In this paper, the sensing characteristics of a photonic crystal fiber (PCF) Sagnac interferometer based on flat-phase birefringence, zero-group birefringence and the Vernier effect have been studied. The temperature-sensitive liquid is filled into the air holes of the PCF. We realize flat-phase birefringence, by which the sensitivity can reach 4.9 nm/ • C and 3.5 nm/ • C. We find a new phenomenon in that there are more interference fringes appearing near the zero-group-birefringence wavelength with the environment changing. Highly sensitive sensors with −19.9 nm/ • C and 28.6 nm/ • C are obtained. We also demonstrate that two cascaded Sagnac interferometers based on PCF can realize the Vernier effect. The sensitivities are 1 nm/ • C (single Sagnac interferometer) and 10.4 nm/ • C (cascaded Sagnac interferometers), and the sensitivity is improved by more than 10 times. The sensitivity is inversely proportional to the difference between free spectral range (FSR) 1 and FSR 2 , and the highest sensitivity reaches 23.2 nm/ • C (−58 500 nm/RIU, resolution: 3.419× 10 −7 RIU) by optimizing the PCF length in Sagnac interferometer 2. The average sensitivity based on two cascaded PCF Sagnac interferometers is up to −309 957 nm/RIU and the resolution is 6.453× 10 −8 RIU as the refractive index of the analyte varies from 1.33 to 1.331, which is very competitive in the field of chemical sensing.
This paper investigates nonlinear vibration of a simply supported rectangular membrane based on large deflection theory. Dynamic stress caused by transverse displacement of the membrane is considered in modeling the membrane. The assumed mode method and the nonlinear finite element method (FEM) are both used as discretization methods for the membrane. In the assumed mode method, an approximate analytical formula of the natural frequency is derived. In the nonlinear FEM, a three-node triangular membrane element is proposed. The difference between the membrane’s dynamical characteristics obtained by these two discretization methods is revealed. Simulation results indicate that natural frequency of the membrane will rise along with the increasing of the vibration amplitude of the membrane, and the natural frequency obtained by the nonlinear FEM is larger than that obtained by the assumed mode method. When the membrane vibration is small, the assumed mode method may achieve a reasonable result, but it may lead to a big error when the membrane vibration is large.
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