Using experimental modal analysis to validate a finite element model of a tennis racket

Abstract

A finite element (FE) model of a tennis racket was created to aid in the design and development of new rackets by allowing engineers to analyse the mechanical properties of the frames without making physical prototypes. This approach saves both time and money but only if the model is an accurate representation of the manufactured racket. The FE model, therefore, needed to be validated. This paper presents a method of dynamically validating the FE model by comparing experimental modal analysis (EMA) data measured from a manufactured racket with the mode shapes calculated by the finite element analysis software. A mechanical shaker was used to excite the racket and a scanning laser Doppler vibrometer (SLDV) measured the response of the racket in three axes of motion. The experimental setup acquired out-of-plane (normal to the plane of the stringbed) bending, torsional and string-bed mode shapes that have been reported in past literature. In addition, in-plane (parallel to the stringbed plane) bending modes were also excited and measured, which have not been reported before. Comparison of the experimental and theoretical data revealed that the natural frequencies and corresponding mode shapes correlate well between the manufactured racket and the FE model, therefore validating the model and the method used to construct the model.