Analytical Study of Torsional and Bending Oscillations of Nonlinear Mechanical Systems

Abstract

The study analyzes the torsional and bending oscillations of nonlinear mechanical systems to identify working parameters that minimize amplitude and improve stability under dynamic loading. Such systems, common in heavy machinery, transportation, and construction, often experience combined torsional and bending stresses that lead to deformation and potential failure. By deriving generalized differential equations and solving them under specific boundary and initial conditions, the study determines frequency characteristics that influence system behavior. The results show that reducing the external force amplitude decreases the risk of low-frequency resonance and improves system stability. This analytical approach provides a foundation for designing safer and more efficient mechanical systems with improved vibration resistance.