Response of deflection and thermal moment of Timoshenko microbeams considering modified couple stress theory and dual-phase-lag heat conduction model

Kumar, Harendra; Mukhopadhyay, Santwana

doi:10.1016/j.compstruct.2021.113620

Cited by 19 publications

(7 citation statements)

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“…We use Hamilton's principle to get the equations of motion and related boundary conditions in this section. The strain energy due to bending can be expressed as [47]:…”

Section: Hamilton's Principle For Timoshenko Microbeam Based On Mcstmentioning

confidence: 99%

“…Khisaeva and Ostoja-Starzewski [44] experimentally validated the damping analysis at a very high frequency for nanomechanical resonator with finite wave propagation using the LS generalized thermoelasticity theory. For the DPL heat conduction model, numerous research works have been conducted to examine thermoelastic damping while taking into account the MCST [45][46][47]. Under the TPL heat conduction model, Kumar [48] has established the formula for dynamic deflection and thermal moment.…”

Section: Introductionmentioning

confidence: 99%

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Thermoelastic vibration of Timoshenko beam under the modified couple stress theory and the Moore–Gibson–Thompson heat conduction model

Singh

Mukhopadhyay

2023

Mathematics and Mechanics of Solids

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In modeling of micro/nanodevices, numerous approaches have been developed that take into account material length scale parameters to capture size effects. In this work, the variational formulation of the microstructure-dependent Timoshenko beam model is developed considering Hamilton’s principle and modified couple stress theory (MCST) which involves the material length scale parameter. The Moore–Gibson–Thompson (MGT) thermoelastic model is employed to present the governing equations of motion and boundary conditions. The numerical outcomes illustrated by classical and non-classical approaches reveal the behavior of both the deflection and thermal moment of the beam. In addition, the dissipation in the deflection and the thermal moment is visually depicted in standardized curves. Several peaks in graphical plots are then detected as a function of the dimensionless time, which bring to light some interesting features of MGT model in the prediction of thermoelastic vibration of the microstructure model of Timoshenko beam.

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“…We use Hamilton's principle to get the equations of motion and related boundary conditions in this section. The strain energy due to bending can be expressed as [47]:…”

Section: Hamilton's Principle For Timoshenko Microbeam Based On Mcstmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermoelastic vibration of Timoshenko beam under the modified couple stress theory and the Moore–Gibson–Thompson heat conduction model

Singh

Mukhopadhyay

2023

Mathematics and Mechanics of Solids

Self Cite

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“…Micro‐ and nano‐electromechanical systems (MEMS and NEMS) have many uses in the biomedical, scientific, and engineering fields. This is because technological advances have made them more portable, sensitive, quick to react, energy efficient, and durable [5]. Improvements in materials science and technology are intimately linked to developments in micro‐ and nanoelectronics.…”

Section: Introductionmentioning

confidence: 99%

Thermally stressed thermoelectric microbeam supported by Winkler foundation via the modified Moore–Gibson–Thompson thermoelasticity theory

2023

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This article offers the first investigation into the thermoelectric vibration of microscale Euler‐Bernoulli beams resting on an elastic Winkler base. We developed the system of equations for thermoelastic microbeams using elastic basis theory and the generalized Moore–Gibson–Thompson (MGT) thermal transport framework with a single‐phase delay. At the front of the microbeam, a graphene strip connected to an electrical power source was employed to generate heat. In addition, the influence of an ultra‐short‐pulsed laser on the vibration of a microbeam is studied, taking into account its heating effect. The microbeam system variables were analyzed after solving the mathematical equations by applying the Laplace transform technique. Graphs showing how different inputs affect different mechanical fields, such as Winkler substrate stiffness, voltage, electrical resistance, and temperature modulus pulses, are also presented. An increase in the Winkler modulus and the shear modulus of the foundation was found to decrease the amount of deflection and axial deformation in the microbeams. The increased beam stiffness has resulted in this decrease.

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“…These parameters, generally called small-scale parameters, make it possible to investigate the size effect. Researchers working on the analysis of various very small-scale nano- and micro-structures have used these size effect theories, such as doublet mechanics theory [ 29 , 30 , 31 , 32 , 33 ], modified couple stress theory [ 34 , 35 , 36 , 37 , 38 , 39 ], nonlocal elasticity theory [ 1 , 40 , 41 , 42 , 43 , 44 , 45 ], nonlocal strain gradient theory [ 46 , 47 , 48 , 49 ] and strain gradient theory [ 50 , 51 , 52 , 53 ]. Researchers use a variety of techniques to analyze an element or structure, such as a rod, beam, plate, frame, etc., whether at the macro, nano, or micro level.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Free Vibration of Embedded Short-Fiber-Reinforced Nano-/Micro-Rods with Deformable Boundary Conditions

2022

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An efficient eigenvalue algorithm is developed for the axial vibration analysis of embedded short-fiber-reinforced micro-/nano-composite rods under arbitrary boundary conditions. In the formulation, nonlocal elasticity theory is used to capture the size effect, and the deformable boundary conditions at the ends are simulated using two elastic springs in the axial direction. In addition, to determine the reinforcing effect of restrained nano-/micro-rods, a new system of linear equations with the concept of the infinite power series is presented. After performing the mathematical processes known as Fourier sine series, Stokes’ transformation and successive integration, we finally obtain a coefficient matrix in terms of infinite series for various rigid or deformable boundary conditions. Some accurate eigenvalue solutions of the free axial vibration frequencies of the short-fiber-reinforced micro-/nano-composite rods with and without being restrained by the means of elastic springs are given to show the performance of the present method. The presence of the elastic spring boundary conditions changes the axial vibration frequencies and corresponding mode shapes.

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Response of deflection and thermal moment of Timoshenko microbeams considering modified couple stress theory and dual-phase-lag heat conduction model

Cited by 19 publications

References 50 publications

Thermoelastic vibration of Timoshenko beam under the modified couple stress theory and the Moore–Gibson–Thompson heat conduction model

Thermoelastic vibration of Timoshenko beam under the modified couple stress theory and the Moore–Gibson–Thompson heat conduction model

Thermally stressed thermoelectric microbeam supported by Winkler foundation via the modified Moore–Gibson–Thompson thermoelasticity theory

Nonlocal Free Vibration of Embedded Short-Fiber-Reinforced Nano-/Micro-Rods with Deformable Boundary Conditions

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