Analysis of vibration and critical buckling load of porous functionally graded material rectangular nanoplates under thermo‐mechanical loading

The present work is an attempt to develop a simple, accurate, and widely applicable finite element formulation for the size‐dependent nonlinear transient analysis of the rotating porous thick and thin functionally graded material (FGM) microblade subjected to load due to centrifugal force and cooling thermal shock. First‐order shear deformation theory in conjunction with von Karman‐type nonlinearity is used in the development of the finite element formulation. The temperature‐dependent material properties of the SUS304 stainless steel and the AISI 1020 carbon steel are taken. The upper layer made of the SUS304 stainless steel is subjected to a cooling thermal shock and the lower layer made of AISI 1020 carbon steel is held constant at room temperature. The governing differential equation for the present analysis is obtained using total Lagrangian formulation in conjunction with the modified coupled stress theory (MCST). Modified Newton–Raphson in conjunction with Newmark average acceleration method is used to obtain the nonlinear transient response of the rotating porous FGM pretwisted blade. The results obtained from the present finite element formulation are first compared for a wide range of parameters. New results are presented to investigate the effect of porosity, intensity of the thermal shock, material scale ratio, rotational velocity, and volume fraction index on the nonlinear transient analysis of a rotating porous thick and thin SUS304/AISI 1020 functionally graded rotating blade under load due to centrifugal force and cooling thermal shock.

Size‐dependent nonlinear transient analysis of rotating porous thick and thin FGM microblade under cooling thermal shock

Pandey

2024

Size‐dependent buckling analysis of functionally graded nanoplate coupled with piezoelectric layers resting on orthotropic foundation based on surface piezo‐elasticity theory

Arani,

Ghorbanpour Arani,

Maraghi

2024

In this study, a refined plate theory by considering stretching effects extended to investigation of quasi‐3D size‐dependent buckling analysis of a functionally graded simply supported nanoplate integrated with piezoelectric face‐sheets resting on orthotropic foundation by taking into account the surface effects. The power law is used to calculate the material properties in the functionally graded core in which the non‐homogeneous core properties are continuously changing along the thickness. Due to the consideration of functionally graded materials and due to the asymmetry in the distribution of material properties in the core, the middle plane and the neutral plane do not coincide. Hence, to consider a reference plane, the concept of a neutral surface is considered. The kinematics of nanoplate are formulated with nonlocal higher order shear deformation theory based on nonlocal strain gradient theory. Additionally, the surface effect is modeled based on surface piezo‐elasticity theory. To check the accuracy and efficiency of the current model, a comprehensive validation and comparative study has been conducted based on the results obtained and the results found in the previous literature. Finally, a comprehensive study is conducted to investigate the effect of various parameters, including different foundations, residual stress, surface effects, stretching effect, neutral surface, aspect ratio, thickness ratio, nanlocal parameter, length scale parameter, gradient index, and initial voltage, which are examined on critical buckling load of nanoplate in details. It is expected that the results of the current study should be utilized in designing micro/nano‐electro‐mechanical systems components based on smart nanostructures.

Nonlinear vibration and parametric excitation of magneto‐thermo elastic embedded nanobeam using homotopy perturbation technique

Selvamani,

Thangamuni,

Yaylacı

et al. 2024

The present study focuses on the modeling and analyzing the nonlinear vibration patterns and parametric excitation of embedded Euler–Bernoulli nanobeams subjected to thermo‐magneto‐mechanical loads. The Euler–Bernoulli nanobeam is developed with external parametric excitation. The governing equation of motion is derived by utilizing nonlocal continuum theory and nonlinear von Karman beam theory. Subsequently, the homotopy perturbation technique is employed to determine the vibration frequencies. Finally, the modulation equation of Euler–Bernoulli nanobeams is derived for simply supported boundary condition. In order to validate our findings, we conduct a comparative analysis against existing literature, thereby underscoring the effectiveness and robustness of our proposed methodology. The influence of stress, magnetic potential, temperature, damping coefficient, Winkler coefficient, and nonlocal parameters are tested numerically on nonlinear frequency‐amplitude and parametric excitation–amplitude responses. The numerical examples indicate the significant impact of physical variables on the nonlinear frequency and parametric excitation. The primary objective of this study is to investigate the effects of external physical variables on the dynamic behavior of nanobeams, particularly in nonlinear regimes. This study provides insights into the design and control of nanostructures under complex load conditions, contributing to developing advanced materials and nanosystems.