Well-posedness of two-phase local/nonlocal integral polar models for consistent axisymmetric bending of circular microplates

Two-phase local/nonlocal mixture models for buckling analysis of higher-order refined shear deformation beams under thermal effect

Abstract The purpose of this study is to investigate vibrations in 2D functionally graded nanobeams (FGN) with memory-dependent derivatives. A sinusoidal variation of temperature is assumed. The dimensionless expressions for axial displacement, thermal moment, lateral deflection, strain and temperature distribution are found in the transformed domain using Laplace Transforms, and the expressions in the physical domain are derived by numerical inversion techniques. The nanobeam is simply supported at the both ends and have constant temperatures. The FGN is a non-homogenous composite structure with constant structural variations along with the layer thickness, changing from ceramic at the bottom to metal at the top. Adding non-local MDD to thermoelastic models opens up new possibilities for the study of thermal deformations in solid mechanics. The effect of different kernel functions and periodic frequency of thermal vibration is illustrated graphically for lateral deflection, axial displacement, strain, temperature, and thermal moment. Article highlights A novel model of vibrations in a functionally graded nanobeams is presented. The medium is subjected to sinusoidal variation of temperature. Dynamic response of memory dependent derivative theory of thermoelasticity and non-local parameter is investigated. The effects of kernel functions and periodic frequency of thermal vibration on all physical fields are investigated and shown graphically. 

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Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives

The small size and clever design of nanoparticles can result in large surface areas. This gives nanoparticles enhanced properties such as greater sensitivity, strength, surface area, responsiveness, and stability. This research delves into the phenomenon of a nanobeam vibrating under the influence of a time-varying heat flow. The nanobeam is hypothesized to have material properties that vary throughout its thickness according to a unique exponential distribution law based on the volume fractions of metal and ceramic components. The top of the FG nanobeam is made entirely of ceramic, while the bottom is made of metal. To address this issue, we employ a nonlocal modified thermoelasticity theory based on a Moore–Gibson–Thompson (MGT) thermoelastic framework. By combining the Euler–Bernoulli beam idea with nonlocal Eringen’s theory, the fundamental equations that govern the proposed model have been constructed based on the extended variation principle. The fractional integral form, utilizing Atangana–Baleanu fractional operators, is also used to formulate the heat transfer equation in the suggested model. The strength of a thermoelastic nanobeam is improved by performing detailed parametric studies to determine the effect of many physical factors, such as the fractional order, the small-scale parameter, the volume fraction indicator, and the periodic frequency of the heat flow.

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Thermoelastic Analysis of Functionally Graded Nanobeams via Fractional Heat Transfer Model with Nonlocal Kernels

Abstract With the extensive applications of the micro/nano-electro-mechanical systems, a great deal of attention has been paid to explore the influences of the arising size-dependent effect and surface effect on their performance. Along with these effects, the nonlocal elasticity, strain gradient theory, and surface elasticity theory were successively proposed. Moreover, it is inevitable for MEMS/NEMS to work in a variable temperature environment, correspondingly, the thermal-induced stress or deformation becomes another issue that needs serious concern. Thermoelastic damping (TED), as a main energy dissipation source, is a major challenge in designing higher-quality factor resonators. However, considering the thermoelastic coupling effect, the aforementioned theories are not capable enough to depict the thermoelastic performance of micro/nano-resonators. To amend this deficiency, based on nonlocal strain gradient theory, a new model for assessing the TED of nanobeam resonators by incorporating the thermal relaxation effect and the surface effect is developed. The corresponding governing equations for the Euler–Bernoulli microbeam resonator model are formulated, and then, solved by means of a complex frequency method. The influences of the nonlocal parameter, strain gradient coefficients, aspect ratio, surface stress and surface elasticity on the TED are examined and discussed in detail.

Thermoelastic damping analysis in nanobeam resonators considering thermal relaxation and surface effect based on the nonlocal strain gradient theory

In extreme heat transfer environments, functionally graded materials (FGMs) have aroused great concern due to the excellent thermal shock resistance. With the development of micro-scale devices, the size-dependent effect has become an important issue. However, the classical continuum mechanical model fails on the micro-scale due to the influence of the size-dependent effect. Meanwhile, for thermoelastic behaviors limited to small-scale problems, Fourier’s heat conduction law cannot explain the thermal wave effect. In order to capture the size-dependent effect and the thermal wave effect, the nonlocal generalized thermoelastic theory for the formulation of an FGM microbeam is adopted in the present work. For numerical validation, the transient responses for a simply supported FGM microbeam heated by the ramp-type heating are considered. The governing equations are formulated and solved by employing the Laplace transform techniques. In the numerical results, the effects of the ramp-heating time parameter, the nonlocal parameter, and the power-law index on the considered physical quantities are presented and discussed in detail.

Nonlocal thermoelastic analysis of a functionally graded material microbeam

A memory-dependent thermal-viscoelastic model and its application in heating-induced nonlocal response analysis of a polymer microbeam

Compared with the fractional order generalized themoelastic theory, the generalized thermoelastic theory based on the memory-dependent derivative has following significant advantages: First, the ge...

Tianhu He

Papers

Nonlocal thermoelastic analysis of a functionally graded material microbeam

A memory-dependent thermal-viscoelastic model and its application in heating-induced nonlocal response analysis of a polymer microbeam

Investigation on the electromagneto-thermoelastic coupling behaviors of a rotating hollow cylinder with memory-dependent derivative