The paper presents a theory of body collision with pit corner. The theory can be successfully applied in approaching tasks coping with the orientation of details in technological processes and control systems, the motion of elements in mechanisms having a gap, collisions in motion of different sport objects, the analysis of car accidents etc. The applied theory deals with car motion after collision with a specific obstacle i.e. pit corner. The study is based on linear and angular momentum theorems and two restitution coefficients of normal impulse from both sides of the obstacle. The obtained results can be used for assessing road accidents in case of car collision with one or more obstacles. The object of contact may involve hitting a plane foundation, the ditch and edging of a highway or a rock in the field.

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Abstract. Rubber and rubber-metal (RM) elements are successfully used as bearing, joints, compensating devices, vibration and shock absorbers in civil engineering and machine building because of rubber and rubberlike materials (elastomers) have a capability of absorbing input energy much better than other construction materials. The elastic properties of rubber in such supports allows reverse backward to its original position under dynamic load action. Along with the instantaneous elastic deformation these materials exhibit a retarded elastic deformation, viscous flow (creep) and relaxation. The mechanical properties of rubber which are necessary for the optimal design of antivibration devices are next: bulk modulus of compression, dynamic and static shear modulus, energy dissipation factor. To describe the relationship between the compressive (or shear) stress σ(t) and strain ԑ(t) the creep and relaxation kernel, taking into account the viscoelastic properties of the rubber, is used. The kernels proposed by A. Rzhanitsin, Y. Rabotnov, M. Koltunov give satisfactory results for the mechanical properties of rubber in the mean frequency domain (10 -3 < ω < 10 3 s -1 ). In this paper for the accounting of dissipative properties of the rubber Rabotnov's kernel is used, the energy loss during one oscillation period is calculated. The flat-type RM absorber with kinematic excitation, which lower base oscillates harmonically is considered, oscillation parameters of the upper base on which the protected object is placed, are calculated. Damping properties are expressed by the ratio of the amplitude of the forced oscillations of the upper base (and object) to the amplitude of driving lower base.

Natural and synthetic rubber (elastomeric materials) are used for fabrication of vibration dampers, shock absorbers, seismic isolation, bearing seals, compensation devices. These elements are applied both in machine manufacturing and in civil engineering. Elastomers absorb input energy much better than other construction materials and this fact gives them many engineering advantages. The disadvantages of elastomeric materials are ageing, accumulation of damage, i.e. changing the mechanical properties over time and lowering their operational capability. The durability of rubber elements under cyclic loading is determined according to various criteria: thermodynamic process of damage, energy damage criterion, entropic damage criterion, engineering damage criterion, dissipative damage criterion. Experiments show that the nature of the destruction process is unidirectional and irreversible. Deformation is accompanied by dissipative heating, which is also facilitated by low thermal conductivity of rubber. To calculate the durability of rubber parts, a large amount of experimental data is required, which is currently insufficient. In this paper, the dissipative damage criterion is considered, which allows determining the limiting number of loading cycles at a given operating temperature and damage parameter. The destruction occurs when the concentration of broken molecular bonds reaches a certain critical level, the numerical value of which is constant of the material. This value is called the damage parameter, which is a constant value for a given material, empirically determined. In addition, it is necessary to know the dynamic shear modulus of the material and the relative deformation of the element. Such approach allows to correctly appoint the grade of rubber for anti-vibration devices at the design stage.