研究目的
Investigating the free vibration of variable cross-section single-layered graphene nano-ribbons (SLGNRs) using the Differential Quadrature Method (DQM) in conjunction with Euler–Bernoulli beam theory and Eringen's nonlocal elasticity theory.
研究成果
The study successfully applies the Differential Quadrature Method (DQM) to analyze the free vibration of variable cross-section single-layered graphene nano-ribbons (SLGNRs). It demonstrates the effects of nonlocal parameter, non-uniform parameter, aspect ratio, and boundary conditions on the frequency parameters. The findings show that the method is efficient and provides results that agree well with known solutions in special cases.
研究不足
The study is limited to theoretical and numerical analysis without experimental validation. The effects of other potential variables or environmental conditions on the vibration characteristics of SLGNRs are not explored.
1：Experimental Design and Method Selection:
The study employs the Differential Quadrature Method (DQM) for analyzing the free vibration of SLGNRs. Euler–Bernoulli beam theory and Eringen's nonlocal elasticity theory are used as theoretical models.
2：Sample Selection and Data Sources:
The study focuses on SLGNRs with exponentially varying cross-section width along their length.
3：List of Experimental Equipment and Materials:
MATLAB is used for numerical computations. No physical equipment is mentioned.
4：Experimental Procedures and Operational Workflow:
The methodology involves developing a MATLAB code to solve the generalized eigenvalue problem derived from the governing differential equation of motion for SLGNRs under various boundary conditions.
5：Data Analysis Methods:
The results are analyzed to study the effects of nonlocal parameter, non-uniform parameter, aspect ratio, and boundary conditions on the frequency parameters of SLGNRs.
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