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.

Visualization of Chladni Patterns at Low-Frequency Resonant and Non-Resonant Flexural Modes of Vibration

“…By examining the frequency responses (see Figs. [5][6][7][8][9][10][11][12] of the plates P1-P4, the resonant and anti-resonant bending vibration modes were identified (see Tables III-VI). In order to fully identify the vibration model shown by Fig.…”

“…Sprinkled particles, such as sand, salt, and sugar grains [9], silica micro-grains [8], tea powder [7], green soybeans [6], flour, baking soda, and baby powder [10] are usually agglomerating on the plate in the regions of nil or very small amplitude of vibration. Thus, they visualize the nodal lines and produce the so-called standard Chladni patterns, which are dominated by the gravitational effects.…”

“…In fact, the resulting velocity of a particle bouncing on the surface of a vibrating plate depends on the plate velocity, the particle velocity before the impact, and the restitution coefficient of the kinetic energy after impact, which can be perceived as a viscous damping coefficient [9], [11]. Since the region for particle deposition on the plate depends on the vector of the resultant velocity, the gravitational effect might be diminished.…”

“…Concerning the mode-mixing phenomenon, although the plate is excited by a harmonic central source, there are successive backward wave reflections on the boundaries of the plate, directed towards the source, and therefore, superposing on the main central mode. As a result, a dissonant sound that irritates the ear can be perceived during the experiments [9], [18]. Due to their numerous applications in the fields of Civil, Structural, Mechanical, Aerospace, and Seismic Engineering [9], [21]- [28], Chladni patterns appearing at relatively higher resonant frequencies on centrally excited square plates have been extensively studied [4], [7], [25].…”

“…As a result, a dissonant sound that irritates the ear can be perceived during the experiments [9], [18]. Due to their numerous applications in the fields of Civil, Structural, Mechanical, Aerospace, and Seismic Engineering [9], [21]- [28], Chladni patterns appearing at relatively higher resonant frequencies on centrally excited square plates have been extensively studied [4], [7], [25]. Thus, Table I presents the dimensions, i.e., the side length L and thickness h, of various thin square plates made in aluminum, the frequency interval explored in the Chladni tests, and the values of the resonant frequencies, as reported by [4], [7], and [25].…”