Figure - available from: AIP Advances
This content is subject to copyright. Terms and conditions apply.
Variation in thermoelastic damping energy Q⁻¹ with thickness (h) for a clamped–clamped diamond circular microplate resonator with axisymmetric and non-axisymmetric vibrations; R/h = 40, 50, and 60, T0 = 298 K; mode (k, l) with k = 1 and l = 1.
Source publication
Thermoelastic damping effects are very important intrinsic losses in microelectromechanical system/nanoelectromechanical system based sensors and filters, which limit the maximum achievable quality factor. Thermoelasticity arises due to coupling between the temperature field and elastic field of the material and its interaction within the material...
Similar publications
The traditional approximation neglects the cosine components of the Coriolis acceleration, and this approximation has been widely used in the study of geophysical phenomena. However, the justification of the traditional approximation is questionable under a few circumstances. In particular, dynamics with substantial vertical velocities or geophysic...
![Influence of ϵ\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/389316784/figure/fig2/AS:11431281316811315@1742266750444/Influence-of-edocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
![Effect of reference temperature T0\documentclass[12pt]{minimal}...](publication/389316784/figure/fig4/AS:11431281316750806@1742266750756/Effect-of-reference-temperature-T0documentclass12ptminimal-usepackageamsmath_Q320.jpg)
In this article, an analytical approach to characterize the breathing mode vibration for thermoelastic nanosphere using the coupled thermoelastic theory is developed. In other words, the inclusion of the temperature field takes into account the concept of heat wave and the energy equation of heat conduction is combined with the elastic theory. The...
In this work, nonlocal strain gradient integral model is applied to investigate the free damping vibration analysis of functionally graded (FG) visco-elastic Timoshenko microbeam with immovable boundary conditions in thermal environment. The microbeam is assumed to be viscoelastic and modeled by Kelvin-Voigt model. The differential governing equati...
This research addresses the phenomena of thermoelastic damping (TED) and frequency shift (FS) of a thin flexible piezoelectro-magneto-thermoelastic (PEMT) composite beam. Its motion is constrained by two linear flexible springs attached to both ends. The novelty behind the proposed study is to mimic the uncertainties during the fabrication of the b...
![Period-doubling bifurcation of Ψ\documentclass[12pt]{minimal}...](publication/369380736/figure/fig1/AS:11431281155692595@1683252605468/Period-doubling-bifurcation-of-PSdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![The profiles of wx\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/369380736/figure/fig2/AS:11431281155674795@1683252605613/The-profiles-of-wxdocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
![The profiles of wx\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/369380736/figure/fig3/AS:11431281155666223@1683252606204/The-profiles-of-wxdocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
![The profiles of wx\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/369380736/figure/fig4/AS:11431281155701967@1683252606403/The-profiles-of-wxdocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
![The profiles of wx\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/369380736/figure/fig5/AS:11431281155651133@1683252606624/The-profiles-of-wxdocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
The complicated dynamics is considered for a system of coupled Klein-Gordon like equations with two symmetric superlinear boundary conditions. The coupled Klein-Gordon like equations become coupled damped Klein-Gordon equations or telegraph equations or wave equations at a certain parameter value. The system is reduced to a discrete iteration of a...
Citations
... Resmi et.al. [52], has studied change in quality factor of thermoelastic beam with temperature due to temperature dependent material properties in vibrating circular plates. Schiwietz et.al. ...
A comprehensive 3-D finite element formulation for the coupled thermoelastic system is proposed based on the Total Lagrangian framework to study the thermoelastic damping (TED) in small scale structures. The proposed formulation takes into account geometric nonlinearity because of large deformation and material nonlinearity where material parameters are functions of temperature and strain field. Using the proposed finite element formulation, the TED quality factor is obtained for 1-D rod undergoing longitudinal vibrations using the eigenvalue analysis. We first validate the accuracy of the finite element implementation with previously known theoretical and numerical results. Subsequently we demonstrate the utility of the proposed numerical framework to study the effect of geometric nonlinearity, temperature and strain dependent material nonlinearity on the thermoelastic damping.In addition, the effect of internal/ external heating and different thermal boundary conditions on TED is discussed
... Consequently, research in thermoelastic damping which limits the maximum achievable quality factor in the resonator is an interesting area. The maximum attainable thermoelastic damping limited quality factor (QTEDmax) in different structures is investigated in various research works as in tuning fork resonators [47], laterally vibrating resonators [48], gyroscopic devices [49], micro/nano flexural thinbeams [50], thickbeams [51], laminated composite micromechanical beam resonators [52], functionally graded microbeams [53], carbon nano tubes [54], rectangular and circular microplate resonators [55][56][57] multi-layered microplates [58][59][60], functionally graded plates [60],rotating microdisks [62], microrings [63] etc. ...
Among the different energy dissipation mechanisms, thermoelastic damping plays a vital role and need tobe alleviated in resonators inorder to enhance its performance parameters by improving its thermoelastic dampinglimited qualityfactor, QTED. The maximum energy dissipation is also interrelated with critical length (???????? ) of theplates and by optimizing the dimensions the peaking of energy dissipation can be diminished. As the size of thedevices is scaled down, classical continuum theories are not able to explain the size effect related mechanicalbehavior at micron or submicron levels and as a result non-classical continuum theories are pioneered with theinception of internal length scale parameters. In this paper, analysis of isotropic rectangular micro-plates based onKirchhoff model applying Modified Coupled Stress Theory is used toanalyzethe size-dependent thermoelasticdamping and its impact on quality factor and critical dimensions.Hamilton principle is adapted to derive thegoverning equations of motion and the coupled heat conduction equation is employed to formulate the thermoelasticdamping limited quality factor of the plates. Five different structural materials (PolySi, Diamond,Si, GaAs andSiC)are used for optimizing QTED which depends on the materialperformance index parameters. ThermoelasticDamping Index [TDI] and thermal diffusion length, lT. According to this work, the maximum QTED is attained forPolySi with the lowest TDI and Lcmax is obtained for SiC which is having the lowest lT. The impact of lengthscaleparameters (l), vibration modes, boundary conditions (Clamped–Clamped and Simply Supported), and operatingtemperatures on QTED and Lcare also investigated. It is concluded that QTED is further maximized by selecting lowtemperatures and higher internal length scale parameters (l).The prior knowledge of QTED and Lchelp the designers tocome out with high performance low loss resonators.
... To model high quality factor resonators, all dissipation mechanisms that cause the quality factor to diminish must be identified. e different energy dissipation mechanisms are classified into extrinsic (e.g., anchor damping [32][33][34] and squeeze film damping [35,36]) and intrinsic losses (e.g., thermoelastic damping [37][38][39]). Extrinsic losses are easily controlled by changing the operating conditions, but intrinsic losses are not able to be managed as fully as extrinsic ones. ...
Among the different energy dissipation mechanisms, thermoelastic damping plays a vital role and needs to be alleviated in vibrating resonators to mitigate parameters by improving the thermoelastic damping limited quality factor, QTED. The maximum energy dissipation is also interrelated with the critical dimension h c of the plates, and by optimizing the dimensions, the peaking of energy dissipation can be diminished. As the size of the devices is scaled down, classical continuum theories become incompetent to explain the size-effect related mechanical nature at the micron and submicron levels, and, as a result, nonclassical continuum theories have been pioneered with the inception of internal length scale parameters. In this work, an analysis of isotropic rectangular microplates based on the Kirchhoff model and a higher order theory like Modified Couple Stress Theory is utilized to study size-dependent thermoelastic damping and its impact on the quality factor and critical dimensions. The Hamilton principle is adapted to derive the governing equations of motion, and the coupled heat conduction equation is employed to formulate the thermoelastic damping limited quality factor of the plates. Five different structural materials (PolySi, diamond, Si, GaAs, and SiC) are used for optimizing QTED and hc, which depends on two material performance index parameters: the thermoelastic damping index (TDI) and the material thermal diffusion length, l T . According to this work, the maximum QTED is attained for PolySi with the lowest TDI, and hcmax is obtained for Si with the maximum l T . The impacts of the dimensionless length-scale parameters (l/h), vibration modes, and boundary conditions (clamped-clamped and simply supported) on QTED and hc are also investigated. From the current analysis, QTED can be further enhanced by selecting higher vibration modes and clamped-clamped boundary conditions. QTED can be maximized by fixing the internal length scale parameter (l) and making the thickness of the beam equal to l. The analytical study is numerically simulated by using MATLAB 2015 software. Prior knowledge of QTED and hc will help designers to produce high-performance and low-loss resonators for the futuristic technological applications.
In IoT, energy dissipation reduction is an essential requirement for achieving high-performance sensors and communication devices. Among the various energy dissipations that limit the performance of IoT devices, thermoelastic energy dissipation is a crucial one which seems to be laborious to control. In thermoelastic damping (TED), due to the coupling between temperature and strain fields in the vibrating structures, irreversible energy dissipation occurs. In this paper, the energy dissipation of a cantilever-type micro/nanobeam resonator at high temperature is analysed and found to be increased as the temperature elevates. Consequently, to reduce thermoelastic energy dissipation at high temperatures, nonzero values for dimensionless length scale parameter are chosen and verified to be effective at all temperatures. The analysis is conducted by MATLAB 2015 and five diverse structural materials (Si, polySi, GaAs, diamond and SiC) are selected. The thermoelastic energy losses of micro/nanobeams are plotted by varying the temperature from 0 to 500 K. The increase in energy losses at elevated temperatures is minimised by the inclusion of the nonzero dimensionless length scale parameters.KeywordsInternet of things (IoT)IoT temperature sensorMicrobeam resonatorsThermoelastic dampingThermoelastic energy dissipationDimensionless length scale parameter
Microbeams are extensively used for many applications in the MEMS/NEMS industry. The structural material properties modulate the performance of the beam-based resonators in microscale. In the current analysis, the flexural behaviour of microbeams subjected to various structural materials is analysed and the bending rigidity, the most significant flexural parameter associated with it, is investigated. As the device dimensions are scaled down, nonclassical continuum theories are applicable in structural domain to represent its dynamic characteristics. The current analysis incorporates modified couple stress theory as the chosen nonclassical elasticity theory to accurately model the vibrating microbeams with five different structural materials: Si, polySi, GaAs, diamond and SiC. In the analysis, the impacts of scaling effect on bending rigidity ratio of microbeams are investigated. Quality factor limited by thermoelastic damping (QTED) is an important performance parameter of resonating microstructures and found to be depending on the flexural characteristics. The variation of bending rigidity ratio with Poisson’s ratio is also investigated. The material order in which bending rigidity varies with dimensionless length parameter is explored for the five structural materials. The size effect parameter (l/h) increases the bending rigidity ratio and eigenfrequencies according to our study. The simulations have been conducted numerically using MATLAB 2015a. The structural materials with high bending rigidity ratio can be chosen for developing low energy dissipation MEMS/NEMS-based resonators in today’s leading edge technologies like IoT and 5G networks.KeywordsMicrobeam resonatorsSize effectsDimensionless length scale parameterDimensionless bending rigidity ratioPoisson’s ratio
Microelectromechanical systems (MEMS) technology is extensively used for making high-performance sensors and actuators in Internet of Things. The ubiquitous advantages and potential applications of MEMS sensors compared to conventional ones paved the way for implementing the diverse micro-sensing technologies in Internet of Things (IoT). Vibrating plate-based MEMS resonant sensors are the most commonly used small structural elements due to its low mass and high-quality factors. The downsizing of devices for achieving minute sensors used in IoT leads to application of higher-order theories. The requirement of enhanced quality factors necessitates the study of characteristics affecting the quality factor and associated energy dissipation. The current analysis explores the significance of mode switching on energy loss which controls the most decisive performance measure for sensors used in IoT applications. The investigation of impact of mode switching on thermoelastic energy dissipation with different structural materials for a rectangular plate-based resonator is included in the study. The energy dissipation is verified to be slightly diminished when operated in higher modes, and the quantification of the impact is accurately done by calculating the percentage reduction in energy losses. While considering the thermoelastic energy dissipation of microplate-based resonators, the influence of mode switching on diamond-based plate resonators is verified to be the most prominent according to our findings. The result analysis of the proposed work helps the engineers for designing resonators with diamond as the structural material operating in higher vibrating modes for IoT and 5G applications.KeywordsMicro/nanoplate rectangular resonatorsEnergy dissipationSize effectsMode switching
Micro/nanobeam-based resonators have found extensive applications in the micro/nanoelectromechanical system industry. Thermoelastic damping (TED) is a major energy loss issue in micro/nanobeam resonators that limits their important performance parameter, namely, the TED limited quality factor (QTED). The critical length (Lc) of a micro/nanobeam is another significant parameter that accounts for the maximum peak in the energy dissipation curve at which QTED assumes a minimum value. To evaluate QTED and Lc explicitly when the size of devices is scaled down, size effects play a decisive role and classical theories are inadequate. In this work, a higher-order theory, namely, modified couple stress theory (MCST), is used to overcome the size effects by including one internal material length scale parameter (l). The material-dependent thermoelastic coupled equations for a deflected Euler-Bernoulli microbeam are presented using variational and Hamilton principles. Moreover, the solutions for QTED are developed on the basis of a complex frequency approach with the appropriate material indices. The effects of material length scale parameters, material performance indices, mechanical boundary conditions (clamped-clamped, simply supported, and cantilever types), mode switching, and plane stress/strain conditions on QTED and Lc are analyzed. Numerical results are extracted from the analytical expressions by using MATLAB R2015a to quantify thermoelastic energy dissipation. The numerically computed QTED and Lc values are fully investigated to design high-performance resonators. The analyses verify that QTED is enhanced by optimizing the structural material and augmenting the material length scale parameter. The material order in which QTED is enhanced is the same for classical theories and MCST, i.e., it is inversely related to the TED index parameter. The influences of boundary types and mode switching on QTED are relatively less in accordance with the analysis. The effect of plane stress condition compared with that of plane strain condition on QTED is also remarkable. The Lc of the beam is determined to be dependent on the thermal diffusion length of the material used. From an adequate material point of view, poly-silicon has been proven to provide the maximum quality factor while silicon carbide yields the maximum Lc. These observations are significant and extremely helpful when designing low-loss micro/nanobeam resonators with superior performance by suitably selecting their geometry and structural materials.
In vibrating structures like resonators, various intrinsic and extrinsic energy dissipation mechanisms exist which limit the maximum achievable quality factor. Among the different types of energy losses, damping caused by thermoelastic effect is a crucial mechanism which arises due to the interaction among thermal and mechanical fields. Thermoelastic damping (TED) limits the maximum attainable quality factor (QTED), and coupling between the strain and temperature fields varies with temperature. In this paper, the effects of temperature on energy dissipation due to TED in a simply supported rectangular microplate resonator is analyzed. When the devices are downsized, size effects should be incorporated, and instead of classical elasticity theories, modified couple stress theory (MCST) is applied to investigate the energy dissipations. The impact of temperature on energy dissipation with and without size effects is investigated by incorporating a length scale parameter (l) which is made dimensionless by dividing it by the plate thickness (l/h). The influence of temperature on QTED in rectangular microplates with and without size effects is analyzed using various structural materials (polySi, SiC, GaAs, diamond, and Si). The thermoelastic energy dissipation seems to be increased with rise in temperature, and with the incorporation of size scaling, owing to the impact of dimensionless length scale parameter, even at elevated temperatures, high QTED is achieved. Thermoelastic energy dissipation in rectangular plate is analyzed by pertaining MCST, and the impact of temperature on energy loss with size effects using l/h is numerically simulated using MATLAB 2015.KeywordsQuality factorThermoelastic energy dissipationSize scalingLength scale parameterMicroplate rectangular resonators
