Impacts of Length Scale Parameter on Material Dependent Thermoelastic Damping in Micro/nanoplates Applying Modified Coupled Stress Theory
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-06-21 |
| Journal | Mechanika |
| Authors | R. Resmi, V.Suresh BABU, M.R. BAIJU |
| Institutions | University of Kerala, A P J Abdul Kalam Technological University |
| Analysis | Full AI Review Included |
Impacts of Material Performance Indices and Length Scale Parameter on Thermoelastic Damping in Micro/Nanoplates
Section titled âImpacts of Material Performance Indices and Length Scale Parameter on Thermoelastic Damping in Micro/NanoplatesâExecutive Summary
Section titled âExecutive SummaryâThis analysis investigates the size-dependent thermoelastic damping (TED) in rectangular micro/nanoplates using the Modified Couple Stress Theory (MCST) to optimize the quality factor (QTED) for high-performance resonators.
- QTED Optimization: The maximum achievable QTED is fundamentally material-dependent, with PolySi yielding the highest QTED (up to 12140.19) due to its minimum Thermoelastic Damping Index (TDI).
- Size Dependency Confirmed: Applying MCST (non-classical theory) confirms that QTED and the Critical Length (Lc) both increase significantly as the internal material length scale parameter (l) increases (from 0 ”m to 1 ”m).
- Critical Length (Lc) Control: Lc, which defines the length at which peak energy dissipation occurs, is maximized by SiC (up to 1.62 ”m). Lc is inversely proportional to the materialâs thermal diffusion length (lr).
- Design Insensitivity: The magnitude of QTED is found to be negligibly affected by changes in mechanical boundary conditions (Simply Supported vs. Clamped-Clamped) or vibration mode switching (Mode (1,1) vs. Mode (2,1)).
- Modeling Approach: Analytical expressions for QTED and Lc were derived using the complex frequency approach based on the Kirchhoff plate model, comparing classical (LR) and non-classical (MCST) continuum theories.
- Design Implication: Engineers should select PolySi for maximum QTED and utilize higher internal length scale parameters (l) to achieve low-loss resonators.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the analysis of rectangular microplates (200 ”m x 200 ”m x 10 ”m) operating at 298 K.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Plate Dimensions (a x b x h) | 200 x 200 x 10 | ”m | Validation geometry |
| Operating Temperature (To) | 298 | K | Room Temperature |
| Max QTED (l=1 ”m) | 12140.19 | Dimensionless | PolySi, Mode (1,1), SS/CC |
| Min QTED (l=1 ”m) | 4799.38 | Dimensionless | SiC, Mode (1,1), SS/CC |
| Max Critical Length (Lc) | 1.62 | ”m | SiC, Clamped-Clamped, l=1 ”m, Mode (2,1) |
| Max TDI (Thermoelastic Damping Index) | 5128 x 10-6 | K-1 | GaAs |
| Min TDI (Thermoelastic Damping Index) | 1113 x 10-6 | K-1 | PolySi |
| Max Thermal Diffusivity (Ï) | 0.577 | cm2/s | Si |
| Min Thermal Diffusivity (Ï) | 0.178 | cm2/s | GaAs |
| Max Percentage QTED Difference (0 to 1 ”m) | 92.13 | % | Diamond plates (MCST vs. LR) |
| Max Percentage Lc Difference (SS to CC) | 41.32 | % | Si plates, l=1 ”m, Mode (1,1) |
Key Methodologies
Section titled âKey MethodologiesâThe study employed a rigorous analytical and numerical approach to quantify TED in micro/nanoplates, focusing on the incorporation of size effects via MCST.
- Constitutive Modeling: The Kirchhoff plate model was adopted for thin plate analysis. The Modified Couple Stress Theory (MCST) was applied, incorporating a single material length scale parameter (l) to capture size dependency, unlike classical elasticity (LR theory, where l = 0).
- Governing Equation Derivation: The dynamic governing equation of motion and the coupled heat conduction equation were derived using the Hamilton principle, accounting for thermoelastic coupling.
- Damping Quantification: The thermoelastic damping limited quality factor (QTED) was calculated using the complex frequency approach. QTED is determined from the ratio of the real and imaginary parts of the complex eigenfrequency (Ï).
- Performance Index Analysis: Two key material performance indices were used:
- Thermoelastic Damping Index (TDI): TDI = Eα2/Cp. TDI is inversely related to QTED.
- Thermal Diffusion Length (lr): lr is inversely related to the Critical Length (Lc).
- Numerical Simulation: The derived analytical expressions were simulated numerically using MATLAB R2015a to assess the quantitative impacts of material choice (PolySi, Diamond, Si, GaAs, SiC), length scale parameter (l = 0, 0.5, 1 ”m), boundary conditions (SS, CC), and mode switching (M-I, M-II).
Commercial Applications
Section titled âCommercial ApplicationsâThe findings are critical for the design and optimization of high-Q micro/nano resonators used in various Microelectromechanical Systems (MEMS) and Nanoelectromechanical Systems (NEMS).
- Mass Sensing: Designing ultra-sensitive mass sensors (e.g., for chemical or biological detection) requires maximizing QTED. PolySi is the optimal material choice for achieving the lowest intrinsic energy loss.
- Electronic Filtering and Communication Systems: High-Q resonators are essential for stable frequency references, filters, and oscillators in RF and communication circuits, where minimizing phase noise is paramount.
- Navigation Systems (Gyros and Accelerometers): High-performance MEMS gyroscopes and accelerometers rely on stable, low-loss resonators. The ability to predict and control Lc allows designers to dimension plates to avoid peak TED dissipation.
- Energy Harvesting: Resonators used in micro-scale energy harvesting devices benefit from high Q factors to maintain oscillation efficiency and stability.
- Material Selection for Size Effects: For nanoscale devices where the internal length scale parameter (l) becomes comparable to the device thickness (h), MCST must be used. Selecting materials with higher l values (e.g., PolySi) enhances QTED, improving device performance as dimensions shrink.
View Original Abstract
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.