Bending and wave propagation analysis of axially functionally graded beams based on a reformulated strain gradient elasticity theory

Wang, Shaopeng; Hong, Jun; Wei, Dao; Zhang, Gongye

doi:10.1007/s10483-023-3042-6

Cited by 6 publications

(2 citation statements)

References 42 publications

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“…The size effect induces distinct mechanical properties in microstructures compared to macrostructures. Currently, many high-order theories are proposed to describe the size effect [35][36][37][38][39][40][41][42][43][44], such as the couple stress theory [45], strain gradient theory [46], non-local elasticity theory [47], surface elasticity theory [48], and reformulated strain gradient elasticity theory [49][50][51]. Utilizing the couple stress theory, Yang et al established the modified couple stress theory (MCST), which specifically accounts for the symmetric curvature tensor with one additional material parameter for isotropic material.…”

Section: Model and Formulationmentioning

confidence: 99%

Size and Temperature Effects on Band Gap Analysis of a Defective Phononic Crystal Beam

Yao,

Wang,

Hong

et al. 2024

Crystals

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In this paper, a new defective phononic crystal (PC) microbeam model in a thermal environment is developed with the application of modified couple stress theory (MCST). By using Hamilton’s principle, the wave equation and complete boundary conditions of a heated Bernoulli–Euler microbeam are obtained. The band structures of the perfect and defective heated PC microbeams are solved by employing the transfer matrix method and supercell technology. The accuracy of the new model is validated using the finite element model, and the parametric analysis is conducted to examine the influences of size and temperature effects, as well as defect segment length, on the band structures of current microbeams. The results indicate that the size effect induces microstructure hardening, while the increase in temperature has a softening impact, decreasing the band gap frequencies. The inclusion of defect cells leads to the localization of elastic waves. These findings have significant implications for the design of microdevices, including applications in micro-energy harvesters, energy absorbers, and micro-electro-mechanical systems (MEMS).

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Section: Model and Formulationmentioning

confidence: 99%

Size and Temperature Effects on Band Gap Analysis of a Defective Phononic Crystal Beam

Yao,

Wang,

Hong

et al. 2024

Crystals

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“…Moreover, the extended modified couple stress theory in the proposed model was included in order to take into account the so-called microstructure effect. In [32], a new size-dependent axially functionally graded (AFG) micro-beam model was developed, in which a reformulated strain gradient elasticity theory (RSGET) was also applied. The strain gradient, velocity gradient, and couple stress effects were included in this new model for the two-component axially functionally graded beam.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Functionally Graded Laminated (FGL) Media—Theoretical Tolerance Modelling

Jędrysiak

2023

Materials

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Dynamic problems of elastic non-periodically laminated solids are considered in this paper. It is assumed that these laminates have a functionally graded structure on the macrolevel along the x1-axis and non-periodic structure on the microlevel. However, along the other two directions, i.e., x2 and x3, their properties are constant. The effects of the size of a microstructure (the microstructure effect) on the behaviour of the composites can play a significant role. This effect can be described using the tolerance modelling method. This method allows us to derive model equations with slowly varying coefficients. Some of these terms can depend on the size of the microstructure. These governing equations of the tolerance model make it possible to determine formulas describing not only fundamental lower-order vibrations related to the macrostructure of these composite solids, but also higher-order vibrations related to the microstructure. Here, the application of the tolerance modelling procedure is shown to lead to equations of the tolerance model that can be used for non-periodically laminated solids. Then, these model equations are mainly used to analyse a simple example of vibrations for functionally graded composites with non-periodically laminated microstructure (FGL). Similar problems were investigated in the framework of the homogenised (macrostructural) model (Jędrysiak et al. 2006); the resulting equations neglect the microstructure effect.

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Buckling behavior of nickel microbeams based on reformulated strain gradient theory

Yıldırım,

Akgöz

2024

Appl. Phys. A

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Bending and wave propagation analysis of axially functionally graded beams based on a reformulated strain gradient elasticity theory

Cited by 6 publications

References 42 publications

Size and Temperature Effects on Band Gap Analysis of a Defective Phononic Crystal Beam

Size and Temperature Effects on Band Gap Analysis of a Defective Phononic Crystal Beam

Dynamics of Functionally Graded Laminated (FGL) Media—Theoretical Tolerance Modelling

Buckling behavior of nickel microbeams based on reformulated strain gradient theory

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