应用数学和力学2026，Vol.47Issue(5)：577-588,12.DOI:10.21656/1000-0887.460067
DNA-微悬臂梁的Rayleigh-Ritz法求解
The Rayleigh-Ritz Solution for DNA-Microcantilevers
摘要
Abstract
DNA-microcantilevers hold significant potential in biosensing due to their nanomechanical proper-ties,yet the assumption regarding uniform curvature and axial strain of the neutral axis remains unverified.To address this,a functional potential energy model coupling the free energy of liquid crystalline DNA molecular layers with the composite beam deformation,was established.An innovative triangular series modal superposi-tion approach was used to characterize displacement fields,and enable the variational solution via the Rayleigh-Ritz method,and a segmented integration strategy was employed to realize the full-domain free energy compu-tation.Then the nonlinear equations governing Ritz coefficients were solved through the fixed-point iteration to yield microcantilever deformations and DNA strand spacing distributions.The results indicate that,the de-formed curvature exhibits pronounced uniformity,providing theoretical support for the uniformity assumption.Convergence analysis demonstrates that,the triangular series expansion order≥10 and the number of beam segments divided≥2 500 ensure solution accuracy for deflection and stress,effectively validating the correct-ness of the uniformity assumption within the coupled model.关键词
DNA-微悬臂梁/纳米力学/自由能/Rayleigh-RitzKey words
DNA-microcantilever/nano-mechanics/free energy/Rayleigh-Ritz分类
数理科学引用本文复制引用
刘承,何小兵,沈旭栋..DNA-微悬臂梁的Rayleigh-Ritz法求解[J].应用数学和力学,2026,47(5):577-588,12.基金项目
浙江省教育厅一般科研项目(Y202352719) （Y202352719）
