Stochastic response analysis for nonlinear vibration systems with adjustable stiffness property under random...

Area of Science:

• Mechanical Engineering
• Applied Mathematics
• Nonlinear Dynamics

Background:

• Nonlinear vibration systems with adjustable stiffness are crucial for broadband applications.
• Analyzing random responses in these systems under excitation is challenging.

Purpose of the Study:

• To propose a novel numerical method for analyzing the random responses of stochastic dynamical systems with adjustable stiffness.
• To provide an efficient and accurate tool for evaluating system behavior under Gaussian white noise excitation.

Main Methods:

• Derivation of a multi-dimensional Fokker-Plank-Kolmogorov equation based on diffusion process theory.
• Solving the equation using a splitting method to obtain stationary probability densities and mean-square responses.
• Validation through application to energy harvesting and Duffing systems with Dahl friction.

Main Results:

• The proposed splitting method accurately predicts stationary probability densities and mean-square responses.
• Effective for both monostable and bistable systems, even under strong excitation.
• Demonstrated superiority over Monte-Carlo simulations and other mainstream methods in terms of accuracy and efficiency.

Conclusions:

• The splitting method offers an efficient and robust approach for random response analysis of nonlinear vibration systems with adjustable stiffness.
• The method is suitable for higher-dimensional problems with advantages in implementation and storage.
• This procedure significantly advances the evaluation of stochastic nonlinear systems.