Within a short run, a novel class of mechanisms and systems has been created with parametric (elastic-dissipative) elements of sign-changing stiffness controlled in a range from positive to negative or quasi-zero values. A great deal of natural and hand-made designs on different physical bases appeared that could reveal such a phenomenon. These mechanisms and systems can cut the stiffness and provide a perfect vibration protection in a frequency range required. However, only some of them either are ready for to substitute or could be used in advanced hybrids in parallel with conventional vibration protection mechanisms and systems in certain types of machines and equipment. The main reason is very small travel where the negative or quasi-zero stiffness can be realized. A small error in passive control or a soft fault in an active one is enough to move such mechanisms and systems to performance degradation. A generic model of the parametric elements with negative and quasi-zero stiffness in small and a transition model to provide these effects in large are formulated. The model analysis led to important predictions on how to obtain an optimal trade-off between the dimensions and performance of the mechanisms and systems of novel class.

Simulation and instrumental measurement are the most reliable methods to examine, prove, and enhance adequacy of theoretical models and prototypes and predict their practical use. A trade-off complex of testing and measuring instruments is presented for designing vibration protection systems. This includes both the standard test equipment and add-on devices to recognize specifics in behavior of the systems with negative and quasi-zero stiffness. This covers the computer-aided tensile machines and special adapters for static and low-cycle testing, optical aids for holographic interferometry and structural testing, electro- and/or hydrodynamic exciters, sets of special infra-frequency accelerometers and external filters, AD/DA-boards, FFT- and/or wavelet analyzers, recording equipment, and standard and special software. The complex developed provides a full cycle of the system experiment, including (a) path-generation and optimization of elastic responses, (b) strain state analysis of parametric elements and mechanism units, (c) simulation and online analysis of dynamic behavior of scaled models of the systems with extremely small stiffness and damping under vibrations in a frequency range starting from near-zero values. The method of laboratory experiment is an integral part of the methodology to investigate the systems in the field.

The infra-low-frequency vibrations are most dangerous and harmful for humans. They affect a person as an operator or passenger of the vehicles and other vibrating machines, and his environment the rest of a day and night. These are longtime and thus devastating effects since human natural frequencies dramatically coincide with forced vibrations of the machines in the same spectra, resulting in permanent broadband resonances. The general and industrial standards regulate exposure time of vibration impacts to humans, since conventional vibration protection systems, to put it mildly, do not quite cope with the functions assigned to them. Moreover, they operate as vibration amplifiers rather than vibration systems just in these frequency spectra. Besides, new potentially hazard vibrations, for example, in the near-zero frequencies appear with advent of the machines of next generation under intensive development, such as high-speed railroad trains for long distances and multiple-purpose helicopters. Fundamentally other design methods and proper technology are required to provide the infra-low-frequency vibration protection of humans inside and outside operating transport vehicles, construction equipment, and other machines, especially since a gap increases between efficiency of the conventional systems and vibration limits required for health, activity, and comfort of humans

The systems with negative and quasi-zero stiffness can provide perfect vibration protection in a wide frequency range including near-zero values. However, it is possible under a certain structure of system damping. Intelligent design approaches are presented to control the structural (hysteretic) components in thin-walled elastic elements and slip ones in movable joints of the mechanisms structuring the vibration protection systems with small stiffness. These involve (a) models for analysis and optimization of the components, (b) novel antifriction materials and composites providing reducing the hysteretic and kinetic frictions up to 0.02 to 0.005, which are adozen times less than using most prevalent materials. For instance, synthesized incompressible lubricants and solid lightweight composites provided a little to no hysteretic friction in the elements designed as the packages of thin plates, and no kinetic friction in the insert liners and guiderails. The use of approaches reduced at least 3.5 to 4 times unwanted level of system damping. These approaches can provide even more drastic, 0.01 to 0.02, decrease in the system damping. Assuming active motion control, this will reduce the system natural frequencies up to 0.15 to 0.2 Hz and improve vibration protection 50 to 300 times and more.

Most routine strategies of motion control in vibration protection systems are based on attenuation of resonant responses using external semi-active or active dampers. In the systems with negative and quasi-zero stiffness, it is simpler because there is no need to know and continually process random signal data from an external vibration source. The control focuses on maintaining a certain balance between the positive and negative stiffness of parametric elements varied in predetermined ranges to keep separation of the system natural frequency spectra and the frequencies of forced vibrations including near-zero values. The control criteria, formulated and quantitatively estimated, provide extremely small stiffness, immobility in a steady state motion, and stabilization in a transient motion of the system without an external damper. The control strategy is validated through designing the systems supplied with active pneumatic suspensions and passive mechanisms of variable negative stiffness. The control algorithms were realized with the help of a two-channel control system and actuators made of commercial hardware and operating in parallel. Efficiency of the algorithms has been estimated through comparison of results of computer simulation and development test of seat suspensions for vibration protection of drivers of heavy trucks and buses and for helicopter pilots.

Results of study in the field and practical use of vibration protection systems with compact mechanisms (removable modules) of negative stiffness are presented, obtained over the years. These are authoring systems considered as an alternative to conventional systems to protect humans against the most dangerous and harmful vibrations. This was proved in the land transport vehicles (electric buses, heavy trucks), construction equipment (wheel cranes and loaders, caterpillar excavators), harvester combines, and in mid-size and heavy helicopters. In some cases, efficiency of vibration protection was increased 100 to 700 times in the infra- and 1500 times in the low-frequency ranges. Using the theory of similarity and dimensions, one can design a lineup of compact systems with payload capacity of 150 to 250,000 N, however, closely approximated in dimensions, for other objects of vibration protection. In active control, operation frequency range of the systems can start from 0.05 to 0.1 Hz. With the advent of fundamentally new structural and functional materials, the possibilities of systems with negative and quasi-zero stiffness seem unlimited. For instance, substituting the parametric elements from spring steels with composites of carbon fibers increases 4−5 times the travel, and we hope to increase longtime durability under nonlinear postbuckling.

Designing and finding a reasonable trade-off between dimensions and performance of structures and mechanisms with parametric elements of negative stiffness in large is a fundamental problem in development and practical use of infra-low-frequency vibration protection systems for humans and engineering. A method is proposed and formulated for modeling the stress-strain under nonlinear postbuckling of the structures and for an optimal dimensioning of the mechanisms. The method is based on the hypotheses and statements of consistent theory of thin shells and includes (a) basic design theory, (b) validation of prediction that parametric elements are to be thin-walled structures to provide viability of the mechanisms and harmony with a vibration protection system, (c) algorithm for modeling geometrically nonlinear deforming the structures and iterative procedure that enables an optimal computable scheme for designing the mechanisms by the FEM, and (d) fundamental relationships between design parameters in terms of compactness and compatibility of the mechanisms with workspace of the systems and for extension the range of stiffness control, where system natural frequencies can be reduced until nearly-zero values. A lineup of geometrically similar mechanisms with negative stiffness in large has been designed for seat suspensions, mountings, and platforms.

Structural design is another strategic point in developing a vibration protection system with mechanisms of negative and quasi-zero stiffness. Missing this stage of the design and errors in designing the structure of mechanisms predisposed to unstable motion can ruin the development idea. A method of structural design of function-generating mechanisms for such systems is proposed. This includes the type and number synthesis of the mechanisms, making this process less empirical and more reasonable and bringing a great number of new candidates. The atlases of the mechanisms for seat suspensions and bogie secondary suspensions for carbody of high-speed trains are elaborated. The method fundamentals are (a) the function-generating mechanism is to be perfectly structured, that is, with a minimal number of redundant constraints; (b) due to unstable motion and transposition of clearances in kinematic pairs, the mechanism with negative stiffness must not directly join the input and output structural elements of function-generating mechanism to avoid structural indeterminacy; (c) mechanisms with negative stiffness shall be joined to the input structural element, and with no more than two kinematic pairs, one of these two is to be higher; (d) an external damping mechanism can be removed from function-generating mechanisms without degradation of the system performance.

Some types of conventional mechanical, pneumatic or other vibration protecting mechanisms with parametric elements of positive stiffness, i.e. having a given load capacity, may reveal the negative or quasi-zero stiffness in small. However, this is considered as a side effect and have no engineering feasibility to be realized in commercial vibration protection systems. This disadvantage can easily be eliminated if join the redundant mechanisms with parametric elements of negative and quasi-zero stiffness in large. Redundant mechanisms can drastically improve the quality of vibration protection in a certain combination and interaction with commercial systems, and without a destroying the system workspace. In this manner, one may arrange a seat suspension, independent wheel suspension, cabin's mounting, table or platform for measuring instrument and in this way protect a man-operator or passenger, power unit, onboard or stationary electronics, and cargo container. It was shown that the mechanisms with negative and quasi-zero stiffness in large, being properly joined to commercial vibration protection systems by using transmissions with short kinematic chain, increased 5 to 57 times the quality of vibration protection in the whole infra-low frequency range including nearly zero values. In some practical cases, this advantage reaches 100 to 300 times and more

Stability in large of the systems with mechanisms of negative and quasi-zero stiffness plays an important role for improvement of the infra-low vibration protection. These mechanisms are predisposed to chaotic vibration motion. Analysis of chaotic vibration and comparative selection of the mechanisms are to be reasonable steps before deciding next steps in designing the vibration protection systems. Their dynamic behavior can be diagnosed and predicted by the qualitative and quantitative methods for analysis of chaotic motion. An algorithm has been developed to study chaotic motion of the mechanisms, and the conditions of dynamic stability of the systems with such mechanisms are formulated. The algorithm is based on the Lyapunov largest exponent and Poincare map of phase trajectory methods and includes (a) formulation of chaotic motion models and criterial experiments for the mechanisms and systems, (b) technique of comparative analysis of the models, (c) computation procedure to estimate their dynamic stability in large, (d) formulation of design and functional parameters for providing stable motion of the systems in the infra-frequency range, including near-zero values. Validity of the algorithm is demonstrated through the development of active pneumatic suspensions supplied with passive mechanisms of variable negative stiffness.