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Piezoelectric quasi-crystal materials possess excellent piezoelectric and phonon-phason coupling effects, ensuring their promising applications in piezoelectric devices, such as sensors and transducers. The performance of piezoelectric devices is closely related to the vibration characteristics. Therefore, the free vibration characteristics of one-dimensional hexagonal piezoelectric quasi-crystal discs are investigated. First, the dynamic equations of one-dimensional hexagonal piezoelectric quasi-crystal discs are derived in the context of three-dimensional phonon-phason-electro-elastic multifield couplings. The traction-free and short-circuit boundary conditions at the upper and bottom surfaces are incorporated into the constitutive equations by introducing the rectangular window function. The double Legendre orthogonal polynomial method is employed to obtain the solutions. To improve the computational efficiency, the analytical expressions of numerical integrations are derived. The influence of the diameter-height ratio and phonon-phason coupling effect on the resonance frequency is then analyzed. Subsequently, based on the finite element method, a simulation program for the free vibration characteristics of one-dimensional hexagonal piezoelectric quasi-crystal discs is developed for the first time to verify the theoretical calculation results. The partial differential equation (PDE) module in the COMSOL software is utilized to conduct the simulation. It is found that, compared with the traditional double orthogonal polynomial method, the analytical double orthogonal polynomial method significantly improves the computational efficiency, with an improvement rate of up to 99%. Changing the diameter-to-height ratio significantly influences the normalized frequency of the phason modes, and the higher-order modes are more sensitive to the change of the diameter-to-height ratio. The normalized frequencies of phonon modes and phason modes increase with the diameter-to-height ratio (D/H). The increase of phonon-phason coupling coefficients leads to a decrease in the normalized frequencies of phonon modes and phason modes, and its influence on the phason modes is more significant. The obtained results lay a basis for designing and optimizing the piezoelectric quasi-crystal sensors and transducers with excellent performance.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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