Effect of a Scaled Cantilever Beam on Natural Frequency

Abstract

This paper deals with the scaling factor's effect on the cantilever beam's natural frequency. Scaling a prototype dimension will make it easier to manufacture and test the dynamic characteristics of structures with enormous sizes. Natural frequency is one of the essential parameters of the vibration characteristics of the system. The phenomenon that often occurs in vibrating structures is the resonance phenomenon. Resonance is a system state in which an abnormally large vibration is generated in response to an external stimulus, happening when the frequency of the disturbance is equal to, or nearly identical to, the natural frequency of the system. This research investigates the scale factor on natural frequency using the analytical method using Euler-Bernoulli beam theory, the MSC Nastran/Patran software, and experimental testing using an impact hammer on a cantilever beam. The three methods were applied to beams with four scaling variations: 1:1, 1:2.04, 1:2.85, and 1:3.48. Based on the results, the natural frequencies increase by the size scale reduction value in the modeling. The natural frequency value in the actual structure has a value equivalent to 1/S of the natural frequency value of the scale, whereas S is defined as the downgrade scale value. This result follows the Similitude theory.