Design of a high frequency accuracy heterodyne laser source working in a wide temperature range

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℃.

A lumped mass finite element formulation with consistent nodal quadrature for improved frequency analysis of wave equations

A lumped mass finite element formulation with consistent nodal quadrature is presented for improved frequency analysis of wave equations with particular reference to the Lagrangian elements with Lobatto nodes.For the Lagrangian Lobatto elements,a lumped mass matrix can be conveniently constructed by employing the nodal quadrature rule that takes the Lobatto nodes as integration points.In the conventional finite element analysis,this nodal quadrature-based lumped mass matrix is usually accompanied by the stiffness matrix computed via the Gauss quadrature.In this work,it is shown that this combination is not optimal regarding the frequency accuracy of finite element analysis of wave equations.To elevate the frequency accuracy,in addition to the lumped mass matrix formulated by the nodal quadrature,a frequency accuracy measure is established as a function of the quadrature rule used in the stiffness matrix integration.This accuracy measure discloses that the frequency accuracy can be optimized if both lumped mass and stiffness matrices are simultaneously computed by the same nodal quadrature rule.These theoretical results are well demonstrated by two-and three-dimensional numerical examples,which clearly show that the proposed consistent nodal quadrature formulation yields much higher frequency accuracy than the conventional finite element analysis with nodal quadrature-based lumped mass and Gauss quadrature-based stiffness matrices for wave equations.

Coarse Mesh Superconvergence in Isogeometric Frequency Analysis of Mindlin–Reissner Plates with Reduced Integration and Quadratic Splines

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.