Estimation of stress and displacement increase caused by heat generation in rubber vibration absorber

Rubber and rubber-like materials (elastomers) are widely used for anti-vibration mounts and shock absorbers for vehicles, machinery, building structures due to their specific properties: ability to absorb vibration and shock loads, low elastic modulus, high mechanical strength, high elongation at brake, reversible elastic deformation. Rubber is a material that is capable of recovering from large deformations quickly and forcibly, which is suitable for work under cyclic loading. During deformation elastomeric materials absorb in an irreversible way part of the energy, causing this deformation. The energy absorbed during each cycle heats the deformed rubber element and dissipates in media. Heat generation in rubber causes additional stresses and deformations which are poorly known, and they are a subject of our study. In the presented paper the work of a rubber anti-vibration mount in the form of a straight circular cylinder under action of cyclic loading is studied.
Poisson’s ratio of the rubber material is μ = 0.5, the weight of the mount is not taken into account. Temperature field is assumed known based on the previous work (it depends on the frequency and amplitude of vibration, heat conductivity and heat capacity of the material, etc.). The stress-strain state analysis was carried out based on the Reissner variational principle. Analytical dependences for temperature additions to stresses and displacements are derived that allows estimating stiffness of the anti-vibration mount and its increase as a result of self-heating. Obtained results may be useful for proper design of anti-vibration mounts allowing changing geometrical dimensions in order to reach the required temperature field.