A simplified strain gradient Kirchhoff rod model and its applications on microsprings and microcolumns

Hong, Jun Hwa; Zhang, Gongye; Wang, Xiao; Mi, Changwen

doi:10.2140/jomms.2020.15.203

Cited by 3 publications

(2 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nonetheless, the practical applications are restricted due to the multitude of material parameters involved, and the challenges of acquiring them experimentally. Mindlin's research led to the development of the simplified strain gradient elasticity theory (SSGET) [31][32][33], also known as the Helmholtztype first gradient elasticity theory [34] and the dipolar gradient elasticity theory [35]. Owing to its simple form, SSGET accurately captures material size effects, and as a result, it has received considerable attention from researchers.…”

Section: Introductionmentioning

confidence: 99%

Size effects on a one-dimensional defective phononic crystal sensor

Shu,

Zhang,

Cong

et al. 2023

Smart Mater. Struct.

Self Cite

View full text Add to dashboard Cite

The influence of size effects on one-dimensional defective phononic crystal sensors based on simplified strain gradient elasticity theory is studied in this paper. Phononic crystals have been widely used in high-sensitivity gas and liquid sensors by introducing defects to disrupt the perfect phononic crystal modes. In comparison with classical elasticity theory, the simplified strain gradient elasticity theory includes two microstructure-related material parameters that can accurately reflect the size effects of the structure. In this paper, the stiffness matrix method was used to calculate the transmission coefficients of the proposed model, avoiding the numerical instability of the transfer matrix method. The results show that the size effects at the microscale affect the perfect phononic crystal bandgap's frequency range, and the microstructure constants impress the resonant frequency while detecting liquids. Consequently, the accuracy of the sensor is reduced. These findings provide a theoretical basis for designing microscale phononic crystal sensors.

show abstract

Section: Introductionmentioning

confidence: 99%

Size effects on a one-dimensional defective phononic crystal sensor

Shu,

Zhang,

Cong

et al. 2023

Smart Mater. Struct.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The bandgap for elastic wave propagation arises from the Bragg scattering and local resonance [11][12][13]. As a result, thin structures (e.g., rods, beams, plates and shells) usually exhibit size-dependent effects at small scales [14][15][16][17][18][19][20][21][22][23][24][25], which cannot be captured by the existing classical theories. The same phenomenon also happens in bandgaps made of micro-/nano-PC structures.…”

Section: Introductionmentioning

confidence: 99%

Tunable Bandgaps in Phononic Crystal Microbeams Based on Microstructure, Piezo and Temperature Effects

Hong

Zhang

et al. 2021

Crystals

Self Cite

View full text Add to dashboard Cite

A new model of non-classical phononic crystal (PC) microbeam for the elastic wave bandgap generation is provided, incorporating microstructure, piezomagnetism, piezoelectricity and temperature effects. The wave equation of a general magneto–electro–elastic (MEE) phononic crystal microbeam is derived, which recovers piezoelectric- and piezomagnetic-based counterparts as special cases. The piezomagnetic and piezoelectric materials are periodically combined to construct the PC microbeam and corresponding bandgaps are obtained by using the plane wave expansion (PWE) method. The effects of the piezomagnetism, piezoelectricity, microstructure, geometrical parameters and applied multi-fields (e.g., external electric potential, external magnetic potential, temperature change) on the bandgaps are discussed. The numerical results reveal that the bandgap frequency is raised with the presence of piezo and microstructure effects. In addition, the geometry parameters play an important role on the bandgap. Furthermore, large bandgaps can be realized by adjusting the external electric and magnetic potentials at micron scale, and lower bandgap frequency can be realized through the temperature rise at all length scales.

show abstract

Size-Dependent Buckling Analysis of Microbeams by an Analytical Solution and Isogeometric Analysis

et al. 2022

View full text Add to dashboard Cite

This paper proposes an analytical solution and isogeometric analysis numerical approach for buckling analysis of size-dependent beams based on a reformulated strain gradient elasticity theory (RSGET). The superiority of this method is that it has only one material parameter for couple stress and another material parameter for strain gradient effects. Using the RSGET and the principle of minimum potential energy, both non-classical Euler–Bernoulli and Timoshenko beam buckling models are developed. Moreover, the obtained governing equations are solved by an exact solution and isogeometric analysis approach, which conforms to the requirements of higher continuity in gradient elasticity theory. Numerical results are compared with exact solutions to reveal the accuracy of the current isogeometric analysis approach. The influences of length–scale parameter, length-to-thickness ratio, beam thickness and boundary conditions are investigated. Moreover, the difference between the buckling responses obtained by the Timoshenko and Euler–Bernoulli theories shows that the Euler–Bernoulli theory is suitable for slender beams.

show abstract

A simplified strain gradient Kirchhoff rod model and its applications on microsprings and microcolumns

Cited by 3 publications

References 42 publications

Size effects on a one-dimensional defective phononic crystal sensor

Size effects on a one-dimensional defective phononic crystal sensor

Tunable Bandgaps in Phononic Crystal Microbeams Based on Microstructure, Piezo and Temperature Effects

Size-Dependent Buckling Analysis of Microbeams by an Analytical Solution and Isogeometric Analysis

Contact Info

Product

Resources

About