Journal
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
Volume 18, Issue 4, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219455418500554
Keywords
Critical buckling load; dynamic response; natural frequency; rectangular nanoplate; symplectic method
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Funding
- National Natural Science Foundation of China [11672054, 11372070]
- National Basic Research Program of China (973 Program) [2014CB046803]
- Natural Science Foundation of Liaoning Province of China [20170540186]
- Fundamental Research Funds for the Central Universities [DUT17LK57]
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In this paper, an analytical Hamiltonian-based model for the dynamic analysis of rectangular nanoplates is proposed using the Kirchhoff plate theory and Eringens nonlocal theory. In a symplectic space, the dynamic problem is reduced to solving a unified Hamiltonian dual equation formed by a total unknown vector consisting of displacements, rotation angles, bending moments and generalized shear forces. The exact solutions for free vibration, buckling and steady state forced vibration are established by the eigenvalue analysis and expansion of eigenfunction without any trial functions. In addition, the explicit expressions of the characteristic equations, mode functions and steady state response of the nanoplate with two opposite edges that are simply supported or guided supported are obtained. To verify the accuracy and reliability of the present method, numerical results are compared with published solutions and excellent agreement is obtained. Comprehensive benchmark results that consider the nonlocal effect on the dynamic behaviors of rectangular nanoplates are also presented in dimensionless tabular and graphical forms.
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