In this study, a nonlinear mathematical model of a thin string oscillating in an isotropic viscoelastic medium is developed. The model addresses external and internal mechanical energy dissipation in the string using components described by nonlinear exponential functions. The differential state equation of the studied item is based on a modified Hamilton–Ostrogradsky integral variation principle. The principle is modified by expanding the Lagrangian with two additional components: one addressing the external and internal mechanical energy dissipation in a system and the other addressing the energy of external non-potential forces acting on a system. To substantiate the existence and uniqueness of the solution to a mixed initial boundary problem, the general theory of nonlinear differential equations is applied. A long, single power line is used as an example; its elements oscillate between two support points of the wire. The computer simulation results for the nonlinear vibrations of the object are presented and analysed.

This study examines the influence of scale effects on the thermomechanical and structural performance of chemically cured, glass-fibre-reinforced polyester composites. Two reinforcement architectures—plain 0/90° fabric and biaxial fabric—were analysed to assess differences in resin flow, curing behaviour, and mechanical characteristics. Differential Scanning Calorimetry (DSC) was employed to characterise cross-linking kinetics at 15 °C, 19 °C, and 25 °C, demonstrating that higher cure temperatures markedly accelerate gelation and cross-linking. Composite plates were manufactured by Light Resin Transfer Moulding (L-RTM), and static tensile tests were conducted in accordance with PN-EN ISO 527-4. The results confirm that reinforcement architecture strongly affects processability and mechanical performance. The 0/90° fabric provided superior resin permeability and shorter infusion times, whereas the biaxial fabric required higher injection pressure and exhibited longer curing duration. Statistical analysis based on Weibull’s brittle strength theory verified the presence of scale effects: larger specimens displayed lower nominal strength due to a higher probability of internal flaws. Multiple regression modelling further revealed relationships between geometric and mechanical parameters: maximum (destructive) stress, Rm, was the dominant factor influencing both specimen thickness and number of layers, while deformation at maximum stress (εm) primarily determined specimen length. These findings highlight the necessity of accounting for size-dependent behaviour when designing and testing polymer composites. Considering scale effects enables more reliable extrapolation from laboratory-scale tests to full-scale components, thereby improving predictability and structural reliability in engineering applications.