Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives

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.

Thermoelastic transient memory response analysis of non-localized nano-piezoelectric plates based on Moore-Gibson-Thompson thermoelasticity theory

“…As for the fractional order derivative, Wang and Li 37 argued that for any given upper positive integral limit and kernel function, the Caputo-type fractional order definition does not reflect the memory effect anymore when time takes on larger values, subsequently, they provided the memory-dependent derivative (MDD) definition. Following their work, Yu et al, Ezzat et al, and Kaur and Singh [38][39][40][41][42][43] established several generalized thermoelastic models by introducing MDD in heat cond-uction equation respectively. Compared to the fractional order heat conduction model, the MDD heat conduction model can characterize the memorydependent and genetic properties of the transient heat transfer process, and in which both the kernel function and the time delay factor can be chosen to more flexibly accommodate the actual situations.…”

An investigation on responses of thermoelastic interactions of transversely isotropic thick circular plate due to ring load with memory-dependent derivatives

“…This study was caused by the action of a transverse distributed moving line load propagating parallel to the infinite simply supported edges of the plate strip at constant speed. Kaur and Singh [16,17] discussed the MDD in nano-beams. Some other researchers also worked on similar research on MDD or semiconductor medium as, Nasr et al [18], Abouelregal et al [19], Abouelregal et al [20].…”

The theory of thermoelasticity with a memory-dependent dynamic response for a thermo-piezoelectric functionally graded rotating rod

“…A mathematical representation of the problem is constructed utilizing Fourier's law of heat transfer with fractional order and three-phase delay derivatives. Based on a memory-dependent concept, Kaur and Singh 28 analyzed the thermoelastic vibrations in 2D functionally graded nanobeams (FGN). The nanobeam has a constant temperature in the middle and is sustained at both ends.…”