Vibration analysis of nanorods by the Rayleigh-Ritz method and truncated Fourier series

Bao, Siyuan; Cao, Jinrui; Wang, Shuodao

doi:10.1016/j.rinp.2018.11.085

Cited by 10 publications

(9 citation statements)

References 28 publications

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“…In addition, according to the boundary conditions of the model, y|x � 0 � 0和y|x � L � 0, and the maximum deflection at the middle part of the suspended span of the rock beam will be w. at is to say, y| x � L/2 � w. en, the deflection curve equation will be established using a Rayleigh-Ritz method [21]:…”

Section: Simplified Model Of Mining Earthquakes In Ick Andmentioning

confidence: 99%

Mechanism and Prevention and Control of Mine Earthquake in Thick and Hard Rock Strata considering the Horizontal Stress Evolution of Stope

Zhang

Huang

et al. 2021

Shock and Vibration

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This study investigated the mechanism, prevention measures, and control methods for earthquake disasters typically occurring in mines with thick and hard rock strata. A mine stope with large faults and thick hard rock strata in Hebei Province was taken as the background study object. Then, theoretical analysis and numerical simulation methods were adopted in conjunction with field monitoring to explore how horizontal stress evolves in the thick and hard hanging roofs of such mines, potentially leading to mining earthquakes. Then, based on the obtained results, a mining design method was proposed to reduce the horizontal stress levels of earthquake mitigation. The results showed that, under the control of large faults, semiopen and semiclosed stopes with thick hard rock strata are formed, which cause influentially pressurized and depressurized zones during the evolution of the overburden movements and horizontal stress. It was determined that the stress concentrations mainly originated from the release and transfer of horizontal stress during the rock fractures and movements in the roof areas, which were calculated using a theoretical estimation model. The horizontal stress concentrations formed “counter torques” at both ends of the thick and hard strata, which prevented the support ending due to tensile failures. As a result, the limit spans were increased. This study proposed a mining strategy of using narrow working faces, strip mining processes, and reasonable mining speeds, which could effectively reduce horizontal stress concentrations and consequently prevent and control mining earthquakes. This study’s research results were successfully applied to the mining practices in working face 16103.

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Section: Simplified Model Of Mining Earthquakes In Ick Andmentioning

confidence: 99%

Mechanism and Prevention and Control of Mine Earthquake in Thick and Hard Rock Strata considering the Horizontal Stress Evolution of Stope

Zhang

Huang

et al. 2021

Shock and Vibration

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“…Clamped boundary conditions are the special case of a Bishop nanorod with axial springs of infinite stiffness. The following values of parameters of the Bishop nanorod (5,5) are used to calculate the the natural frequencies given in Tables 1-2 (ρ = 9517 kg/m 3 , E = 6.85 TPa, and L = 24.4 nm). It can be seen from Table 1, the presented natural frequencies of the proposed model are in excellent agreement with those computed in ref [26].…”

Section: Model Validationmentioning

confidence: 99%

“…Results derived by introducing Equation ( 3) into Equation ( 6) and neglected density body forces̃and̃are substituted into Equation (5). Then, stress σ xx , σ xy , and σ xz obtained in terms of the displacement u are obtained as follows:…”

Section: Nonlocal Bishop Nanorod Modelmentioning

confidence: 99%

“…Numanoğlu and Civalek [4] have explored the nonlocal dynamic torsional response of nanorods embedded in elastic media. Bao et al [5] have presented the free longitudinal vibration analysis of nanorods with an attached mass object under elastic boundary conditions. Ecsedi and Baksa [6] have studied the free axial vibration of single walled carbon nanorod embedded in an elastic medium by adopting Rayleigh model.…”

Section: Introductionmentioning

confidence: 99%

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Axial dynamic analysis of a Bishop nanorod with arbitrary boundary conditions

2020

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In the present work, axial vibrational behavior of nanorods with different boundary conditions is researched. Bishop's rod theory is implemented to simulate the axial deflection. Size‐dependency is captured by using Eringen's nonlocal elasticity theory. Based on nonlocal deformable boundary conditions and Stokes’ transformation, a system of linear equations is derived and then constructed an Eigen value problem. Several numerical examples are presented to investigate the significance of various parameters such as geometric parameters, vibrational modes, various values of nonlocal parameter and axial spring parameters on the axial frequencies of nanorods. The numerical examples indicate that the deformable boundary conditions and small scale parameter have considerable effects on the axial vibration response.

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“…Numanoğlu and Civalek [47] conducted the torsional vibration of nanorods surrounded by elastic matrix by nonlocal FEM. The Rayleigh-Ritz method and truncated Fourier series were used by Bao et al [48], for vibration analysis of nanorods.…”

Section: Introductionmentioning

confidence: 99%

Temperature change effect on torsional vibration of nanorods embedded in an elastic medium using Rayleigh–Ritz method

Abdullah

Hosseini-Hashemi

Hussein

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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This paper studies torsional vibration of carbon nanotubes/nanorods embedded in an elastic medium under thermal stresses. Nonlocal theory is applied to the nanorod equations. The thermal stresses act in axial and other directions, and their amounts vary as temperature changes. The elastic medium is modeled as a rotational spring around the nanorod. Hamilton's principle is used to obtain motion equation. Rayleigh-Ritz method is used to solve the differential equation of motion. Effect of nonlocal scale coefficient, low and high temperatures, elastic medium stiffness, and nanorod diameter and length is investigated. Influence of temperature on the frequencies depends on the values of stiffness of elastic medium, and nanotube diameter and length.

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Vibration analysis of nanorods by the Rayleigh-Ritz method and truncated Fourier series

Cited by 10 publications

References 28 publications

Mechanism and Prevention and Control of Mine Earthquake in Thick and Hard Rock Strata considering the Horizontal Stress Evolution of Stope

Mechanism and Prevention and Control of Mine Earthquake in Thick and Hard Rock Strata considering the Horizontal Stress Evolution of Stope

Axial dynamic analysis of a Bishop nanorod with arbitrary boundary conditions

Temperature change effect on torsional vibration of nanorods embedded in an elastic medium using Rayleigh–Ritz method

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