ESDU 19006:2020

$126.75

Force Limited Random Vibration Testing – the Computation of the Semi-Empirical Constant C2 for Test Article and Supporting Structure

Published By	Publication Date	Number of Pages
ESDU	2020-04	40

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Category: ESDU

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Description

INTRODUCTION

General

During the early phase of the launch (lift-off) a spacecraft will be exposed to severe random acoustic loads. Acoustic loads are the cause of structure-borne random mechanical vibrations inside the spacecraft. Before launch the spacecraft system is tested to be sure it will withstand (survive) the acoustic loads. Additionally, a validated mathematical model has to be developed with which the dynamical structural responses can be calculated.

In the test set-up these acoustic loads (sound pressures) are simulated as a reverberant (diffuse) acoustic sound field, both analytically and during acoustic tests in a reverberant acoustic chamber, which is more or less an approximation of the real acoustic environment under the fairing of the launch vehicle.

The mathematical description of a diffuse sound field and the simulation during testing in a reverberant acoustic chamber are well known and, in general, accepted in spacecraft design. Lightweight large areas of structures (solar arrays, antennae, etc.) are very sensitive to the quite severe acoustic loads and within the spacecraft the acoustic loads are transferred into random mechanical vibrations, the so-called structure-borne noise.

These mechanical random vibrations excite the spacecraft mounted instruments, equipment and other units by random enforced accelerations. In general, the random enforced acceleration specifications are provided to investigate analytically and by test the stiffness and strength characteristics of the subsystems. The random enforced acceleration specifications are derived from the acoustic random response characteristics estimated by fluid/structure response interaction analysis (finite element analysis (FEA), boundary element analysis (BEA) or statistical energy analysis (SEA)) or by an acoustic test in a reverberant chamber.

The dynamic response characteristics between two or more elastic structures show peaks and valleys at resonances and anti-resonances. In practice, the generation of a random enforced acceleration specification means that the peaks are enveloped to achieve a more or less smoothed random acceleration specification as shown in Sketch 2.2. The enveloped random acceleration specification is conservative at anti-resonance frequencies, where valleys in the dynamic responses will be encountered. The random vibration specification will be applied during the design and qualification process of instruments, equipment and units against the random vibration environment. For convenience the test item (instrument, equipment, unit, etc.) is called the load and the supporting structure (panels, side walls, etc.) the source.

During the random vibration test the load is placed on a shaker system to apply the random acceleration specification. The impedance of the shaker head or shaker slip table is significantly greater than the structural impedance of the source. The boundary condition of the load during the vibration test is quite different from the supported load during launch.

At approximately the natural frequencies of the load (at low modal damping) a large increase of the dynamic mass of the load will occur and the response at the interface of the load/source combination will decrease. This is the same as the principle of the reduction of responses using auxiliary mass spring systems (absorbing vibration (Den Hartog, 1985)). At resonance the source with a normal structural impedance will not be able to put enough energy in the load to maintain the vibration levels, but the shaker is certainly able to put the required energy into the load. Following the random vibration specification the shaker system will over-test the load considerably. That means the random response acceleration and random force response are higher than may be expected during the launch event.

To avoid over-testing of the subsystem during the random vibration test the specified random enforced acceleration vibration specification will be adapted. That means that at the resonant frequency (frequencies) of the load the input spectrum will be reduced or notched. In general, the adapted (notched) random vibration acceleration spectrum is defined based on either on limiting it to allowable responses (response limited vibration test) or on an allowable force spectrum (force limited vibration test). The force limits are defined at the interface between the load and the shaker. An example of a notched random vibration spectrum is shown in Sketch 2.3. In general, the notches will occur at the natural frequencies of the load when the interface force are beyond the specified force limits in fact, at the anti-resonances in the load/source combination. Many methods for defining the notched spectra are discussed in the literature review in this Item.

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