Eigenvibrations of Kirchhoff Rectangular Random Plates on Time-Fractional Viscoelastic Supports via the Stochastic...

Area of Science:

• Computational Mechanics
• Structural Dynamics
• Viscoelasticity

Background:

• Understanding the dynamic behavior of structures supported by viscoelastic materials is crucial for engineering applications.
• Time-fractional derivatives offer a more accurate representation of viscoelastic material behavior compared to traditional models.

Purpose of the Study:

• To investigate the natural vibrations of thin Kirchhoff-Love plates supported by time-fractional viscoelastic foundations.
• To apply the Stochastic Finite Element Method (SFEM) for analyzing probabilistic structural responses under uncertainty.
• To estimate probabilistic relative entropy and safety measures for foundation plate dynamics.

Main Methods:

• The Finite Element Method (FEM) serves as the deterministic core for solving structural eigenvibrations.
• Subspace iteration and continuation methods are employed to solve the non-linear eigenproblem.
• Probabilistic analysis utilizes Monte-Carlo simulation, semi-analytical approaches, and the generalized stochastic perturbation method.

Main Results:

• Numerical investigation of probabilistic structural responses, including second-order characteristics, considering input uncertainty.
• Estimation of probabilistic relative entropy and safety measures.
• The study quantifies the influence of fractional-order viscoelastic supports on plate vibration characteristics.

Conclusions:

• The SFEM provides a robust framework for analyzing the dynamics of plates on viscoelastic foundations with fractional behavior.
• The findings are applicable to the design and analysis of foundation plates interacting with viscoelastic soils.
• This research contributes to a deeper understanding of uncertainty quantification in structural dynamics problems.