Longitudinal vibration analysis of nanorods with multiple discontinuities based on nonlocal elasticity theory using wave approach

Loghmani, Masih; Yazdi, Mohammad Reza Hairi; Bahrami, Mohammad

doi:10.1007/s00542-017-3619-y

Cited by 4 publications

(4 citation statements)

References 72 publications

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“…Figure 4 shows that Ω 1 (1) decreases through the first half of the step location ratio and return to increase by going to the end. It can be seen that the results are in good agreement with Loghmani, Yazdi [24] results.…”

Section: Example 1 This Example Presents the Analysis Of Twosegment N...supporting

confidence: 87%

“…For the present case the cut off frequency is obtained by setting j = 0 as shown in Eq. (24). Moreover, the waves stop propagating after certain frequency called escape frequency (Ω es ) .…”

Section: Wave Characteristics (Spectrum and Dispersion Relations)mentioning

confidence: 99%

“…Numanoğlu et al [23] presented the effect of nonlocal parameter, boundary conditions, attachments and length on the axial vibration behavior of nanorod using Eringen's nonlocal theory. Loghmani et al [24] analysed the free axial vibration of several cracked, stepped nanorod with attached mass at the tip of the rod. Ebrahimi et al [25] investigated static stability and vibration analysis of a functionally graded nanobeams.…”

Section: Introductionmentioning

confidence: 99%

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Longitudinal Vibration Analysis of a Stepped Nonlocal Rod Embedded in Several Elastic Media

Taima

El-Sayed

Farghaly

2022

J. Vib. Eng. Technol.

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Purpose Mechanical properties of 1D nanostructures are of great importance in nanoelectromechanical systems (NEMS) applications. The free vibration analysis is a non-destructive technique for evaluating Young's modulus of nanorods and for detecting defects in nanorods. Therefore, this paper aims to study the longitudinal free vibration of a stepped nanorod embedded in several elastic media. Methods The analysis is based on Eringen’s nonlocal theory of elasticity. The governing equation is obtained using Hamilton’s principle and then transformed into the nonlocal analysis. The dynamic stiffness matrix (DSM) method is used to assemble the rod segments equations. The case of a two-segment nanorod embedded in two elastic media is then deeply investigated. Results The effect of changing the elastic media stiffness, the segments stiffness ratio, boundary conditions and the nonlocal parameter are examined. The nano-rod spectrum and dispersion relations are also investigated. Conclusion The results show that increasing the elastic media stiffness and the segment stiffness ratio increases the natural frequencies. Furthermore, increasing the nonlocal parameter reduces natural frequencies slightly at lower modes and significantly at higher modes.

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Section: Example 1 This Example Presents the Analysis Of Twosegment N...supporting

confidence: 87%

Section: Wave Characteristics (Spectrum and Dispersion Relations)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Longitudinal Vibration Analysis of a Stepped Nonlocal Rod Embedded in Several Elastic Media

Taima

El-Sayed

Farghaly

2022

J. Vib. Eng. Technol.

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“…When the dimensionless restraint stiffness is assumed to be above 10 4 , the natural frequency change is no longer apparent and tends to a constant value. It has been studied how discontinuous nanobeams with defects cracks and steps can vibrate longitudinally on different boundaries by Loghmani et al [66]. It is noted that as crack parameters decrease, the natural frequency decreases, and in addition, we observe that as the nonlocal parameters increase, the natural frequency decreases and tends to approach each other.…”

Section: Buckling and Vibration Of Nonlocal Micro-/nano-beamsmentioning

confidence: 59%

A review on the size-dependent bulking, vibration and, wave propagation of nanostructures

Wang

Zhao

et al. 2023

J. Phys.: Condens. Matter

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Size effect is a typical characteristic of micro-/nano-materials, which can contribute to a variety of size-dependent behaviors, phenomena, and properties, such as stiffness softening, deformation springback, etc. The intrinsic causes of size effects are micro-structural properties of materials, and the sensitivity of microstructural properties of materials is closely related to the smallest structural unit of the crystal, crystal defects and geometric dimensions, and is heavily influenced by the material’s field conditions. The modeling method based on nonlocal theory and gradient theory in the model is not only consistent with experimental and molecular dynamics simulation results, but also provides a solid explanation for the size effect underlying ”softening” and ”hardening” behaviors. Taking this as a basic point, this paper further considers the real working environment of materials, and systematically reviews the static and dynamic mechanical behavior cases of various nano-structures, mainly involving bulking, vibration and wave propagation of micro-beams and plates under different theories. A description and discussion of the differences in mechanical properties resulting from size effects under various theoretical frameworks and three key bottleneck problems are provided: the selection of kernel functions, the determination of size parameters, and the physical meaning of boundary conditions at higher orders. A summary is provided of the possible avenues and potentials for size effect models in future research. Many studies have shown that size parameters have a significant impact on the mechanical behavior of micro-/nano-structures, and these effects will increase as the size of the structure decreases. Nevertheless, different theories have varying scopes of application and size effects, and further research is needed to develop a unified size-dependent theory with universal applicability. A major focus of this paper is on the size effect of micro-/nano-structures, as well as provides the necessary data support to resolve the bottleneck problem associated with the size effect in the processing and manufacturing industries, and realizes the design and optimization of micro-scale parts based on their size.

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Axial dynamics of functionally graded Rayleigh-Bishop nanorods

Arda

2020

Microsyst Technol

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Longitudinal vibration analysis of nanorods with multiple discontinuities based on nonlocal elasticity theory using wave approach

Cited by 4 publications

References 72 publications

Longitudinal Vibration Analysis of a Stepped Nonlocal Rod Embedded in Several Elastic Media

Longitudinal Vibration Analysis of a Stepped Nonlocal Rod Embedded in Several Elastic Media

A review on the size-dependent bulking, vibration and, wave propagation of nanostructures

Axial dynamics of functionally graded Rayleigh-Bishop nanorods

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