# Study of Systems of Active Vibration Protection of Navigation Instrument Equipment
###### Abstract
To solve the resonance problem, a device is needed that determines the \"jump\" point, both for harmonic resonance and in the region of higher-order instability. In structures with a cubic-nonlinear stiffness characteristic, even in the presence of a region of quasi-zero stiffness, it is very difficult to obtain such a characteristic [6; 7; 12]. There is a high probability that such a characteristic exists and is directly related to the exponent of the function describing the nonlinear stiffness characteristic [38; 39]. However, without the introduction of active links to adjust the stiffness, it is impossible to obtain such a characteristic [40]. The solution to this problem determines a qualitatively new approach to the organization of the structure of the device, i.e., the vibration isolator. In addition to the direct connection with the torque transmission elements, the vibration isolator must also have feedback that determines its self-adjustment according to some selected criteria. Therefore, to determine the natural frequencies of the controlled vibration isolator, the use of the root method is one of the most accurate and reliable [41; 42]. It is based on measuring the vibrational response of the system by means of impulse disturbances with a root frequency. In the literature, there are many scientific studies and articles describing the principle of action and application of the root method for determining the natural frequencies of a controlled vibration isolator [43; 44; 45]. Many authors provide practical recommendations for using this method, including the vibration response measurement, the obtained data processing, and the analysis of the results [46]. It is also noted in the literature [47] that the accuracy of determining the natural frequencies of the controlled vibration isolator depends on a number of factors, such as the accuracy of the measuring equipment, the quality of impulse disturbances, etc. Some studies are devoted to the study of the influence of various factors on the accuracy of determining the natural frequencies of a controlled vibration isolator using the root method. Prospective methods of improving the operational characteristics of equipment from the point of view of reducing the degree of influence of external disturbing factors, such as kinematic, vibration, and acoustic factors, are passive, active and compensatory methods [48; 49]. Passive methods include methods of design and technological improvements that make it possible to reduce the impact of sound and vibration without additional energy sources and do not require information about the nature of the excitation effect [49]. Active methods include those that are based on the use of external information and additional energy sources and enable compensation for mechanical disturbing factors [50]. Compensatory methods are based on the ideology of compensation of manifestations of excitement and do not require the use of energy sources and information about the nature of external influence [51]. Methods of damping vibration, which propagates through supporting structures, are widely used [52; 53; 54]. One of the means of broad-band vibration isolation in the medium and high-frequency areas of the sound range is to cover the elements and housings of devices with a vibration-absorbing coating, but this method leads to an increase in the total mass of the object, and the significant non-linearity of the frequency characteristic of vibration isolation coatings forces us to look for new methods and means of combating vibration. The use of active methods involves the creation by special generators of an additional exciting field of the same physical structure with a given amplitude-phase characteristic. [55]. Recently, such methods have been widely used in electronic equipment protection systems.