Thermoelastic damping effect on in-extensional vibration of rotating thin ring

Sensitive devices such as resonant sensors and radio frequency micro-electro-mechanical system (RF-MEMS) filters etc., require high Quality factors (Q-factors) defined as the ratio of total system energy to dissipation that occurs due to various damping mechanisms. Also, thermoelastic damping is considered to be one of the most important factors to elicit energy dissipation due to the irreversible heat flow of oscillating structures in the micro scales. In this study, the Q-factor for thermoelastic damping is investigated in rotating thin rings with in-plane vibration. First, in order to obtain the temperature profile of the model, a heat conduction equation for the thermal flow across the radial direction is solved based on the bending approximation so-called in-extensional approximation of the ring. Using the temperature distribution coupled with a displacement, a governing equation of the ring model can then be derived. Eventually, an eigen-value analysis is performed to obtain the natural frequency of rotating thin rings, and the analytical and numerical values of Q-factors can then be determined by the definition. Furthermore, the effects of rotating speed, dimensions of the ring, mode numbers and ambient temperatures on the Q-factor are discussed in detail.     

Circumferential thermoelastic waves in orthotropic cylindrical curved plates without energy dissipation

In this article, the propagation of guided thermoelastic waves in the circumferential direction of orthotropic cylindrical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green-Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The coupled wave equations and heat conduction equation are solved by the Legendre orthogonal polynomial series expansion approach. The convergency of the method is discussed through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding pure elastic cylindrical plate are also shown to analyze the influence of the thermoelasticity on elastic modes. The displacement, temperature and stress distributions are shown to discuss the differences between the elastic modes and thermal modes. A thermoelastic cylindrical plate with a different ratio of radius to thickness is considered to discuss the influence of the ratio on the characteristics of circumferential thermoelastic waves.     

Geometric effects on thermoelastic damping in MEMS resonators

The effects of geometry on the energy dissipation induced by thermoelastic damping in MEMS resonators are investigated numerically using a finite element formulation. The perturbation analysis is applied to derive a linear eigenvalue equation for the exponentially decaying rate of the mechanical oscillation. The analysis also involves a Fourier method that reduces the dimensionality of the problem and considerably improves the computational efficiency. The method is first validated by comparing the two-dimensional model to the existing analytical solutions for a simply supported beam system, and then it is extended to a three-dimensional axisymmetric geometry to obtain the energy loss as a function of the geometric parameters in a silicon ring resonator. The computational results reveal that there is a peak value for the resonant frequency when the radial width of the ring varies. In addition, the quality factor (Q-factor) decreases with the radial width as a monotonic function.     

Thermoelastic vibrations in micro-/nano-scale beam resonators with voids

In this paper the closed form expressions for the transverse vibrations of a homogenous isotropic, thermoelastic thin beam with voids, based on Euler-Bernoulli theory have been derived. The effects of voids, relaxation times, thermomechanical coupling, surface conditions and beam dimensions on energy dissipation induced by thermoelastic damping in (micro-electromechanical systems) MEMS/(nano-electromechanical systems) NEMS resonators are investigated for beams under clamped and simply supported conditions. Analytical expressions for deflection, temperature change, frequency shifts and thermoelastic damping in the beam have been derived. Some numerical results with the help of MATLAB programming software in case of magnesium like material have also been presented. The computer simulated results in respect of damping factor and frequency shift have been presented graphically.     

Near-field thermoelastic imaging coupled with infrared detection

Near-field thermoelastic imaging is a simple way to investigate the thermal and coupled thermoelastic properties of materials. A few microscopes, deriving from the atomic force microscope, have been used to observe and to quantify the samples observed. But the main problem is the absolute measurement of the temperature, because surface topography and thermal expansion contributions are not easily discernible. In the proposed SThEM (scanning thermoelastic microscope), the tip is excited at the resonance frequency of the cantilever and the sample is periodically heated by the Joule effect. Thus the static contributions (drift, topography) are reduced. Moreover, a radiometric sensor, operating in the far field, has been added in order to quantify the temperature. This multi-acquisition microscope enables one to investigate small objects at the nanoscale with complementary information at the micrometric scale.     

Analysis of Frequency Spectrum of Laser-Induced Vibration of Microbeam Resonators

The vibration phenomenon during pulsed laser heating of micro-beams is investigated. The beam is made of silicon and is heated by a laser pulse with a non-Gaussian temporal profile and with an ultrashort pulse duration of 2ps, which incites vibration due to the thermoelastic damping effect. This coupled thermoelastic problem is solved using an analytical-numerical technique based on the Laplace transformation. The damping ratio and resonant frequency shift ratio of beams due to the air damping effect and the thermoelastic damping effect are also examined and discussed.     

Analysis of the coupled thermoelastic vibration for axially moving beam

The coupled thermoelstic vibration characteristics of the axially moving beam are investigated. The differential equation of motion of the axially moving beam under the thermoelastic coupling is established based to the equilibrium equation and the thermal conduction equation involving deformation term. The eigenequation is deduced and the dimensionless complex frequencies of the axially moving beam with different boundary conditions under the coupled thermoelastic case are calculated by the differential quadrature method. The curves of the real parts and imaginary parts of the first three-order dimensionless complex frequencies versus the dimensionless axially moving speed are obtained. The effects of the dimensionless coupled thermoelastic factor, the ratio of length to height, the dimensionless moving speed on the stability of the beam are analyzed.     

Thermoelastic vibrations of a semi-infinite strip

The forced vibrations of a thermoelastic strip (x₁ϵ [0, l], x₂ ⩾ 0) produced by a prescribed heating at the boundary x₂ = 0 are considered. The analysis is based on classical coupled thermoelastic theory (plane strain) and finite Fourier transforms. The solution of the problem under discussion is expressed in terms of the Lamé scalar and vector potentials.     

Thermoelastic damping in torsion microresonators with coupling effect between torsion and bending

Predicting thermoelastic damping (TED) is crucial in the design of high Q MEMS resonators. In the past, there have been few works on analytical modeling of thermoelastic damping in torsion microresonators. This could be related to the assumption of pure torsional mode for the supporting beams in the torsion devices. The pure torsional modes of rectangular supporting beams involve no local volume change, and therefore, they do not suffer any thermoelastic loss. However, the coupled motion of torsion and bending usually exists in the torsion microresonator when it is not excited by pure torque. The bending component of the coupled motion causes flexural vibrations of supporting beams which may result in significant thermoelastic damping for the microresonator. This paper presents an analytical model for thermoelastic damping in torsion microresonators with the coupling effect between torsion and bending. The theory derives a dynamic model for torsion microresonators considering the coupling effect, and approximates the thermoelastic damping by assuming the energy loss to occur only in supporting beams of flexural vibrations. The thermoelastic damping obtained by the present model is compared to the measured internal friction of single paddle oscillators. It is found that thermoelastic damping contributes significantly to internal friction for the case of the higher modes at room temperature. The present model is validated by comparing its results with the finite-element method (FEM) solutions. The effects of structural dimensions and other parameters on thermoelastic damping are investigated for the representative case of torsion microresonators.     

The thermoelastic excitation of air-solid interface waves using the pulsed laser

In the 1920s, the solid-solid interface wave, Stoneley wave, was first studied by Stoneley. From the 1930s to 1940s, the fluid-solid interface waves, usually called Scholte wave or Scholte-Stoneley wave, were studied by Cagniard and Scholte respec-tively[1]. The Scholte wave corresponds to the real root of the fluid-solid interface secu-lar equation, which is usually called the Scholte equation, and the velocity of Scholte wave is only slightly lower than the longitudinal velocity of the f…     

Suppression of thermoelastic damping in MEMS beam resonators by piezoresistivity

Microelectronic mechanical (MEM) beam resonators with high quality factors are always preferred in practical applications. As one of the damping sources, thermoelastic damping (TED) caused by irreversible heat flows is usually considered as an upper limit of the overall damping effect. A new method is proposed in this work to compensate TED by taking advantage of the piezoresistive effect. Such a method is implemented by applying an electrostatic field along the beam length with a negative piezoresistive coefficient. During a resonance, the stretched part of the beam generates a higher electrical power density and thus a higher temperature, while the compressed region leads to a lower temperature. Such a temperature distribution is opposite to the temperature change caused by the thermoelastic effect. The working principle is described by a set of coupled differential equations, which are subsequently solved by the finite element method. The result indicates that the TED in the beam resonators can be completely compensated when the strength of electrical field is tuned to a critical value, namely CEF. The value of the CEF is further analyzed by a series of parametric studies on various material properties and geometric factors.     

Analysis of thermoelastic dissipation in circular micro-plate resonators using the generalized thermoelasticity theory of dual-phase-lagging model

This study investigates the thermoelastic dissipation of micro-plate resonators by using the generalized thermoelasticity theory of dual-phase-lagging model. Explicit formulae of thermoelastic damping and frequency shift are derived. Influences of the plate thickness and vibration frequency on the thermoelastic damping are examined. Phenomena distinct from those of classical theory are observed in the numerical results of thermoelastic damping in micro-plate resonators. These results may bring new insights into the study of thermoelastic damping at submicrometer or nanometer scale.     

Giant strain-sensitivity of acoustic energy dissipation in solids containing dry and saturated cracks with wavy interfaces

Mechanisms of acoustic energy dissipation in heterogeneous solids attract much attention in view of their importance for material characterization, nondestructive testing, and geophysics. Due to the progress in measurement techniques in recent years, it has been revealed that rocks can demonstrate extremely high strain sensitivity of seismoacoustic loss. In particular, it has been found that strains of order 10(-8) produced by lunar and solar tides are capable of causing variations in the seismoacoustic decrement on the order of several percent. Some laboratory data (although obtained for higher frequencies) also indicate the presence of very high dissipative nonlinearity. Conventionally discussed dissipation mechanisms (thermoelastic loss in dry solids, Biot and squirt-type loss in fluid-saturated ones) do not suffice to interpret such data. Here the dissipation at individual cracks is revised taking into account the influence of wavy asperities of their surfaces quite typical of real cracks, which can drastically change the values of the relaxation frequencies and can result in giant strain sensitivity of the dissipation without the necessity of assuming the presence of unrealistically thin (and, therefore, unrealistically soft) cracks. In particular, these mechanisms suggest interpretation for observations of pronounced amplitude modulation of seismo-acoustic waves by tidal strains.     

Decoherence of Entangled States Calculated by a Systematic Approximate Method

In this paper the coherent-state approximation （CA） method is used to deal with the problem of the decoherence of the entangled states of two two-state systems. As the base of the discussion, the dissipation of one two-state system has been investigated at first. The improved results calculated by CA are given in the paper. It is shown that the right approaching behavior and scaling law have been obtained when CA is applied to the problem of dissipation of two two-state systems coupled with environment. The whole evolution process and calculated results of the decoherence of the entangled states show also the scaling law, right approaching behavior, and rich phenomenon.     

Thermal field simulation and heat zone optimization for the growth of 50-mm basal-plane-faceted sapphire ribbons

The global heat transfer during growth of 50-mm basal-plane-faced sapphire ribbons in a cylindrical heat zone has been numerically simulated for different heat shield configurations. The ribbon thermoelastic strains were computated to estimate the heat zone quality. It is shown that shield adjustment and redistribution of radiative heat fluxes inside the heat zone make it possible to essentially decrease the thermal field curvature in the ribbon around the crystallization front and, therefore, decrease the thermoelastic strains by a factor of 2 to 3 (to 20 MPa).     

Thermoelastic damping of the axisymmetric vibration of circular plate resonators

Thermoelastic damping is recognized as a significant loss mechanism at room temperature in micro-scale circular plate resonators. In this paper, the governing equations of coupled thermoelastic problems are established for axisymmetric out-of-plane vibration of circular plate. Then the analytical expression for thermoelastic damping is obtained. The effects of environmental temperature, plate dimensions and boundary conditions on the thermoelastic damping are studied.     

Dynamic stability of thermoelastic coupling moving plate subjected to follower force

The dynamic characteristics and stability of the moving thermoelastic coupling rectangular plate subjected to uniformly distributed tangential follower force are investigated. Based on the heat conduction equation containing the thermoelastic coupling term and the thin plate theory, the thermoelastic coupling differential equation of motion of the rectangular plate under the action of uniformly distributed tangential follower force is established. Dimensionless complex frequencies of the moving thermoelastic coupling rectangular plate with four edges simply supported, two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method. The effects of the dimensionless thermoelastic coupling factor and dimensionless moving speed on the stability and critical load of the moving plate are analyzed. The results show that the divergence loads of the first order mode increase with the increase of the dimensionless thermoelastic coupling factor, and decrease with increasing the dimensionless moving speed.     

The effect of dissipation on the resistive admittance of an elastic medium

The effect of dissipation on the real part of the admittance of an elastic half-space is typically thought to be unimportant if the loss factor ζ of the elastic medium is small. However, dissipation induces losses in the near field of the source and, provided the size of the source is small enough, this phenomenon can be more important than elastic wave radiation. Such losses give rise to a fundamental limit in the quality factor of an oscillator attached to a substrate. Near field losses associated with strains in the elastic substrate can actually be larger than intrinsic losses in the oscillator itself if the internal friction of the substrate is larger than the internal friction of the oscillator. For a uniform stress applied to a disk of radius a, a monopole source, such phenomena become significant for k(L)a<ζ, while for higher order multipole sources of order l, near field losses are important for (k(L)a)(l+1)<ζ, a far less restrictive constraint.     

Thermoelastic damping in micro-scale circular plate resonators

The governing equations of coupled thermoelastic problems are established for out-of-plane vibration of a circular plate. The analytical expression for thermoelastic damping is obtained. Then the thermoelastic damping is studied under different environmental temperature, plate dimensions and boundary conditions.     

Relaxation model of the orientational phase transition in fullerite C60

The model of thermal behavior of a thermoelastic medium is developed in the context of the Landau theory of phase transitions. In the framework of this model, two different problems are considered with allowance for order parameter relaxation: the problem of relatively slow uniform heating (cooling) of the medium under external hydrostatic pressure and the problem of order parameter relaxation at thermal isolation. A finite value of the relaxation constant τ of the order parameter is demonstrated to bring about the heating (cooling) rate dependence of the physical quantities, such as specific heat. The relaxation time of the order parameter is shown to be twice larger than the temperature relaxation time, as a consequence of the Landau expansion of the free energy.