When vibrating while immersed in a liquid, the vibration frequency of the tuning fork decreases as its depth in the liquid increases. When the depth of the tuning fork in the liquid is fixed, the vibration selleck chemical frequency also decreases as the liquid density increases. The relation between liquid density �ѡ� and vibration cycle of the tuning fork T is as indicated by Equation (5). As long as the vibration cycle of the resonant component in the liquid is measured, the density of the liquid under test can be calculated, thus enabling on-line density measurements of liquids in real-time.2.2.3. Resonant Frequency Dependence on TemperatureTemperature affects its performance if there are gradients around the sensor. The impact of temperature on the natural frequency is mainly due to the impact on the elastic modulus of the material.
The relation between interaction potential energy U(r) and their distance r of two atoms for various types of crystals can be written as:U(r)=?Arn+Brm(6)where A, B, n and m are constants which are greater than zero. The first item is the attractive energy, and the second is the repulsive energy [11]. Now we choose a simple cubic crystal as model to calculate the relation between E and T, set the crystal under tension along the axis, so when the tension changes by df, the atomic spacing r changes by dr, then the cross-sectional area r2 of unit cell is unchanged. Therefore, the elastic modulus of crystal is:E=dfr2drr=dfrdr(7)where dfr2 and drr are the stress and strain, respectively.
The binding force f of the crystal only relates to the first item of Equation (6), and its size is given by:f(r)=dU(r)dr=nArn+1(8)Differentiating Equation (8) wi
Fiber Bragg gratings (FBGs) are receiving much attention for fiber sensor applications due to their small size, absolute measurement capability, immunity to electromagnetic interference, wavelength multiplexing, and distributed sensing possibilities. Since they are readily made by controlling the period, length, amplitude, apodization, and chirp of a fiber grating, FBGs have been extensively studied as optical fiber sensors for measuring temperature [1], strain [2], pressure [3], acceleration [4], torsion [5], flow [6], etc. FBG sensors offer high sensitivity, real-time processing, and long-term stability, as well as other important advantages.However, due to the thermo-optic coefficient AV-951 of silica and its thermal expansion nevertheless coefficient, FBG sensors have a temperature-dependent Bragg wavelength shift of 13.