研究目的
To analyze the nonlinear free vibration and post-buckling of nanobeams with flexoelectric effect using Eringen’s differential model and Timoshenko beam theory, and to investigate the influence of various parameters on their dynamic response.
研究成果
The flexoelectric effect significantly influences the nonlinear free vibration and post-buckling behavior of nanobeams, reducing stiffness and natural frequencies. Increases in amplitude ratio and nonlocal parameter raise frequency ratios. Buckling occurs at specific flexoelectricity constants, providing an upper estimate for material properties. The findings are crucial for designing nano-electro-mechanical systems like energy harvesters and sensors, emphasizing the need to account for flexoelectricity in nanoscale applications.
研究不足
The study is theoretical and based on continuum mechanics models, which may not fully capture atomic-scale effects. Assumptions include neglecting certain strain gradient terms and using specific boundary conditions. The flexoelectricity constants have discrepancies between theoretical and experimental values, leading to assumptions in the model. The analysis is limited to static and free vibration responses; dynamic or forced vibrations are not considered.
1：Experimental Design and Method Selection:
The study uses Eringen’s differential model for nonlocal elasticity, Timoshenko beam theory to account for shear deformation, von-Kármán strain-displacement relation for geometric nonlinearity, electrical Gibbs free energy, and Hamilton’s principle to derive equations of motion. The multiple scales method is employed for solving the nonlinear governing equations analytically.
2：Sample Selection and Data Sources:
The nanobeam is modeled with specific boundary conditions (pinned-pinned and clamped-clamped), and material properties are based on BaTiO3, with parameters such as Young’s modulus, piezoelectric constant, dielectric constant, flexoelectric constants, and mass density obtained from literature.
3：List of Experimental Equipment and Materials:
No specific experimental equipment or materials are mentioned as the study is theoretical and computational, focusing on mathematical modeling and simulation.
4：Experimental Procedures and Operational Workflow:
The workflow involves deriving governing equations using the specified theories, applying boundary conditions, solving equations using the multiple scales method, and analyzing results for linear and nonlinear frequencies under various parameters (nonlocal parameter, amplitude ratio, input voltage, flexoelectricity constant).
5：Data Analysis Methods:
Analytical solutions are obtained, and results are compared with existing literature (e.g., Reddy and Eltaher et al.) for validation. Effects of parameters are discussed through tables and figures.
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