Thermoelastic Damping in Axially Stressed Beam

2008 ◽  
Author(s):  
Sandeep Kumar ◽  
Amanul Haque
Keyword(s):  
Axial Stress ◽  
Approximate Expression ◽  
Exact Expression ◽  
Q Factor ◽  
Thermoelastic Damping ◽  
General Behavior ◽  
Limiting Case

Zener’s approximate expression for thermoelastic damping was first known attempt to quantify the thermoelastic damping. Recently, an exact expression of thermoelastic damping for thin unstressed beams, which is widely used, is arrived at. Further, it has been experimentally verified that application of tensile axial stress results in increase in the Q-factor. Since the existing expressions do not take into account the effect of axial stress thermoelastic-damping expression is revised in order to accommodate the effect of axial stress on Q-factor. This expression explains the general behavior observed in experiments. In limiting case of unstressed beam, this new expression converges to current expression for thermoelastic damping.

scholarly journals A Study on the Trimming Effects on the Quality Factor of Micro-Shell Resonators Vibrating in Wineglass Modes

Micromachines ◽  
2019 ◽  
Vol 10 (10) ◽  
pp. 695
Author(s):  
Lu ◽  
Xi ◽  
Xiao ◽  
Shi ◽  
Zhuo ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Quality Factor ◽  
Second Harmonic ◽  
Great Influence ◽  
Fem Simulation ◽  
Q Factor ◽  
Thermoelastic Damping ◽  
Frequency Trimming ◽  
Quality Factor Q ◽  
Anchor Loss

Frequency trimming based on mass and stiffness modification is an important post-fabrication process for micro-shell resonators (MSRs). However, the trimming effects on the quality factor are seldom studied, although they may have great influence on the performance of the resonator. This paper presents a study on the quality factor (Q-factor) variation of trimmed micro-shell resonators (MSR). Thermoelastic damping (QTED) and anchor loss (Qanchor) are found to be the dominant energy loss mechanisms resulting in the reduction of the overall Q-factor, according to finite element method (FEM). The effects of different trimming methods on QTED and Qanchor are studied here, respectively. It is found that trimming grooves ablated in the rim of the resonator can cause a ~1–10% reduction of QTED, and the length of trimming groove is positively related to the reduction of QTED. The reduction of QTED caused by the mass adding process is mainly related to the thermal expansion coefficient and density of the additive and contact area between the resonator and additive masses. Besides, the first and second harmonic errors caused by asymmetrical trimming can cause a 10–90% reduction of Qanchor. Finally, trimming experiments were conducted on different resonators and the results were compared with FEM simulation. The work presented in this paper could help to optimize the trimming process of MSRs.

An Efficient Method for Simulating Frequency-Dependent Friction in Transient Liquid Flow

1975 ◽  
Vol 97 (1) ◽  
pp. 97-105 ◽  
Author(s):  
A. K. Trikha
Keyword(s):  
Liquid Flow ◽  
Method Of Characteristics ◽  
Computation Time ◽  
Approximate Expression ◽  
Test System ◽  
Exact Expression ◽  
Frequency Dependent ◽  
Efficient Procedure ◽  
Liquid Line ◽  
Frequency Domains

An efficient procedure is developed for simulating frequency-dependent friction in transient laminar liquid flow by the method of characteristics. The procedure consists of determining an approximate expression for frequency-dependent friction such that the use of this expression requires much less computer storage or computation time than the use of the exact expression. The derived expression for frequency-dependent friction approximates the exact expression very well in both time and frequency domains. Calculated results for a test system are compared with the experimental results so show that the approximate expression predicts accurately the surge pressures, pressure wave distortion as well as pressure attenuation in a liquid line.

scholarly journals The effect of thermoelastic damping on the total Q-factor of stateof-the-art MEMS gyroscopes with complex beam-like suspensions

2010 ◽  
Vol 5 ◽  
pp. 1296-1299 ◽  
Author(s):  
T. Künzig ◽  
M. Niessner ◽  
G. Wachutka ◽  
G. Schrag ◽  
H. Hammer
Keyword(s):  
Q Factor ◽  
Thermoelastic Damping ◽  
Mems Gyroscopes

ELASTIC WAVES ALONG A CYLINDRICAL BORE

Geophysics ◽  
1962 ◽  
Vol 27 (3) ◽  
pp. 327-333 ◽  
Author(s):  
J. E. White
Keyword(s):  
Elastic Waves ◽  
Low Frequency ◽  
Elastic Solid ◽  
Approximate Expression ◽  
Compressional Wave ◽  
Axially Symmetric ◽  
Low Frequencies ◽  
Phase Velocities ◽  
Pierre Shale ◽  
Limiting Case

This paper concerns axially symmetric solutions for waves propagating along a cylinder in an infinite elastic solid. Solutions are presented describing unattenuated propagation along the axis at phase velocities higher than shear and compressional speeds in the solid, in contradiction to earlier publications. Special attention is given to the limiting case of phase velocity equal to compressional speed in the solid, which at low frequencies very closely approximates the coupling of a fluid‐filled borehole to a plane compressional wave in the surrounding solid. Comparison with some experiments in a uniform section of Pierre shale show excellent agreement at low frequencies. In the low‐frequency limit, these solutions reduce to an approximate expression for borehole coupling published earlier by the author.

Transverse bending of infinite and semi-infinite thin elastic plates. III

1958 ◽  
Vol 54 (2) ◽  
pp. 288-299 ◽  
Author(s):  
W. A. Bassali ◽  
M. Nassif ◽  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Isotropic Plate ◽  
Plate Theory ◽  
Outer Boundary ◽  
Exact Expression ◽  
Transverse Displacement ◽  
Elastic Plates ◽  
Classical Plate Theory ◽  
Transverse Bending ◽  
Elastically Restrained ◽  
Limiting Case

ABSTRACTWithin the restrictions of the classical plate theory, complex variable methods are used in this paper to develop an exact expression for the transverse displacement of an infinitely large isotropic plate having a free outer boundary and elastically restrained at an inner circular boundary, the plate being subjected to a general type of loading distributed over the area of a circle. The limiting case of a half-plane clamped along the straight edge and acted upon normally by the same loading is also considered.

Some Properties of large-amplitude electrostatic waves (Allis modes)

1973 ◽  
Vol 9 (1) ◽  
pp. 117-130 ◽  
Author(s):  
W. W. Neel ◽  
R. W. Flynn
Keyword(s):  
Large Amplitude ◽  
Electron Distribution ◽  
Maximum Amplitude ◽  
Approximate Expression ◽  
Plasma Waves ◽  
Electrostatic Waves ◽  
Solitary Pulse ◽  
Limiting Case ◽  
Trapped Electron ◽  
Electrostatic Plasma Waves

Allis modes are large-ampliturde, undamped electrostatic plasma waves, in which the trapped electron distribution is the analytic continuation of the untrapped distribution. Allis modes can be pulse-like, as well as periodic. As the amplitude of the periodic solutions increases, the frequency decrsases and the wavelength increases, leading finally to solitary pulse solutions as a limiting case, reached when an appreciable number of electrons are trapped by the wave. These pluse-like solutions imply a maximum amplitude to Allis modes, and a maximum d.c. current they can drive. A simple approximate expression gives the non-linear properties of Allis modes in terms of the linear properties and the maximum amplitude.

Thermoelastic Damping Based Design, Sensitivity Study and Demonstration of a Functional Hybrid Gyroscope Resonator for High Quality Factor

2021 ◽  
Vol 29 (1) ◽  
pp. 70-96
Author(s):  
N.G. Sharma ◽  
◽  
Sundararajan T. ◽  
G.S. Singh ◽  
◽  
...  
Keyword(s):  
Thin Film ◽  
Quality Factor ◽  
Sensitivity Study ◽  
Fused Silica ◽  
High Quality Factor ◽  
Q Factor ◽  
Thermoelastic Damping ◽  
High Quality ◽  
Field Problem ◽  
Macro Scale

The most critical element of Hemispherical Resonator Gyroscope (HRG) is the high quality factor (Q-factor) mechanical resonator. This paper discusses the role of thermoelastic damping (TED) on effective Q-factor. Finite element method (FEM) is used to solve this highly coupled field problem involving vibration, solid mechanics, heat transfer and thermodynamics. The major contribution of this paper is the sensitivity analysis of the effect of material property, operating temperature and dimensions to arrive at macro scale resonator configuration. Hybrid hemispherical-cylindrical configuration is proposed by studying the performance parameters such as effective mass and angular gain.The uniqueness of the present work is the sensitivity study of ultra thin film coating (volume fraction of 0.01%), coating variations and different coating configurations. The coating can reduce the Q-factor by a few orders compared to uncoated shell. It has been found that coating material selection and coating configuration are very important factors. Another significance of the present work is the realization and detailed characterization of the hybrid fused silica resonator. Thin film gold coating is done on the 3D surfaces of the realized precision resonator. Detailed coating characterization is carried out using sophisticated instruments. Very fine balancing to the order of a few mHz is achieved after coating. Q-factor measurement of the coated resonator is carried out using LDV and achieved a few millions in the final functional hybrid resonator.

Two-Temperature Thermoelastic Damping of a Gold Nano-Beam Resonator with Variable Young's Modulus

2019 ◽  
Vol 24 (3) ◽  
pp. 540-545 ◽  
Author(s):  
Hamdy M. Youssef ◽  
Alaa A. El-Bary
Keyword(s):  
Young’S Modulus ◽  
Room Temperature ◽  
Young's Modulus ◽  
Time Parameter ◽  
Q Factor ◽  
Beam Length ◽  
Thermoelastic Damping ◽  
Beam Resonator ◽  
Temperature Parameter ◽  
Two Temperature

This paper deals with the thermoelastic damping (Q-factor) of a gold nano-beam resonator and is based on twotemperature thermoelasticity models. An explicit formula of the Q-factor has been derived when Young’s modulus is variable as a function of the room temperature. The length of the beam and Young’s modulus has been studied with comparison being made between the Biot model and the Lord-Shulman model (L-S). The numerical results show that the values of beam length, the relaxation time parameter, and the two-temperature parameter have a strong influence on the thermoelastic damping quality factor.

Effect of Geometric and Material Properties on Thermoelastic Damping (TED) of 3D Hemispherical Inertial Resonator

2016 ◽  
Author(s):  
Jiewen Liu ◽  
Joshua Jaekel ◽  
Dharamdeo Ramdani ◽  
Nabeel Khan ◽  
David S.-K. Ting ◽  
...  
Keyword(s):  
Material Properties ◽  
Design Parameters ◽  
Q Factor ◽  
Thermoelastic Damping ◽  
High Quality ◽  
Hemispherical Shell ◽  
Edge Defects ◽  
Wine Glass ◽  
Quality Factor Q ◽  
Crucial Parameter

High quality factor (Q-factor) is a crucial parameter for the development of precision inertial resonators. Q-factor indicates efficiency of a resonator in retaining its energy during oscillations. This paper explores the effects of different design parameters on Q-factor of a 3D hemispherical (wine-glass) inertial resonator. Thermo-elastic damping (TED) loss mechanisms in a 3D non-inverted wine-glass (hemispherical) shell resonator is systematically investigated and presented in this paper. We investigated TED loss resulting from the effects of hemisphere geometric parameters (such as thickness, height, and radius), mass imbalance, thickness non-uniformity, and edge defects. We used glassblowing to fabricate hemispherical 3D shell resonators. The results presented in this paper can facilitate selecting efficient geometric and material properties for achieving desired Q-factor in 3D inertial resonators. Enhancing the Q-factor in MEMS based 3D resonators can further enable the development of high precision resonators and gyroscopes.

Vibratory Penetration of Soils

1967 ◽  
Vol 89 (4) ◽  
pp. 759-765 ◽  
Author(s):  
M. Senator
Keyword(s):  
Coulomb Friction ◽  
Approximate Expression ◽  
Analog Computer ◽  
Approximate Theory ◽  
Harmonic Force ◽  
Force Amplitude ◽  
Limiting Case ◽  
Important Design ◽  
Small Excess ◽  
Good Agreement

An approximate expression is found for the penetration rate of a flexible penetrator, modeled as two masses joined by an elastic member with damping, with applied bias and harmonic forces. Modified Coulomb friction is used to characterize soil resistance. The approximate theory is compared with analog computer measurements and with an exact theory (developed for the limiting case of zero front mass and internal damping) and is found to give good agreement in lite range of small excess harmonic force amplitude. A comparison with a rigid penetrator is also made, and the flexible penetrator is shown to have the important design advantage of smaller weight or smaller applied harmonic force for equal penetration rates.

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