Vol.26, No.1, 2026, pp. 158–163
https://doi.org/10.69644/ivk-2026-01-0158

The application of continuously inhomogeneous structural materials in various spheres of modern engineering constantly increases. Very often these materials are used for manufacturing different members and components of machines and mechanisms which perform non-uniform motion. Inertia loads generated by acceleration have to be taken into account when studying fracture in non-uniformly moving members. The current paper concentrates on the effect of energy dissipation on lengthwise fracture in a continuously inhomogeneous beam member that moves up at a varying acceleration. The beam has nonlinear viscoelastic behaviour. A theoretical model with a linear spring and a nonlinear dashpot subjected to time-dependent stress is applied for describing the viscoelastic behaviour of the beam. There are two symmetric lengthwise cracks in the moving beam. The lengthwise fracture under the action of the inertia loads is analysed by the J integral. The effect of energy dissipation is taken into account in the analysis by using the reduced specific strain energy. The latter is extracted from the stress in the spring only (the dashpot dissipates the energy). The J integral solution is checked-up by deriving the strain energy release rate in the beam under inertia loads with considering the effect of energy dissipation. A detailed analysis of the influence of the acceleration of the beam, energy dissipation, mass distribution, and parameters of the viscoelastic model on lengthwise fracture is performed. Applications of the analysis in structural design of moving beams with taking into account the energy dissipation are presented.

Keywords: • continuously inhomogeneous beam • lengthwise fracture • varying acceleration • energy dissipation