Resonant plate testing is a shock test method that is frequently used to simulate pyroshock events in the laboratory. Recently, it was discovered that if the unit under test is installed at an off-center location, a tri-axial accelerometer would record a shock response in three directions and the resulting shock response spectra implied that the test may have qualified the component in three directions simultaneously. The purpose of this research project was to evaluate this idea of multi-axis shock testing to determine if it was truly a multi-axis shock environment and if such a test could be used as an equivalent component qualification test. A study was conducted using generic, additively manufactured components tested on a resonant plate, along with an investigation of plate motion to evaluate the component response to off- center plate excitation. The data obtained here along with the analytical simulations performed indicate that off-center resonant plate tests are actually not three-axis shock tests, but rather single axis shocks at an arbitrary angle dictated by the location of the unit under test on the plate. This conclusion is supported by the fact that only one vectored shock input is provided to the component in a resonant plate test. Thus, the output response is a coupled response of the transverse plate vibration and the rotational motion of the component on the plate. Additionally, a multi-axis shock test defined by three single axis test environments always results in a significant component over-test in one direction.
When designing or analyzing a mechanical system, energy quantities provide insight into the severity of shock and vibration environments; however, the energy methods in the literature do not address localized behavior because energy quantities are usually computed for an entire structure. The main objective of this paper is to show how to compute the energy in the components of a mechanical system. The motivation for this work is that most systems fail functionally due to component failure, not because the primary structure was overloaded, and the ability to easily compute the spatial distribution of energy helps identify failure sensitive components. The quantity of interest is input energy. That input energy can be decoupled modally is well known. What is less appreciated is that input energy can be computed at the component level exactly, using the component effective modal mass. We show the steady state input energy can be decomposed both spatially and modally and computed using input power spectra. A numerical example illustrates the spatial and modal decomposition of input energy and its utility in identifying components at risk of damage in random vibration and shock environments. Our work shows that the modal properties of the structure and the spectral content of the input must be considered together to assess damage risk. Because input energy includes absorbed energy as well as relative kinetic energy and dissipated energy, it is the recommended energy quantity for assessing the severity for both random vibration and shock environments on a structure.
Several programs at Sandia National Laboratories have adopted energy spectra as a metric to relate the severity of mechanical insults to structural capacity. The purpose being to gain insight into the system's capability, reliability, and to quantify the ultimate margin between the normal operating envelope and the likely system failure point -- a system margin assessment. The fundamental concern with the use of energy metrics was that the applicability domain and implementation details were not completely defined for many problems of interest. The goal of this WSEAT project was to examine that domain of applicability and work out the necessary implementation details. The goal of this project was to provide experimental validation for the energy spectra based methods in the context of margin assessment as they relate to shock environments. The extensive test results concluded that failure predictions using energy methods did not agree with failure predictions using S-N data. As a result, a modification to the energy methods was developed following the form of Basquin's equation to incorporate the power law exponent for fatigue damage. This update to the energy-based framework brings the energy based metrics into agreement with experimental data and historical S-N data.
Materials subject to cyclic loading have been studied extensively and experimentally determined comparisons of stress to number of cycles are used to estimate fatigue life under various loading scenarios. Fatigue data are traditionally presented in the form of S-N curves. Normally, S-N data are derived from cyclic loading but the S-N results are also applicable to random vibration loading and, to some extent, shock. This paper presents an alternate presentation of fatigue data in terms of input energy and number of cycles to failure. In conjunction with this study, a series of shock tests was conducted on 3D printed cantilever beams using a 6-DOF shaker table. All of the beams were tested to failure at shock levels in the low-cycle fatigue regime. From these data, a nominal fatigue curve in terms of input energy and number of shocks to failure was generated and compared with the theoretical developments.
Vibration and shock qualification testing of components can be an expensive and time-consuming process. If the component is small, often two or more units can be mounted on a fixture and tested simultaneously to reduce test time. There is an inherent danger in simultaneously testing two or more identical components as the fundamental natural frequencies and mode shapes of the individual components will be nearly identical with some slight variation due to manufacturing variability. Testing in this manner can create a situation where closely spaced vibration modes produce unwanted interference between the two units under test. This phenomenon could result in a case where one unit is over-tested while the other is under-tested. This paper presents some experimental results from simultaneously testing pairs of components which show distinct interference between the units. Some analysis will also be presented showing how variations in the components can alter the intended test response, potentially impacting component qualification.
The relationship between the damage potential of a series of relatively low level shocks and a single high level shock that causes severe damage is complex and depends on many factors. Shock Response Spectra are the standard for describing mechanical shock events for aerospace vehicles, but are only applicable to single shocks. Energy response spectra are applicable to multiple shock events. This paper describes the results of an initial study that sought to gain insight into how energy response spectra of low amplitude shocks relate to energy response spectra of a high amplitude shock in which the component of interest fails. The study showed that maximum energy spectra of low level shocks cannot simply be summed to estimate the energy response spectra of a high level, failure causing single shock. A power law relationship between the energy spectra of a low amplitude shock and the energy spectra of the high amplitude shock was postulated. A range of values of the exponent was empirically determined from test data and found to be consistent with the values typically used in high-cycle fatigue S-N curves.