Free vibration response of functionally graded material （FGM） beams is studied based on the Levinson beam theory （LBT）. Equations of motion of an FGM beam are derived by directly integrating the stress-form equati...Free vibration response of functionally graded material （FGM） beams is studied based on the Levinson beam theory （LBT）. Equations of motion of an FGM beam are derived by directly integrating the stress-form equations of elasticity along the beam depth with the inertial resultant forces related to the included coupling and higherorder shear strain. Assuming harmonic response, governing equations of the free vibration of the FGM beam are reduced to a standard system of second-order ordinary differential equations associated with boundary conditions in terms of shape functions related to axial and transverse displacements and the rotational angle. By a shooting method to solve the two-point boundary value problem of the three coupled ordinary differential equations, free vibration response of thick FGM beams is obtained numerically. Particularly, for a beam with simply supported edges, the natural frequency of an FGM Levinson beam is analytically derived in terms of the natural frequency of a corresponding homogenous Euler-Bernoulli beam. As the material properties are assumed to vary through the depth according to the power-law functions, the numerical results of frequencies are presented to examine the effects of the material gradient parameter, the length-to-depth ratio, and the boundary conditions on the vibration response.展开更多
文摘5G新空口(New Radio, NR)定义了侧行链路(Sidelink, SL)模式2资源分配机制,使用户能自主选择预留资源进行数据传输,以满足基站覆盖范围外终端间直接通信的需求;随着移动通信技术的快速发展,智能终端间直接通信对于速率的要求越来越高,有限的授权频谱成为限制速率的瓶颈,使用非授权频段可以缓解授权频谱资源短缺的问题,进一步提升网络的传输速率;非授权频谱中的NR(NR in the Unlicensed Spectrum, NR-U)采用先听后说(Listen Before Talk, LBT)接入非授权信道,LBT不确定性会引起NR SL用户接入预留资源失败,带来额外的传输时延。针对上述问题,提出一种基于终端自主侦听的非授权接入方法,通过配置候选预留子信道资源,提升了模式2资源分配机制下NR SL用户采用LBT机制接入非授权信道的成功率。仿真结果表明,所提机制能有效提升NR SL系统在非授权频段的性能。
基金supported by the National Natural Science Foundation of China(No.11272278)
文摘Free vibration response of functionally graded material （FGM） beams is studied based on the Levinson beam theory （LBT）. Equations of motion of an FGM beam are derived by directly integrating the stress-form equations of elasticity along the beam depth with the inertial resultant forces related to the included coupling and higherorder shear strain. Assuming harmonic response, governing equations of the free vibration of the FGM beam are reduced to a standard system of second-order ordinary differential equations associated with boundary conditions in terms of shape functions related to axial and transverse displacements and the rotational angle. By a shooting method to solve the two-point boundary value problem of the three coupled ordinary differential equations, free vibration response of thick FGM beams is obtained numerically. Particularly, for a beam with simply supported edges, the natural frequency of an FGM Levinson beam is analytically derived in terms of the natural frequency of a corresponding homogenous Euler-Bernoulli beam. As the material properties are assumed to vary through the depth according to the power-law functions, the numerical results of frequencies are presented to examine the effects of the material gradient parameter, the length-to-depth ratio, and the boundary conditions on the vibration response.
