Abstract
Point-driven modern Chladni figures subject to the symmetry breaking are systematically unveiled by developing a theoretical model and making experimental confirmation in the orthotropic brass. The plates with square shape are employed in the exploration based on the property that the orientation-dependent elastic anisotropy can be controlled by cutting the sides with a rotation angle with respect to the characteristic axes of the brass. Experimental results reveal that the orientation symmetry breaking not only causes the redistribution of resonant frequencies but also induces more resonant modes. More intriguingly, the driving position in some of new resonant modes can turn into the nodal point, whereas this position is always the anti-node in the isotropic case. The theoretical model is analytically developed by including a dimensionless parameter to consider the orientation symmetry-breaking effect in a generalized way. It is numerically verified that all experimental resonant frequencies and Chladni patterns can be well reconstructed with the developed model. The good agreement between theoretical calculations and experimental observations confirms the feasibility of using the developed model to analyze the modern Chladni experiment with orientation symmetry breaking. The developed model is believed to offer a powerful tool to build important database of plate resonant modes for the applications of controlling collective motions of micro objects.
Highlights
Chladni sound figures of vibrating plates which greatly impressed Napoleon in 18th century[1] have inspired many essential research in modern physics such as quantum chaos[2], self-organization of granular media[3,4], microscale acoustofluidics[5,6], and pattern formation[7,8]
It has been confirmed that the resonant spectra reveal explicit redistribution and occurrence of new resonant modes under the orientation symmetry breaking effect which leads the degenerate level splitting of the orthotropic plates
The driving position in some new resonant modes has been found to turn into a nodal point, whereas this position is always an antinode in the isotropic plates
Summary
Chladni sound figures of vibrating plates which greatly impressed Napoleon in 18th century[1] have inspired many essential research in modern physics such as quantum chaos[2], self-organization of granular media[3,4], microscale acoustofluidics[5,6], and pattern formation[7,8]. Since the elastic anisotropy ubiquitously exists in materials such as copper, brass, silicon, sapphire, etc., which are commonly used in industry and semiconductor engineering, developing a general model to analyze modern Chladni figures for systems with broken orientation symmetry is greatly important to improve accuracy of actuating devices for micro-particles. Point-driven modern Chladni system subject to orientation symmetry breaking is thoroughly explored by developing a generalized model and making experimental confirmation in the orthotropic brass plates. By including a dimensionless parameter to consider the orientation symmetry-breaking effect in a generalized way, a theoretical model is analytically developed to reconstruct all experimental observations. The good agreement between theoretical calculations and experimental results confirms the feasibility of using the developed model to efficiently analyze the vibrating modes and to effectively determine some critical elastic parameters of the anisotropic plates to greatly benefit various applications in practice
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