Response probability distribution of built-up vibro-acoustic systems

Area of Science:

• Mechanical Engineering
• Acoustics
• Structural Dynamics

Background:

• Built-up structures combine stiff and flexible components, making their vibro-acoustic response sensitive to imperfections.
• Existing models often struggle to accurately capture the uncertainty associated with flexible components.

Purpose of the Study:

• To develop a novel method for analyzing the vibro-acoustic response of built-up structures with uncertain flexible components.
• To model the uncertainty using a nonparametric stochastic approach for high modal density subsystems.
• To compute the response probability density function for improved prediction.

Main Methods:

• Modeling the low modal density master system as deterministic.
• Representing high modal density subsystems stochastically via a diffuse wave field.
• Calculating the response probability density function and subsystem energies.
• Utilizing singular noncentral complex Wishart distribution for mean squared response amplitude.

Main Results:

• The master system's mean squared response amplitude follows a singular noncentral complex Wishart distribution.
• Subsystem energies approximately follow a chi-square distribution under specific variance conditions.
• For single degree of freedom systems, response distributions are chi-square or exponential.

Conclusions:

• The proposed stochastic modeling approach effectively captures vibro-acoustic response uncertainty in built-up structures.
• The method provides accurate predictions, validated against Monte Carlo simulations on plate structures.
• This work offers a robust framework for analyzing complex systems with inherent uncertainties.