Characterization of functionally graded elastic materials using a thickness-shear mode quartz resonator

The overall goal of this study is to develop thickness shear mode (TSM) resonators for the real-time, label-free, non-destructive sensing of biological adhesion events in small populations (hundreds) of neurons, in a cell culture medium and subsequently in vivo in the future. Such measurements will enable the discovery of the role of biomechanical events in neuronal function and dysfunction. Conventional TSM resonators have been used for chemical sensing and biosensing applications in media, with hundreds of thousands of cells in culture. However, the sensitivity and spatial resolution of conventional TSM devices need to be further enhanced for sensing smaller cell populations or molecules of interest. In this report, we focus on key challenges such as eliminating inharmonics in solution and maximizing Q-factor while simultaneously miniaturizing the active sensing (electrode) area to make them suitable for small populations of cells. We used theoretical expressions for sensitivity and electrode area of TSM sensors operating in liquid. As a validation of the above design effort, we fabricated prototype TSM sensors with resonant frequencies of 42, 47, 75, and 90 MHz and characterized their performance in liquid using electrode diameters of 150, 200, 400, 800, and 1,200 μm and electrode thicknesses of 33 and 230 nm. We validated a candidate TSM resonator with the highest sensitivity and Q-factor for real-time monitoring of the adhesion of cortical neurons. We reduced the size of the sensing area to 150–400 μm for TSM devices, improving the spatial resolution by monitoring few 100–1,000s of neurons. Finally, we modified the electrode surface with single-walled carbon nanotubes (SWCNT) to further enhance adhesion and sensitivity of the TSM sensor to adhering neurons (Marx, 2003).

Functionally Graded Material (FGM) is a heterogeneous composite material that consists of a gradient compositional variation of the constituent materials from one surface of the material to the other. These continuous changes result in gradient material properties. Since ceramic has good heat resistance and metal has high strength, FGM made by ceramic and metal can work at super high temperatures or under a high-temperature-difference field. It is a primary to reduce thermal stress by selection of different effective material properties for the intermediate composition of the EGM and to prevent destruction by thermal stress. FGM is manufactured at a high temperature and then residual thermal stresses are produced during cooling to room temperature. In this paper, the elastic-plastic thermal stresses induced in a ceramic-metal FGM plate (FGP) taking the fabrication process into consideration are discussed. The region near the heat resistant surface is produced by metal particle reinforced ceramic while the region near the cooling surface is vice versa. As the metal and the ceramic near the middle region of the FGM are perfectly mixed, it is impossible to consider the particle-reinforced material. In this study, the FGP is divided into three regions. First, the region near the cooling surface is metal rich and then the metal is considered as a matrix while the ceramic is considered as particles. Second, the region near the heat resistant surface is ceramic rich so that the ceramic is considered as a matrix while the metal is considered as particles. Third, in the middle part between the previous two regions the metal and ceramic are perfectly mixed. In the third region macroscopic analysis is considered because the difference between the volume fractions of the ceramic and the metal is small and it is difficult to consider one of them as a matrix or particles. The effects of the distribution parameter of the composition and the fabrication temperature on the thermal stress variations are discussed.

A system of approximate first-order equations is extracted from an infinite system of 2-D equations for piezoelectric crystal plates with thickness-graded material properties, which is deduced from the 3-D equations of linear piezoelectricity. These equations are used to study mechanical effects on the thickness-shear (TS), flexural (F), and face-shear (FS) vibrations of an AT-cut quartz plated with two identical electrodes. Dispersion curves are calculated from the present 2-D equations as well as the 3-D equations. The comparison of these curves shows that the agreement is very close for all three frequency branches of TS, F, and FS modes in a range up to the 1.5 times the fundamental TS frequency and for gold and aluminum electrodes with R, the ratio of the mass of the electrodes to that of the plate, equal to 0.05. without introducing any correction factors. In order to assess electrode effects, spectra of omega vs. a/bq (length-to-thickness ratio of the quartz) are computed for plates with gold and aluminum electrodes and different R ratios. And the spectrum of omega vs. R is computed for plates with aluminum electrodes and a given a/bq ratio. For a plate with gold electrodes, the frequencies of predominant TS, F, and FS modes are decreasing as R increases, but the amount of frequency changes for the TS mode is much greater than those for the other two modes. However, for a plate with aluminum electrodes, the frequencies of the TS and FS modes are decreasing, but those of the F modes are increasing as R increases.

Monitoring of biofilm growth with thickness-shear mode quartz resonators in different flow and nutrition conditions

Nonlinear vibration of sandwich plate with functionally graded material (FGM) core and carbon nano tubes reinforced (CNTs) nano-composite layers by considering temperature-dependent material properties are studied in this paper. Base on Classical plate theory (CPT), the governing partial differential equations of motion for sandwich plate are derived using Hamilton principle. The Galerkin procedure and multiple scales perturbation method are used to find relation between nonlinear frequency and amplitude of vibration response. The dynamic responses of the sandwich plate are also investigated in both time and frequency domains. Then, the effects of nonlinearity, excitation, power law index of FG core, volume fraction of carbon nanotube, the function of material variations of FG core, temperature changes, scale transformation parameter and damping factor on the frequency responses are investigated.

The high temperature occurs due to the combustion gas from engine in unmanned aerial vehicles (UAV). The high temperature may cause serious damages in UAV structure. The Functionally Graded Material (FGM) is chosen as a candidate material of the engine duct structure. A functionally graded material (FGM) is a two- component mixture composed by compositional gradient materials from one material to the other. In contrast, traditional composite materials are homogeneous mixtures, and involve compositions between the desirable properties of the component materials. Since significant proportions of an FGM contain the pure form of each material, the need for compromise is eliminated. The properties of both components can be fully utilized. Thermal stress analysis of FGM layers (20, 40, 60, 80 and 100) is performed in this paper. In addition, the creep behavior of FGM applied in duct structure of an engine is analyzed for better understanding of FGM characteristics.

Material engineering has become one of the corner stones in various engineering applications. The scientific alteration of base materials into various inorganic and organic compounds has resulted in the development of Functionally Graded Material (FGM). FGM can be described as a cutting edge material in which the particular material's properties could be made varied as the dimension changes. The aims of this study was to review on FGM's applications and its manufacturing processes. In addition, the mathematical idealization of the FGM was also reviewed. Based on the review, since FGMs are highly heterogeneous, it can be idealized as their mechanical properties changes smoothly with respect to their spatial coordinates. Nonetheless, in order to analyze FGMS in an efficient manner, the homogenization schemes are needed to be simplified from their complicated heterogeneous microstructures. Closed-form solutions of some fundamental solid mechanics' problems can be obtained by this idealization. Conclusively, FGM is unique in relation to any of the individual materials that structures it. Suggestively, this provide a limitless possibility for future engineering applications.

Natural frequency analysis of anisotropic functionally graded material (FGM) annular sector plates on Winkler elastic foundations based on three-dimensional theory of elasticity was investigated. The three-dimensional graded finite element formulation was derived based on the principle of minimum potential energy and the Rayleigh-Ritz method. For an orthotropic FGM, the material properties were assumed to have in-plane polar orthotropy and transverse heterogeneity according to an exponential law, whereas the mass density was assumed to be constant. For an isotropic FGM, material properties varied continuously through the thickness direction according to a power-law distribution, whereas Poisson’s ratio was set to be constant. The effects of material gradient exponents, different sector angles, different thickness ratio, Winkler parameter and two different boundary conditions on the natural frequencies and mode shapes of FGM annular sector plates have been investigated. Numerical solution was compared with the result of an FGM annular circular plate, which showed good agreement.

Adaptive PF-CZM for multiphysics fracture analysis in functionally graded materials

Sensor and other applications are causing an increased use of quartz resonators at high-temperatures. The Q of a quartz resonator is limited by a number of different mechanisms including the properties of the quartz itself. The Q of all quartz resonators is limited by interaction between the active mode and the thermal phonon bath. Above cryogenic temperatures this intrinsic thermal loss is nearly independent of temperature. Defect and impurities in the quartz also limit the Q of a crystal. At high temperatures alkalis thermally escape from their original interstitial site adjacent to the substitutional aluminum drift randomly along the open Z-axis channel. The release and drift of these ions causes a thermally activated loss which increases rapidly with temperature. In swept quartz the alkalis have been replaced by hydrogen which bonds to an oxygen atom adjacent to the aluminum. The free-ion loss is not present in these swept samples. Instead, the Al-OH center produces a traditional loss peak at about 600 K. We have compared the lithium and sodium free ion-loss and the Al-OH loss in AT-cut, BT-cut, and SC-cut resonator blanks prepared from the same bar of quartz. For Li-compensated samples the thermally-activated free-ion loss is largest in the AT-cut sample and smallest in the SC-cut with the BT intermediate. The AT-cut Na-compensated blank showed the expected free-ion loss that was slightly smaller than that seen in the Li-compensated blank. The Na-compensated SC and BT-cut samples had an unusual loss that increased with T above about 400 K. The 600 K Al-OH peak in the H-compensated SC-cut blank was about 1/3/sup rd/ the strength of the peak in the AT-cut blank. The H-compensated BT-cut blanks behaved strangely and further investigation is needed.

A layerwise finite element formulation for free vibration analysis of functionally graded sandwich shells

The unified formulations of finite cylindrical layer methods (FCLMs) based on the Reissner mixed variational theorem (RMVT) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, multilayered functionally graded material (FGM) circular hollow cylinders and laminated composite ones under pure axial compression, external pressure, and combined axial compression with external pressure. The material properties of the FGM layer are assumed to obey the power-law distributions of the volume fraction of the constituents through the thickness coordinate. In these formulations, the cylinder is divided into a number of finite cylindrical layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-surface variations of the primary variables of each individual layer, respectively, as well as the related order of each primary variable can be freely chosen, such as the layerwise linear, quadratic or cubic function distribution through the thickness coordinate. The accuracy and convergence of the RMVT-based FCLMs developed in this article are assessed by comparing their solutions with both the exact 3D and accurate two-dimensional (2D) solutions available in the literature. A parametric study for variations of the lowest critical load parameters with the material-property gradient index, and the load intensity, orthotropic, length-to-radius ratio, and radius-to-thickness ratios is carried out.

Functionally Graded Materials (FGMs) can outperform their homogeneous counterparts. Advances in digitalization technologies, mainly additive manufacturing, have enabled the synthesis of materials with tailored properties and functionalities. Joining dissimilar metals to attain compositional grading is a relatively unexplored research area and holds great promise for engineering applications. Metallurgical challenges may arise; thus, a theoretical critical analysis is presented in this paper. A multidisciplinary methodology is proposed here to unify optimal design, multi-feed Wire-Arc Additive Manufacturing (WAAM), and image-based characterization methods to create structure-specific oriented FGM parts. Topology optimization is used to design FGMs. A beam under pure bending is used to explore the layer-wise FGM concept, which is also analytically validated. The challenges, limitations, and role of WAAM in creating FGM parts are discussed, along with the importance of numerical validation using full-field deformation data. As a result, a conceptual FGM engineering workflow is proposed at this stage, enabling digital data conversion regarding geometry and compositional grading. This is a step forward in processing in silico data, with a view to experimentally producing parts in future. An optimized FGM beam, revealing an optimal layout and a property gradient from iron to copper along the build direction (bottom-up) that significantly reduces the normal pure bending stresses (by 26%), is used as a case study to validate the proposed digital workflow.

This work presents a finite element formulation for the vibration analysis of functionally graded material (FGM) plates containing microstructural defects operating in thermal environments. The material properties are assumed to be temperature-dependent and are modeled as higher-order functions of temperature. The volume fractions of the constituent materials are varied through the plate thickness according to a power-law distribution. The effective material properties of the FGM are evaluated using both the Mori–Tanaka homogenization scheme and the rule of mixtures. The kinematics of the FGM plates are described using an efficient layerwise theory. The governing equations of motion, constitutive relations, and boundary conditions are derived using on Hamilton’s principle. The stiffness coefficients of the plates are computed using a sub-laminate mechanics approach, wherein the plate thickness is discretized into several thin sublayers, each assumed to possess uniform material properties. This approach is particularly effective for micromechanical models where exact analytical integration of stiffness coefficients is difficult due to the complex polynomial variation of properties across the thickness. A four-noded quadrilateral finite element, previously developed for laminated and FGM shells, is extended in this study to analyze the dynamic behavior of FGM plates with microstructural defects and temperature dependent material properties. The natural frequencies are obtained using a subspace iteration technique, while the transient responses under step and impulse excitations are computed using the state-space form of the governing dynamic equations. The proposed finite element model is validated against three-dimensional elasticity and Ritz-based semi-analytical solutions, demonstrating excellent accuracy and reliability across varying thermal environments. A detailed parametric study is also carried out to investigate the effects of temperature, inhomogeneity index, porosity concentration, boundary conditions, and geometric parameters on the natural frequencies and transient responses of porous FGM plates.

An electromechanically coupled zigzag theory is presented for static and free vibration responses in functionally graded material (FGM) plates bonded with piezoelectric layers. It has the capability to consider continuity as well as discontinuity in material properties at all interfaces. The displacement field approximation, which is initially layer based, has been made layer independent by using continuity conditions on displacements and transverse shear stresses as well as zero traction conditions on top and bottom surfaces. Material properties in FGM layers vary continuously in the thickness direction. Piezoelectric layers have constant property across their thickness. Extended Hamilton’s principle for piezoelectric continuum has been used in deriving governing equations of motion and boundary conditions. An analytical solution is obtained for elastic as well as piezoelectric layer bonded FGM plates. Static and free vibration responses have been obtained in a number of FGM plates, with each plate considered to contain a number of FGM layers with discontinuity or continuity in material properties at the interfaces. Wherever available, present responses have been compared with three-dimensional exact solutions and other shear deformation theories. The effects of the aspect ratio, length-to-width ratio, and different schemes for effective material property calculation have been illustrated.