
Fractal and Fractional, Год журнала: 2025, Номер 9(6), С. 357 - 357
Опубликована: Май 29, 2025
This article aims to clarify the applicability of He’s two-scale fractal dimension transform by replacing tα with τ. It demonstrates potential capture influence parameter on system’s damping frequency, particularly when viscoelastic term (damping) does not equal half fractional inertia force term. The analysis examines elastomer materials’ dynamic amplitude–time response, considering viscohyperelastic effects related material’s energy dissipation capacity. To determine amplitude oscillations for nonlinear equation motion a body supported subjected uniaxial stretching, harmonic balance perturbation method, combined and Ross’s formula, is employed. Numerical calculations demonstrate effectiveness transformation in capturing phenomena associated time derivative deformation. due correlation between rate viscoelasticity structure media materials, which reflected oscillation decay. Furthermore, approach introduced El-Dib replace original an equivalent linear oscillator integer derivatives used further assess qualitative quantitative performance our derived solution. proposed elucidates calculus determining systems, where order terms varies.
Язык: Английский