Thermal vibration buckling of smart magneto electro elastic sandwich nano plates with biocompatible FGM core layer

This study examined the thermomechanical vibration behavior of foam core-layered nanocomposite beams exposed to external magnetic fields and thermal loads. Nanobeams have three different distributions of ceramic or metal foam structures reinforced with graphene pellets (GPLs) in the core layer and ceramic, metal, and ceramic + metal material configurations in the surface layers. To model the micromechanical behavior, the layer wise motion equations of the sandwich nanobeam were created with Hamilton principles by using the sinusoidal higher-order shear deformation theory together with the nonlocal strain gradient elasticity theory. The Lorentz force induced by the external magnetic field and the thermal forces resulting from the nonlinear temperature increase were adapted to the equations of motion. According to the results of the analysis studies, it has been observed that the metal or ceramic foam structure in the core layer is important to the thermomechanical behavior of the nanobeam. It has also been observed that the foam distribution (surface intense, core intense, and uniform) and foam void ratio affect the thermal resistance of the nanobeam. It has been observed that graphene reinforcement in the core layer increases the thermal resistance of the sandwich nanobeam up to 850–1500 K, depending on the configuration of the sandwich nanobeam, but after this temperature, graphene reinforcement reduces the thermal resistance of the beam. In addition, it has been observed that the applied external magnetic field can change the thermal vibration behavior of the sandwich nanobeam, and it has been shown that the magnetic field can be used to increase the thermal resistance of nano sensor beams operating under severe temperature conditions.

Chapter Nine - Vibration of FG beams

This research addresses the three-dimensional thermomechanical wave propagation behavior in sandwich composite nanoplates with a metamaterial honeycomb core layer and double functionally graded (FG) ultra-stiff surface layers. Due to its potential for high-temperature applications, pure nickel (Ni) is preferred for the honeycomb core layer, and an Al2O3/Ni ceramic-metal matrix is preferred for the surface layers. The functional distribution of graphene platelets (GPLs) in three different patterns, Type-U, Type-X, and Type-O, in the metal-ceramic matrix with a power law distribution provides double-FG properties to the surface layers. The mechanical and thermal material characteristics of the core and surface layers, as well as the reinforcing GPLs, are temperature-dependent. The pattern of temperature variation over the plate thickness is considered to be nonlinear. The sandwich nanoplate’s motion equations are obtained by combining the sinusoidal higher-order shear deformation theory (SHSDT) with nonlocal integral elasticity and strain gradient elasticity theories. The wave equations are established by using Hamilton’s principle. Parametric simulations and graphical representations are performed to analyze the effects of honeycomb size variables, wave number, the power law index, the GPL distribution pattern, the GPL weight ratio, and the temperature rise on three-dimensional wave propagation in an ultra-stiff sandwich plate. The results of the analysis reveal that the 3D wave propagation of the sandwich nanoplate can be significantly modified or tuned depending on the desired parameters and conditions. Thus, the proposed sandwich structure is expected to provide essential contributions to radar/sonar stealth applications in air, space, and submarine vehicles in high or low-temperature environments, protection of microelectromechanical devices from high noise and vibration, soft robotics applications, and wearable health and protective equipment applications.

In this research, the dynamic instability region (DIR) of the sandwich nano-beams are investigated based on nonlocal strain gradient elasticity theory (NSGET) and various higher order shear deformation beam theories (HSDBTs). The sandwich piezoelectric nano-beam is including a homogenous core and face-sheets reinforced with functionally graded (FG) carbon nanotubes (CNTs). In present study, three patterns of CNTs are employed in order to reinforce the top and bottom face-sheets of the beam. In addition, different higher-order shear deformation beam theories such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT) are considered to extract the governing equations for different boundary conditions. The beam is subjected to thermal and electrical loads while is resting on Visco-Pasternak foundation. Hamilton principle is used to derive the governing equations of motion based on various shear deformation theories. In order to analysis of the dynamic instability behaviors, the linear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, nonlocal parameter, strain gradient parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, dimensionless geometric parameters, Visco-Pasternak foundation parameters, applied voltage and temperature change on the dynamic instability characteristics of sandwich piezoelectric nano-beam.

In this research, the dynamic instability region (DIR) of the sandwich nano-beams are investigated based on nonlocal strain gradient elasticity theory (NSGET) and various higher order shear deformation beam theories (HSDBTs). The sandwich piezoelectric nano-beam is including a homogenous core and face-sheets reinforced with functionally graded (FG) carbon nanotubes (CNTs). In present study, three patterns of CNTs are employed in order to reinforce the top and bottom face-sheets of the beam. In addition, different higher-order shear deformation beam theories such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT) are considered to extract the governing equations for different boundary conditions. The beam is subjected to thermal and electrical loads while is resting on Visco-Pasternak foundation. Hamilton principle is used to derive the governing equations of motion based on various shear deformation theories. In order to analysis of the dynamic instability behaviors, the linear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, nonlocal parameter, strain gradient parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, dimensionless geometric parameters, Visco-Pasternak foundation parameters, applied voltage and temperature change on the dynamic instability characteristics of sandwich piezoelectric nano-beam.

In this study, the thermomechanical buckling behavior of sandwich smart nanoplates with magneto-electro-elastic surface layers was modeled and examined together with high-order plate theory and nonlocal strain gradient elasticity theory. It consists of a functionally graded material (FGM) metal-ceramic foam structure containing four different foam distributions in the core layer of the sandwich nanoplate. FGM core structure includes pure metal, pure ceramic, pure ceramic–metal and pure metal-cerasssmic combinations. The equations of motion were obtained by Hamilton’s principle as a result of the electro-elastic and magneto-strictive coupling effects, as well as the reflection of thermal loads, spring foundation and shear foundation effects into the energy equations, and the equations of motion were solved by the Navier method. Thermal effects, foundation effects, the effects of electric and magnetic potentials applied to the smart surface layers, and the effects of the properties of the foam structure in the core layer on the thermo-mechanical buckling behavior of the smart sandwich nanoplate have been examined in a broad framework. It is thought that the results of this study will be beneficial in the design and production of smart nano electro-mechanical systems that are intended to operate in high temperature environments. The buckling behavior of the smart plate can be adjusted with the properties of the core layer, the properties of the foundation coefficients and the applied external electric and magnetic potentials for a desired temperature operating environment.

The kiri tree produces low-density wood, which serves as an excellent material for particleboards (PB) due to the correspondingly low bulk density of the particles and better glue utilization. In this study, kiri particles (KPs) are used in surface and core layers to explicitly improve certain strength properties of three-layered PBs. Six variants of three-layered PBs were produced from KPs and industrial particles (IPs) with a target density of 500 kg m−3. The composition of the PBs was 100% KPs, 100% IPs, KPs in the surface layer with IPs in the core layer and vice versa, and KPs and IPs, respectively, in the surface layer with a 50/50% mixture of KPs and IPs. KPs in the surface layer improved bending strength and bending MOE for all different core layers. The internal bond strength increased accordingly with the amount of KPs in the core layer. Thickness swelling was lower with KPs in the surface layer for panels with all different core layers. Water absorption was lower with KPs in the surface layer for most of the panels. Density profiles reveal that the variants with lowest density in the core layer do not necessarily show the lowest IB results, which indicates that IB is more dependent on the compression of the particles and resulting enhanced adhesion than on density alone. Screw withdrawal resistance was not affected by the surface layer, but it increased with the overall amount of KPs in the PB.

This study modeled and analyzed the thermomechanical vibration behavior of three-layer nanoplates featuring a butterfly auxetic core and functionally graded surface layers reinforced with graphene pellets. The equations of motion for the sandwich nanoplate were formulated utilizing higher-order plate theory and non-local strain gradient elasticity theories. The butterfly auxetic structure was parametrically modeled based on length and thickness parameters, and the surfaces were examined as FGM+GPRL+Foam. The influence of the auxetic core structure, functionally graded materials (FGM), graphene reinforcement, foam void ratio, and foam type on the thermal vibration characteristics of the sandwich nanoplate was examined comprehensively. The findings underscore the pivotal influence of core inclination angles on stability and vibrational characteristics, the diverse reactions of the foam structure, and the substantial performance enhancements afforded by graphene reinforcing in the surface layers. The auxetic core structure delivers enhanced performance relative to traditional designs, where material dimensions and structural characteristics are crucial for optimizing natural frequency. The findings of this work are anticipated to enhance advanced aviation applications, specifically in the protection of components subjected to high temperatures in aircraft and rocket engines, as well as in regulating the thermal vibration characteristics of nano electromechanical devices.

This study examines the thermal buckling behavior of a three-layered nano-sandwich plate composed of functionally graded (FG) metal-ceramic face sheets and an auxetic butterfly core. The face sheets transition from silicon nitride (Si3N4) on the outer surfaces to nickel (Ni) at the center, while the core layer consists of an auxetic butterfly structure made of nickel. The governing equations are formulated using higher-order shear deformation theory (HSDT) to accurately capture the effects of transverse shear deformation. The stress–strain relationships incorporate nonlocal strain gradient elasticity, ensuring the inclusion of small-scale effects. The Von-Kármán nonlinear strain–displacement relations are employed to describe large deformations. The elastic modulus of the non-porous graphene platelets (GPLs) reinforced metal matrix is determined using the Halpin–Tsai micromechanics model. The thermal buckling problem is solved numerically for simply supported (SSSS) boundary conditions by applying an analytical-numerical approach. The effects of auxetic core parameters (a1, b1, β1, and β2), FG face sheet properties (material grading index, graphene reinforcement, foam structure), and nonlocal parameters are systematically analyzed. The results indicate that the auxetic butterfly core significantly enhances the thermal stability of the sandwich plate by improving the load distribution. The material grading index, graphene reinforcement, and foam structure also play a crucial role in enhancing buckling resistance. Nonlocal effects introduce additional flexibility, impacting the overall structural response.

This study focuses on modeling and analyzing the thermomechanical vibration behavior of sandwich nanobeams made from biocompatible zirconia and Ti-6Al-4V materials. The sandwich nanobeam is composed of the materials mentioned earlier, featuring a porous structure in the core layer. The sandwich nanobeam experiences significant thermal load and is subjected to a horizontal external electromagnetic field. The equations of motion for the sandwich nanobeam were derived through the application of the sinusoidal high-order shear stress theorem and the constitutive equation based on nonlocal strain gradient elasticity. The equations were converted into equations of motion using Hamilton’s principle, incorporating the thermal load and the Lorentz force generated in the electromagnetic field, and solved using the Navier method. Analyses were conducted on the thermomechanical vibration behavior of the sandwich nanoplate, taking into consideration the properties of the sandwich layers, the impact of temperature, and the intensity of the applied horizontal magnetic field. The impact of the porous core layer in the sandwich nanoplate on the porosity volume ratio and porosity distribution function in thermomechanical behavior has been established. Research has demonstrated that the application of an external magnetic field can effectively mitigate the adverse impacts of thermal loads caused by high temperatures.

Chapter Six - Static analysis of FG rectangular plates

Second Order Shear Deformation Theory (SSDT) for Free Vibration Analysis on a Functionally Graded Quadrangle Plate

In the present study, the effect of in-plane thermal loading on vibrational behaviour of functionally graded (FG) nanobeams are carried out by presenting both Navier type solution and differential transform method. Classical and first order shear deformation beam theories are adopted to count for the effect of shear deformations. Thermo-mechanical properties of FG nanobeam are supposed to vary smoothly throughout the thickness based on power-law model and material properties are assumed to be temperature-dependent. Eringen’s nonlocal elasticity theory is exploited to describe the size dependency of FG nanobeam. Using Hamilton’s principle, the nonlocal equations of motion together with corresponding boundary conditions are obtained for the free vibration analysis of FG nanobeams based on Euler–Bernoulli and Timoshenko beam theories. According to the numerical results, it is revealed that the proposed modeling and semi analytical approach can provide accurate frequency results of the FG nanobeams as compared to analytical results and also some cases in the literature. In following a parametric study is accompanied to examine the effects of the several parameters such as temperature change, gradient indexes, small scale parameter, mode number and boundary conditions on the natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the vibration behaviour of a FG nanobeam are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.

ABSTRACTIn the present research, free vibration study of functionally graded (FG) nanobeams with graded nonlocality in thermal environments is performed according to the third-order shear deformation beam theory. The present nanobeam is subjected to uniform and nonlinear temperature distributions. Thermo-elastic coefficients and nonlocal parameter of the FG nanobeam are graded in the thickness direction according to power-law form. The scale coefficient is taken into consideration implementing nonlocal elasticity of Eringen. The governing equations are derived through Hamilton's principle and are solved analytically. The frequency response is compared with those of nonlocal Euler–Bernoulli and Timoshenko beam models, and it is revealed that the proposed modeling can accurately predict the vibration frequencies of the FG nanobeams. The obtained results are presented for the thermo-mechanical vibrations of the FG nanobeams to investigate the effects of material graduation, nonlocal parameter, mode number, slenderness ratio, and thermal loading in detail. The present study is associated to aerospace, mechanical, and nuclear engineering structures that are under thermal loads.

The aging resistance properties of poplar plywood prepared with soy protein-based adhesives were investigated. The shear strength of soybean meal/bisphenol epoxy resin (SM/EP) adhesive increased by 197.5% (surface layer) to 1.19 MPa and 153.5% (core layer) to 1.09 MPa compared to soybean meal (SM) adhesive. Wet-dry cycles of 25 ± 3 °C, 63 ± 2 °C, and 95 ± 2 °C accelerated the aging of poplar plywood with soy protein-based adhesive. After eight 25 ± 3 °C wet-dry cycles, the shear strength of plywood bonded with SM/EP adhesive was reduced to 0.88 MPa (surface layer) and 0.71 MPa (core layer). Furthermore, the shear strength of SM adhesive gradually decreased to 0 (surface and core layer) after six and five 25 ± 3 °C wet-dry cycles. The shear strength of SM/EP adhesives was reduced to 0.96 MPa and 0.79 MPa (surface and core layer) after eight 63 ± 2 °C wet-dry cycles, and 0.53 MPa and 0.27 MPa (surface and core layer) after eight 95 ± 2 °C wet-dry cycles. Vertical density profiles indicated that the decrease of shear strength could be attributed to several factors: The small molecules were dissolved, the molecular chains of the adhesives were hydrolyzed by water, and the interior and thermal stress destroyed the bonding structure.