Response variation of Chladni patterns on vibrating elastic plate under electro-mechanical oscillation

Abstract

Fine grain particles such as sugar, sand, salt etc. form Chladni patterns on the surface of a thin plate subjected to acoustic excitation. This principle has found its relevance in many scientific and engineering applications where the displacement or response of components under the influence of vibration is vital. This study presents an alternative method of determining the modal shapes on vibrating plate in addition to other existing methods like the experimental method by Ernst Chladni. Three (3) finite element solvers namely: CATIA 2017 version, ANSYS R15.0 2017 version and HYPERMESH 2016 version were employed in the modelling process of the 0.40 mm x 0.40 mm plate and simulation of corresponding mode shapes (Chladni patterns) as well as the modal frequencies using Finite Element Method (FEM). Result of modal frequency obtained from the experimental analysis agreed with the FEM simulated, with HYPERMESH generated results being the closest to the experimental values. It was observed that the modal frequencies obtained from the FEM and experimental approach increased as the excitation time increased. ANSYS R15.0 and HYPERMESH software clearly represented the modal lines and mode shapes for each frequency which CATIA software was somewhat limited. This study has shown that FEM is an effective tool that can save time and energy invested in acoustic experiments in determining modal frequencies and patterns.

Keywords: Vibration, Chladni patterns, Modal frequency, Thin plate, Experimental analysis