A scaling method for vibrating structures using global sensitivity analysis

Scaling vibrating structures is a common engineering issue, e.g., large structures that are investigated on a laboratory scale model. Those investigations require scaling laws to scale up the laboratory model to the original structure or vice versa. Scaling laws are usually derived from a similarity analysis or from the equations of motion. Both methods are hardly applied to more complex structures, because the influence of design parameters on the structural vibrations is unknown. This paper proposes a method to derive scaling laws for vibrating structures based on a global sensitivity analysis (GSA). GSA covers the design parameter space as a whole and can predict structural vibrations depending on the effects of design parameters and the effects of interactions between design parameters. After performing GSA the scaling law is set up, and vibrations can be calculated. The method will be exemplified for a vibrating simply supported rectangular plate. The accuracy of the scaling law is analyzed by comparing it to a scaling law derived from the equations of motion. Using the effects of design parameters as well as their interactions will increase the accuracy of the scaling law. The method can be applied to more complex structures in a next step.