On the Vibration of Thin Cylindrical Shells Under Internal Pressure

Fung, Y. C.; Sechler, E. E.; Kaplan, Ali Nadi

doi:10.2514/8.3934

Cited by 95 publications

(15 citation statements)

References 3 publications

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“…Unfortunately, these studies have been done in complicated systems where it is difficult to uncouple the effects of the vibrating structure from the pulsation of the granular material. In particular, understanding the source of measured tube wall vibration frequencies without a good numerical or theoretical model is difficult [9]. Further, a study has been conducted where the measured natural frequency of free vertical oscillation of the structure was significantly larger than the pulsation frequency, suggesting resonance did not occur [4].…”

Section: Introductionmentioning

confidence: 99%

Silo music and silo quake: granular flow-induced vibration

et al. 2004

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Acceleration and sound measurements during granular discharge from silos are used to show that silo music is a sound resonance produced by silo quake. The latter is produced by stick-slip friction between the wall and the granular material in tall narrow silos. For the discharge rates studied, the occurrence and frequency of flow pulsations are determined primarily by the surface properties of the granular material and the silo wall. The measurements show that the pulsating motion of the granular material drives the oscillatory motion of the silo and the occurrence of silo quake does not require a resonant interaction between the silo and the granular material. IntroductionThe discharge of granular materials from silos is often characterized by vibrations or pulsations of the silo, termed 'silo quake', and a loud noise, termed 'silo music' [1][2][3][4][5][6][7][8]. Both of these are undesirable as silo quake may cause structural failure and silo music is a source of noise pollution. Unfortunately, the numerous conflicting studies published in the literature [1][2][3][4][5][6][7][8] do not give the silo designer a simple model to understand the physical processes that cause the pulsations, and to guide silo design or modification that would prevent the pulsations or at least minimize their effect. The purpose of this study is to investigate the cause of the noise and the pulsations, and the interaction between the motion of the granular material and the motion of the structure.Several studies of the discharge of granular material from silos have noted fluctuations in discharge rate and the production of noise and vibration [1][2][3][4][5][6][7][8]. The top of the granular material has been observed to move in discrete steps even though the discharge from the bottom of the silo was continuous [4,6]. For smooth-walled, tall, narrow silos, pulsations occurred during both mass and mixed flow. The pulsations were observed to stop at a critical height of granular material in the silo [1,3]. Methods suggested for preventing pulsations include roughening the walls in the transition zone between the bunker and the orifice [1][2][3] and placement of inserts along the silo walls [4].In an early study, Phillips [6] observed the motion of sand in a tube, which had a glass face, and was closed at the lower end by a flat bottom having a central orifice. When the orifice was opened, the sand in the upper part of the tube moved downward intermittently in jerks. Phillips noted, "when the flow begins, a curious rattling sound is heard which changes to a distinct musical note". He also did experiments in which the tube was first partly filled with mercury and then filled with sand. Once again, the free surface of the sand descended intermittently when the mercury was allowed to flow through the orifice. He observed that the length of the column of sand increased by about 2% during the 'stick' phase. Further, the motion of the granular material caused the wall of the tube to vibrate. Thus both silo music and silo quake occur...

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Section: Introductionmentioning

confidence: 99%

Silo music and silo quake: granular flow-induced vibration

et al. 2004

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“…Considering the tiny fiber taper being used to excite the microbubble vertically, outer diameter of microbubble is far larger than that of fiber taper and the axial dimension (≈cm) of sensor is far larger than its transverse dimension (≈100 μm), and it will be a reasonable simplified model by approximating the sensor with cylindrical shell model. The breathing mode mechanical resonant frequency of the sensor can be described as [ 42–44 ]

f^{2} = \frac{1}{4 π^{2} ρ H} {\frac{E H}{R^{2}} \frac{{(π / L)}^{4}}{{[{(π / L)}^{2} + {(n / R)}^{2}]}^{2}} + D [{(π / L)}^{2} + {(n / R)}^{2}] + N_{x} {(\frac{π}{L})}^{2} + N_{φ} {(\frac{n}{R})}^{2}}

where R is the outer radius, H is the wall thickness, and L is the distance between two UV glue points. E is the Young's modulus and ρ is the mass density.…”

Section: Resultsmentioning

confidence: 99%

Ultrahigh‐Resolution Optical Fiber Thermometer Based on Microcavity Opto‐Mechanical Oscillation

Liu

Jiang

Liu

et al. 2022

Advanced Photonics Research

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High‐resolution temperature measurement is nerve‐wracking obstruction for precise characterization of many physical, chemical, and biological processes. To solve this problem, a novel microcavity–optomechanical–oscillation‐based thermometer is proposed. The microcavity serving as a link parametrically couples the mechanical resonator and optical resonator in the same structure and provides a natural and highly sensitive temperature transduction mechanism and ultrahigh‐resolution optical demodulation. The mathematical model of geometrical parameters, mechanics, and material properties for temperature response mechanism is established and verified experimentally. The proposed thermometer has a thermal sensitivity of 11 300 Hz °C−1 and an ultrahigh‐temperature resolution of 1 × 10−4 °C, to the best of one's knowledge, which is the highest temperature resolution with a silica cavity.

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“…The modal response of thin-walled tanks is particularly sensitive to variations in pressure [7]. Pressure sensitivity complicates each of the mass measurements discussed above at low tank pressures.…”

Section: Spectral Density Methodsmentioning

confidence: 99%

“…Tank wall stiffness is sensitively dependent on the ullage pressure in the tank. For thin-walled tanks at low pressure, variations in the tank pressure due to draining, filling, or pressurizing operations can have a significant effect on the modal frequencies of low-lying modes (ω k ≪ ω c ) [7]. Changes in pressure can therefore confound mass measurements as the stiffness effect on modal frequencies is counter to the effect of changes in effective mass.…”

Section: Modal Stiffnessmentioning

confidence: 99%

Modal Propellant Gauging: High-resolution and non-invasive gauging of both settled and unsettled liquids in reduced gravity

et al. 2019

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The modal response of a liquid-filled tank to external acoustic excitation can be used to infer with high resolution the mass of contained liquid, the mass flow rate of liquids into and out of the tank, and changes in tank pressure. Both contained liquid mass and internal ullage pressure affect the modal response of the tank walls through fluid mass-loading of the tank walls and pressureinduced wall stiffening, respectively. Modal Propellant Gauging refers to the technology that exploits these shifts in modal frequencies to infer the mass of propellant in a tank. MPG is a noninvasive gauging technology that has demonstrated gauging resolutions of 1% for settled propellants and 2-3% for unsettled, sloshing propellants. Extensive parabolic flight testing of the MPG system on model tanks has been conducted to validate the technology in reduced gravity. MPG testing on a qualification tank for the Orion Program's European Service Module has also been conducted and is reported here. Finite element modeling of the Orion ESM ″upper" tank is discussed and compared with measurement data. Three computational approaches to mass determination, Peak Tracking, Point Sensor, and Spectral Density methods, are described here. Use cases are defined and analyzed in the context of the Orion ESM Qualification tank data, and an implementation scheme for continuous mass gauging on the Orion ESM is discussed.

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On the Vibration of Thin Cylindrical Shells Under Internal Pressure

Cited by 95 publications

References 3 publications

Silo music and silo quake: granular flow-induced vibration

Silo music and silo quake: granular flow-induced vibration

Ultrahigh‐Resolution Optical Fiber Thermometer Based on Microcavity Opto‐Mechanical Oscillation

Modal Propellant Gauging: High-resolution and non-invasive gauging of both settled and unsettled liquids in reduced gravity

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