A system is provided for testing a component. This system includes a support structure, an excitation system and a sensor system. The support structure is configured to support the component. The excitation system includes a plurality of permanent magnets and a plurality of electromagnets. The permanent magnets are arranged in an array and configured for rigid connection to the component. Each of the electromagnets is associated with a respective one of the permanent magnets. The excitation system is configured to respectively control interaction of the electromagnets with the permanent magnets to excite a vibratory response in the component. The sensor system is configured to output data indicative of the vibratory response.