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This paper aims to apply the novel numerical model to analyze the effect of pillar material on the response of compound quartz crystal resonator (QCR) with an array of pillars. The performance of the proposed device compared to conventional QCR method was also investigated.

A finite element method model was developed to analyze the behavior of QCR coupled with an array of pillars. The model was composed of an elastic pillar, a solution and a perfectly matched layer. The validation of the model was performed through a comparison between its predictions and previous experimental measurements. Notably, a good agreement was observed between the predicted results and the experimental data.

The effect of pillar Young’s modulus on the coupled QCR and pillars with a diameter of 20 µm, a center-to-center spacing of 40 µm and a density of 2,500 kg/m³ was investigated. The results indicate that multiple vibration modes can be obtained based on Young’s modulus. Notably, in the case of the QCR–pillar in air, the second vibration mode occurred at a critical Young’s modulus of 0.2 MPa, whereas the first mode was observed at 3.75 Mpa. The vibration phase analysis revealed phase-veering behavior at the critical Young’s modulus, which resulted in a sudden jump-and-drop frequency shift. In addition, the results show that the critical Young’s modulus is dependent on the surrounding environment of the pillar. For instance, the critical Young’s modulus for the first mode of the pillar is approximately 3.75 Mpa in air, whereas it increases to 6.5 Mpa in water.

It was concluded that the performance of coupled QCR–pillar devices significantly depends on the pillar material. Therefore, choosing pillar material at critical Young’s modulus can lead to the maximum frequency shift of coupled QCR–pillar devices. The model developed in this work helps the researchers design pillars to achieve maximum frequency shift in their measurements using coupled QCR–pillar.

The decline in the share of agriculture in both output and employment is a central feature of structural transformation. The authors present the distinct features between developed and developing countries in the process of agricultural share decline and dig into the real changes that occurred in the agricultural sector during the rapid decline in the agricultural share.

Taking the declining share of agriculture as a clue, the authors depict heterogeneous characteristics in the declining share of agriculture in developed and developing countries. Secondly, by criticizing the factor substitution hypothesis, the authors argue that the essence of agricultural transformation is the process of agricultural industrialization characterized by the combination, reconstruction, and continual changes of agricultural production factors. Finally, based on the theory of agricultural industrialization, this paper analyzes the combination of factors in different stages of declining agricultural share in typical economies.

In this paper, the authors find that the rapid decline in agricultural employment share is accompanied by an increase in the returns to agricultural production in developed economies. In contrast, the decline in agricultural employment share in developing economies lags, and agricultural production efficiency is way much poorer than that of developed economies. Taking the United States and Japan as examples, the authors find that the agricultural sector underwent agricultural industrialization, featured by reconstruction and upgrades of production factors combination.

The authors systematically reveal why huge changes occurred in the agricultural sector in developed economies during structural transformation, and also provide further thoughts and lessons for developing countries to accomplish agricultural modernization.