Differential Quadrature Element Method for Free Vibration of Strain Gradient Beams with Elastic Boundary Conditions
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Numerous literatures on the vibrational analysis of structures based on the strain gradient elasticity theory (SGET) are only restricted to classic boundary conditions. However, the boundary conditions of structures in the engineering are different from those classic cases in nature. The purpose of this work is to develop a strong form differential quadrature element method (DQEM) to study the vibration of the strain gradient beams (SGB) with elastic boundary conditions.
Vibration of gradient elastic materials with elastic boundary conditions is studied by an SGB model. This model is characterized by a sixth-order differential equation (SODE). A strong-form DQEM is developed to calculate six-order boundary-value problems. Excellent accuracy, simplicity, and high computational efficiency of the DQEM have been demonstrated by comparing with exact solution and available results.
Results and conclusions
Numerical results verify the good reliability and accuracy of the DQEM. Numerical results show that the nonlocal effect parameter, boundary spring Stiffness, and high-order boundary conditions have important influence on the vibrational behaviors of the SGBs.
KeywordsStrain gradient beam Differential quadrature element method Vibration Elastic boundary conditions
This work was supported in part by the National Natural Science Foundation of China under Grants 11522217 and 11632003, and in part by the Fundamental Research Funds for the Central Universities of China.