration test with the component attached to its next-level assembly (the Box) was first performed to provide data that multi-axis tests of the component would aim to replicate. The following two tests aimed to reproduce the component responses of the first test through multi-axis testing. The first of these tests is a more “traditional” vibration test with the removable component attached to a “rigid” plate fixture. A second set of these tests replaces the fixture plate with flexible fixtures designed using topology optimization and created using additive manufacturing. These two test approaches are compared back to the truth test to determine how much improvement can be obtained in a laboratory test by using a fixture that is more representative of the compliance of the component’s assembly.
The ability to measure full-field strains is desirable for analytical model validation or characterization of test articles for which there is no model. Of further interest is the ability to determine if a given environmental test’s boundary conditions are suitable to replicate the strain fields the test article undergoes in service. In this work, full-field strain shapes are estimated using a 3D scanning laser Doppler vibrometer and several post-processing methods. The processing methods are categorized in two groups: direct or transformation. Direct methods compute strain fields with only spatial filtering applied to the measurements. Transformation methods utilize SEREP shape expansion/smoothing of the measurements in conjunction with a finite element model. Both methods are used with mode shapes as well as operational deflection shapes. A comparison of each method is presented. It was found that performing a SEREP expansion of the mode shapes and post-processing to estimate strain fields was very effective, while directly measuring strains from ODS or modes was highly subject to noise and filtering effects.
Multi-degree of freedom testing is growing in popularity and in practice. This is largely due to its inherent benefits in producing realistic stresses that the test article observes in its working environment and the efficiency of testing all axes at one time instead of individually. However, deriving and applying the “correct” inputs to a test has been a challenge. This paper explores a recently developed theory into deriving rigid body accelerations as an input to a test article through sub-structuring techniques. The theory develops a transformation matrix that separates the complete system dynamics into two sub-structures, the test article and next level assembly. The transformation does this by segregating the test article’s fixed base modal coordinates and the next level assembly’s free modal coordinates. This transformation provides insight into the damage that the test article acquires from its excited fixed base shapes and how to properly excite the test article by observing the next level assembly’s rigid body motion. This paper examines using next level assembly’s rigid body motion as a direct input in a multi-degree of freedom test to excite the test article’s fixed base shapes in the same way as the working environment.
Structural dynamic testing is a common method for determining if the design of a component of a system will mechanically fail when deployed into its field environment. To satisfy the test's goal, the mechanical stresses must be replicated. Structural dynamic testing is commonly executed on a shaker table or a shock apparatus such as a drop table or a resonant plate. These apparatus impart a force or load on the component through a test fixture that connects the unit under test to the apparatus. Because the test fixture is directly connected to the unit under test, the fixture modifies the structural dynamics of the system, thus varying the locations and relative levels of stress on the unit under test. This may lead to a false positive or negative indication if the unit under test will fail in its field environment depending on the environment and the test fixture. This body of research utilizes topology optimization using the Plato software to design a test fixture that attaches to the unit under test that matches the dynamic impedance of the next level of assembly. The optimization's objective function is the difference between the field configuration and the laboratory configuration's frequency response functions. It was found that this objective function had many local minima and posed difficulties in converging to an acceptable solution. A case study is presented that uses this objective function and although the results are not perfect, they are quantifiably better than the current method of using a sufficiently stiff fixture.
Qualification of products to their vibration and shock requirements in a laboratory setting consists of two basic steps. The first is the quantification of the product's mechanical environment in the field. The second is the process of testing the product in the laboratory to ensure it is robust enough to survive the field environment. The latter part is the subject of the “Boundary Condition for Component Qualification” challenge problem. This paper describes the challenges in determining the appropriate boundary conditions and input stimulus required to qualify the product. This paper also describes the step sand analyses that were taken to design a set of hardware that demonstrates the issue and can be used by round robin challenge participants to investigate the problem.
In the aerospace industry, hail strikes on a structure are an environment that must be considered when qualifying a product. Performing a physical test on a product would require a test setup that would launch a fabricated hail stone at an expensive prototype. This test may be difficult or impossible to execute and destructive to the product. Instead of testing, a finite element model (FEM) may be used to simulate the damage and consequences of a hail strike. In order to use a FEM in this way, an accurate representation of the input force from a hail stone must be known. The purpose of this paper is to calculate the force that a hail stone imparts on an object using the inverse method SWAT-TEEM. This paper discusses the advantages of using SWAT-TEEM over other force identification methods and exercises the algorithm for a test series of hail strikes that include multiple angles of attack and multiple velocities which include speeds that are supersonic.
During an environment, it is desirable to know the forces or inputs on the system of interest. With the inputs, one can directly use a finite element or experimental model to predict responses not measured in a field test. One can attempt to measure point forces using force gauges, however, these gauges are insufficient due to the inability to place a gauge at a forcing interface or to measure a force applied over an area. SWAT (Sum of weighted acceleration technique) is a method that uses mode shapes as a modal filter with measured accelerations and to solve the inverse problem and calculate the forces and moments on the system. This paper will examine an application where the use of a force gauge is impossible due to the external forces being applied over an area. The paper will calculate the sum of the forces and moments imparted on the system and will use a finite element model to check the plausibility of the calculated forces.