A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum mechanics.This paper uses the concept of a variational derivative and its laws of operation to investigate the ...A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum mechanics.This paper uses the concept of a variational derivative and its laws of operation to investigate the derivation of Lagrange's equation,which is then applied to nonlinear elasto-dynamics.In accordance with the work-energy principle and the energy conservation law,kinetic and potential energies are proposed for rigid-elastic coupling dynamics,whose governing equation is established by manipulating Lagrange's equation.In addition,case studies are used to demonstrate the application of the proposed method to spacecraft dynamics.展开更多
The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, the...The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, thermal-electrical change, surrounding elastic medium and the Van der Waals forces are all taken into consideration. The governing equation of buckling for CNTs subjected to thermo-electro-mechanical loadings has been established based on an elastic shell model of continuum mechanics. Reasonable simplifications are made to get the explicit expression of the critical buckling shear stress of DWCNTs, and numerical experiments are conducted for further research. It is shown that under certain electric and temperature field the critical buckling shear stress of DWCNTs only depends on the wave number of buckling modes. On the other hand, all the related impact factors have enormous influence on the critical buckling shear stress under a certain buckling mode. The critical buckling shear stress changes linearly with the axial-to-shear stress ratio, as well as the thermal and electric change. Axial compression tends to make DWCNTs unstable, while axial tension benefits the buckling stability. The critical buckling shear stress is directly proportional to the applied voltage. At room or lower temperature, the critical shear stress for infinitesimal buckling increases as the temperature change increases, while it decreases at a higher temperature. The conclusions are useful for the design of nano-structures related to the buckling stability of DWCNTs.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10272034)
文摘A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum mechanics.This paper uses the concept of a variational derivative and its laws of operation to investigate the derivation of Lagrange's equation,which is then applied to nonlinear elasto-dynamics.In accordance with the work-energy principle and the energy conservation law,kinetic and potential energies are proposed for rigid-elastic coupling dynamics,whose governing equation is established by manipulating Lagrange's equation.In addition,case studies are used to demonstrate the application of the proposed method to spacecraft dynamics.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10902040, A020602)the Specialized Research Fund for the Doctoral Program of Higher Education(New Teachers)+2 种基金the Foundation for Distinguished Young Talents in Higher Education of Guangdong(Grant No. LYM08016)the Foundation for Outstanding Doctoral Dissertation of Guangdongthe Fundamental Research Funds for the Central Universities, South China University of Technology (Grant Nos.2009ZM0238,2009ZM0280)
文摘The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, thermal-electrical change, surrounding elastic medium and the Van der Waals forces are all taken into consideration. The governing equation of buckling for CNTs subjected to thermo-electro-mechanical loadings has been established based on an elastic shell model of continuum mechanics. Reasonable simplifications are made to get the explicit expression of the critical buckling shear stress of DWCNTs, and numerical experiments are conducted for further research. It is shown that under certain electric and temperature field the critical buckling shear stress of DWCNTs only depends on the wave number of buckling modes. On the other hand, all the related impact factors have enormous influence on the critical buckling shear stress under a certain buckling mode. The critical buckling shear stress changes linearly with the axial-to-shear stress ratio, as well as the thermal and electric change. Axial compression tends to make DWCNTs unstable, while axial tension benefits the buckling stability. The critical buckling shear stress is directly proportional to the applied voltage. At room or lower temperature, the critical shear stress for infinitesimal buckling increases as the temperature change increases, while it decreases at a higher temperature. The conclusions are useful for the design of nano-structures related to the buckling stability of DWCNTs.
