###### Abstract  
In vibration tests, the behavior of the structure depends on its mechanical boundary conditions, which are represented in physical tests by connecting elements with mechanical properties. Adjustable impedance elements are machine elements fulfilling the task of an adjustable connection on a vibration test bench and therefore represent a variety of properties. Their mechanical properties must be known over wider ranges than comparable compliant structures tested in the literature. This paper is dedicated to vibration testing of the adjustable impedance elements themselves, taking the influences of fixtures and measuring devices of the test bench into account. Different approaches for measuring the frequency response functions are applied to freely vibrating masses at a hydraulic and an electrodynamic test bench. Mass cancellation and the frequency-dependent measurement systems function have shown their usefulness in characterizing the biodynamic response of hand-arm models before. This measurement method is extended to be transferable to machine elements to obtain reliable results under a wider range of test conditions. The necessity for dynamically calibrated measurement of the frequency response functions is demonstrated for different free vibration masses and for two compliant elements on two different test benches to provide results over a wide range of test conditions. dynamic calibration; vibration testing; measurement approach; mechanical impedance; compliant structures; adjustable impedance elements; frequency response function +
Footnote †: journal: Applied Sciences  
12 October 2021  
11960  
testing, the AIE is attached to the test rig by fixtures, their influence must be considered as well when evaluating the samples [2; 3]. Approximate rigid boundary conditions are to be used, so that the fixtures would not have any influence on the test results [2; 4]. This can only be implemented for limited frequency bands and leads to unrealistic dynamic interfaces [4]. Dynamic resonance and anti-resonance phenomena in the fixture can cause the test object to be non-uniformly loaded [5]. Real interfaces have real mounting conditions, and corresponding mechanical stiffness, damping and inertia [6; 7]. For vibration testing these properties influence the test results, but are generally not specified, and usually not even known [2]. Dynamic testing differs from static testing in its dependence on time. Especially in vibration testing, delays between measurement signals are crucial, which can be attributed to the sensors and electronic circuits of the measurement system or during computational processing. [PERSON] et al. [8] show the use of AIEs for testing and validation of aircraft components and hand-held power tools. AIEs are comparable to compliant structures that are frequently investigated in research. In the literature, comparable compliant elements can be found under the terms adjustable, controllable or variable--stiffness, damping or compliant--connection, mechanism, actuator or element. [PERSON] et al. [9], [PERSON] et al. [10] and [PERSON] et al. [11] have reviewed the field of adjustable compliant structures and have provided a broad basis for the use of these elements. In particular, they have focused on the use of these structures in the field of robotics. In search for measurement methods in the field of vibration testing for AIEs, the measurement methods of different adjustable compliant structures were analyzed. Most of the published papers address elements with adjustable stiffness. These elements are only measured and characterized in the static range [12; 13; 14; 15]. Although this is sufficient to validate the adjustability of the stiffness, it is not sufficient for the use in vibration testing, because the behavior over the whole frequency range of the later tests must be known. Fewer published papers are also dynamically investigated, e.g., as free vibration response to pendular movement [16].