Maximum entropy approach for modeling random uncertainties in transient elastodynamics.

Area of Science:

• Mechanical Engineering
• Structural Dynamics
• Computational Mechanics

Background:

• Analyzing random uncertainties in dynamical systems is crucial for accurate mechanical system predictions.
• Existing methods often require detailed local parameter information, limiting their applicability.
• Predicting transient responses to impulsive loads in linear structural dynamics presents significant challenges.

Purpose of the Study:

• To present a new nonparametric approach for analyzing random uncertainties in dynamical systems.
• To enable prediction of transient responses in mechanical systems subjected to impulsive loads.
• To develop a probability model independent of local mechanical model parameters.

Main Methods:

• Modeling random uncertainties using a nonparametric approach.
• Employing the entropy optimization principle to deduce the probability model.
• Utilizing algebraic properties of generalized mass, damping, and stiffness matrices.
• Leveraging Monte Carlo numerical simulation for transient response computation.

Main Results:

• An explicit construction and representation of the probability model were obtained.
• The probability model is well-suited for algebraic calculus and Monte Carlo simulations.
• Analysis of the convergence properties of the stochastic solution concerning the random reduced matrix model dimension.
• Successful demonstration through a presented example.

Conclusions:

• The proposed nonparametric approach effectively models random uncertainties in dynamical systems.
• The method provides a robust framework for predicting transient responses to impulsive loads.
• The developed probability model offers computational advantages for structural dynamics analysis.