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This work is focused on the topology optimization of structures that are subjected to harmonic force excitation with prescribed frequency and amplitude. As an important objective of such a design problem, the natural resonance frequency of the structure is driven far away from the prescribed excitation frequency for the purpose of avoiding resonance and reducing the vibration level. Therefore when the excitation frequency is higher than the natural resonance frequency of the structure, the natural resonance frequency will decrease, then the optimum topology configuration will be distorted with large amount of gray elements. A MAC (Modal Assurance Criteria) based excitation frequency increasing method is proposed to obtain a desired configuration. MAC is adopted here to track the natural resonance frequency which can provide the baseline reference for the current excitation frequency during the optimum iterative procedure. Then the excitation frequency increases progressively up to its originally prescribed value. By means of numerical examples, the proposed formulation can generate effective topology configurations which can avoid resonance.

Using low nitrogen (N)–tolerant maize varieties serves as a viable means to curtail N fertilizer application while improving crop yield. To investigate the differences in carbon and nitrogen metabolic processes, and the hormones within kernels located at varying positions along the ear, between low N–tolerant and low N–sensitive maize varieties. Furthermore, this research aims to elucidate the ramifications of these observed disparities on kernel weight and yield, particularly when cultivated under low N conditions. The low N–tolerant maize variety (ZH311) and low N–sensitive maize variety (XY508) were applied. The in–situ filed experiment with three N fertilizer treatments of 0 N (0 kg·N ha−1), 150 N (150 kg·N ha−1) and 300 N (300 kg·N ha−1) was conducted in 2017–2019. The apical kernel weight of ZH311 was less affected by low N (0 N and 150 N) and the yield was 25.3–22.9% higher than XY508. The kernel weight was significantly and positively correlated with kernel starch and protein content. The starch and protein contents of ZH311 apical kernels were 6.3–7.3% and 12.4–14.4%, higher than XY508 under low N. It was indicated that the main factor affecting starch accumulation in the apical kernels was Susy activity and protein accumulation was IAA/GA 3 , Z+ZR/GA 3 and GOGAT activity by the redundancy analysis. Under low N, the Susy and GOGAT activity, IAA/GA 3 and Z+ZR/GA 3 in the apical kernel of ZH311 were higher than XY508 by 51.4–39.3% and 65.4–46.9%, 62.1–33.1% and 41.8–48.2%. We have demonstrated to improve the maize yield by increasing the apical kernel weight, which resulted in enhancing the uniformity of the kernel weight along the ear. Under low N conditions, the low N–tolerant maize variety was shown to facilitate the starch and protein biosynthesis by increasing the activity of key enzymes in the carbon and the nitrogen metabolism processes such as Susy and GOGAT in the apical kernels, and optimizing the hormone balance between IAA/GA 3 and Z+ZR/GA 3 , to increase the kernel weight and yield. The findings of this investigation will help understand the underlying factors contributing to the yield variations exhibited among distinct low N–tolerant maize varieties when cultivated under conditions of limited N availability. These insights could serve as the theoretical basis for breeding of low N–tolerant maize varieties and practical guidance for the formulation of N fertilizer management strategies. [Display omitted] • Apical kernel weight and grain yield of ZH311 were less affected by low N stress. • Apical kernels of ZH311 had more starch and protein content under low N conditions. • Higher Susy activity promoted starch formation in the apical kernels of ZH311. • Optimized hormone balance and GOGAT activity in the apical kernels of ZH311 promoted protein synthesis. [ABSTRACT FROM AUTHOR]