Optimization of Shaker Locations for Multiple Shaker Environmental Testing

For flight payloads or systems in free flight, Impedance Matched Multi-Axis Testing (IMMAT) can provide an accurate laboratory reproduction of the flight vibration environment at multiple response locations. IMMAT is performed by controlling multiple shakers attached to the system of interest, usually through slender rods so that the shakers impart negligible moments or shear forces at the attachment. The attachment usually requires that the shakers not physically support the system. Thus, IMMAT is different from other multi-degree of freedom testing where shakers for slip tables or with vertical bearings drastically change the impedance by their rigid attachment to the system or payload. Consequently, IMMAT shakers are generally smaller than used for traditional testing. In the laboratory IMMAT test, bungee cords can support the system to simulate free flight. For a system that is a flight payload, bungee cords can support a portion of the next level of assembly (such as a rack or rail) with the attached payload to greatly improve the laboratory reproduction of the payload environment with the approximate attachment impedance. Engineering judgment has historically been the basis for IMMAT test planning but provides no pre-test metrics to show whether the test setup can meet the desired requirements. For successful test planning, engineers need tools to optimize the number and location of shakers and predict the requirements for the shakers and amplifiers. Electrodynamic shakers and amplifiers have physical limitations such as maximum available amplifier current, voltage or power and shaker force or stroke. If shakers and amplifiers can barely meet required levels with a well-designed IMMAT test, improper shaker placement can cause exceedance of the limitations and failure of the test to meet required levels. We present a tool to optimize the number and locations of shakers with an objective function that performs a least square fit of the flight cross spectral density matrix while minimizing requirements on the amplifiers or shakers. In this work, an optimized IMMAT test with four shakers attached to a test article closely reproduces the vibration environment generated by a field acoustic test. The optimization is based on a model. The model consists of a modal model (derived from a finite element model) of the test article coupled to a simple calibrated electro-mechanical model of the shakers. The optimization selects shaker locations to minimize the req