To ensure the frequency accuracy of a heterodyne laser source in the ambient temperature range of-20℃ to 40℃, a duallongitudinal-mode thermally stabilized He–Ne laser based on non-equilibrium power locking was desi...To ensure the frequency accuracy of a heterodyne laser source in the ambient temperature range of-20℃ to 40℃, a duallongitudinal-mode thermally stabilized He–Ne laser based on non-equilibrium power locking was designed. The ambient adaptive preheating temperature setting scheme ensured the laser could operate normally in the range of-20℃ to40℃. The non-equilibrium power-locked frequency stabilization scheme compensated for the frequency drift caused by different stabilization temperatures. The experimental results indicated that the frequency accuracy of the laser designed in this study could reach 5.2 × 10^(-9)in the range of-20℃ to 40℃.展开更多
A frequency accuracy study is presented for the isogeometric free vibration analysis of Mindlin–Reissner plates using reduced integration and quadratic splines,which reveals an interesting coarse mesh superconvergenc...A frequency accuracy study is presented for the isogeometric free vibration analysis of Mindlin–Reissner plates using reduced integration and quadratic splines,which reveals an interesting coarse mesh superconvergence.Firstly,the frequency error estimates for isogeometric discretization of Mindlin–Reissner plates with quadratic splines are rationally derived,where the degeneration to Timoshenko beams is discussed as well.Subsequently,in accordance with these frequency error measures,the shear locking issue corresponding to the full integration isogeometric formulation is elaborated with respect to the frequency accuracy deterioration.On the other hand,the locking-free characteristic for the isogeometric formulation with uniform reduced integration is illustrated by its superior frequency accuracy.Meanwhile,it is found that a frequency superconvergence of sixth order accuracy arises for coarse meshes when the reduced integration is employed for the isogeometric free vibration analysis of shear deformable beams and plates,in comparison with the ultimate fourth order accuracy as the meshes are progressively refined.Furthermore,the mesh size threshold for the coarse mesh superconvergence is provided as well.The proposed theoretical results are consistently proved by numerical experiments.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 52175500, 52175501, and 52061135114)。
文摘To ensure the frequency accuracy of a heterodyne laser source in the ambient temperature range of-20℃ to 40℃, a duallongitudinal-mode thermally stabilized He–Ne laser based on non-equilibrium power locking was designed. The ambient adaptive preheating temperature setting scheme ensured the laser could operate normally in the range of-20℃ to40℃. The non-equilibrium power-locked frequency stabilization scheme compensated for the frequency drift caused by different stabilization temperatures. The experimental results indicated that the frequency accuracy of the laser designed in this study could reach 5.2 × 10^(-9)in the range of-20℃ to 40℃.
基金supported by the National Natural Science Foundation of China (Grant Nos.12072302 and 11772280)the Natural Science Foundation of Fujian Province of China (Grant No.2021J02003).
文摘A frequency accuracy study is presented for the isogeometric free vibration analysis of Mindlin–Reissner plates using reduced integration and quadratic splines,which reveals an interesting coarse mesh superconvergence.Firstly,the frequency error estimates for isogeometric discretization of Mindlin–Reissner plates with quadratic splines are rationally derived,where the degeneration to Timoshenko beams is discussed as well.Subsequently,in accordance with these frequency error measures,the shear locking issue corresponding to the full integration isogeometric formulation is elaborated with respect to the frequency accuracy deterioration.On the other hand,the locking-free characteristic for the isogeometric formulation with uniform reduced integration is illustrated by its superior frequency accuracy.Meanwhile,it is found that a frequency superconvergence of sixth order accuracy arises for coarse meshes when the reduced integration is employed for the isogeometric free vibration analysis of shear deformable beams and plates,in comparison with the ultimate fourth order accuracy as the meshes are progressively refined.Furthermore,the mesh size threshold for the coarse mesh superconvergence is provided as well.The proposed theoretical results are consistently proved by numerical experiments.
基金supported by the National Natural Science Foundation of China(Grant Nos.12072302 and 11772280)the Natural Science Foundation of Fujian Province of China(Grant No.2021J02003)the Natural Science Foundation of Hebei Province of China(Grant No.A2018209319).
