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Sampling and Reconstruction of Functions—Part II
Published in Eleanor Chu, Discrete and Continuous Fourier Transforms, 2008
The Fourier transform may be expressed as a function of the angular frequency ω instead of the the rotational frequency f. Noting that because ω = 2πf, we have f = ω/2π, df = (1/2π) dω, and we modify the two de ning integrals by changing the variable as shown below. X(f)=∫−∞∞x(t)e−j2πftdt=∫−∞∞x(t)e−jωtdt=X˜(ω).
Measurement Systems: Sensors and Transducers
Published in Patrick F. Dunn, Michael P. Davis, Measurement and Data Analysis for Engineering and Science, 2017
Patrick F. Dunn, Michael P. Davis
A turbine flowmeter has a rotor placed inside the flow. Its rotational frequency typically is sensed by an inductive pickup sensor that operates as a reluctance tachometer. For this flowmeter, the volumetric flow rate equals the product of a device-specific constant, Ct, and the rotational frequency, ωr. Thus, the input/output relation for the turbine flowmeter is () Q=Ctωr,
Sensors in Engineering and Science
Published in Patrick F. Dunn, Fundamentals of Sensors for Engineering and Science, 2019
A turbine flowmeter has a rotor placed inside the flow. Its rotational frequency typically is sensed by an inductive pickup sensor that operates as a reluctance tachometer, as described before. For this flowmeter, the volumetric flow rate equals the product of a device-specific constant and the rotational frequency.
Transmission phenomenon at the interface between isotropic and semiconductor nanostructure based on nonlocal theory
Published in Waves in Random and Complex Media, 2021
Hashmat Ali, Aftab Khan, Adnan Jahangir
Since the upper and lower mediums are rotating with uniform angular frequency , therefore, the waves propagating through the media may be affected by the rotational frequency. Figure 3(a,h) indicates the variations in reflection/ transmission coefficients versus angle of incidence for different values of rotational frequency. These observations are made at a constant value of the nonlocal parameter, i.e. which physically means that the nonlocal stresses are acting upon the medium at some fixed nonlocal point 0.03 nm located from the local point. (a)–(g) Effect of rotation on the reflection/transmission coefficients in nonlocal media.
An efficient dimensionality-independent algorithm for failure probability-based global sensitivity analysis by dual-stage adaptive kriging model
Published in Engineering Optimization, 2021
Wanying Yun, Zhenzhou Lu, Xian Jiang, Pengfei He
The turbine disc shown in Figure 6 is a key component in aeroengine rotating structures which endures the centrifugal force and thermal stress in the processes of starting and accelerating. Combined with its complex shape, stress concentrations may appear in the pin hole and at the bottom of the tongue-and-groove during the process of work. After working for a period of time, cracks may appear at these positions. The load applied on the aeroengine turbine disc is where , , and are the mass density, coefficient, rotational speed and cross-sectional moment of inertia, respectively. , where is the rotational frequency. Considering the safety and applicability, the limit state function is established as follows: where is the ultimate strength and is the cross-sectional area. All random input variables , , , , and are assumed as independent variables, with the distribution types and parameters listed in Table 6.
Study on bearing force of marine propeller induced by longitudinal vibration of propulsion-shafting*
Published in Ships and Offshore Structures, 2020
Donglin Zou, Fangrui Lv, Na Ta, Zhushi Rao
Meanwhile, it can be seen that the frequency of the transverse and vertical forces on each blade is twice the vibration frequency. This is because these forces are modulated by rotational frequency (the modulated frequency is equal to the sum or the subtraction of the rotational frequency and the vibration frequency). In this example, the rotational frequency of the shaft is the same as the vibration frequency, so the modulated frequency of the transverse and vertical forces is twice of the vibration frequency, and a static component is also produced as shown in Figures 13 and 14.