• Steel and Composite Structures
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• 제46권4호
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• pp.553-563
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• 2023

In the current research, the nonlinear free vibrations of curved pipes made of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) materials are investigated. It is assumed that the FG-CNTRC curved pipe is supported on a three-parameter nonlinear elastic foundation and is subjected to a uniform temperature rise. Properties of the curved nanocomposite pipe are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite pipe are temperature-dependent. The governing equations of the curved pipe are obtained using a higher order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the pipe. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved nanocomposite pipe. For the case of nanocomposite curved pipes which are simply supported in flexure and axially immovable, the motion equations are solved using the two-step perturbation technique. The closed-form expressions are provided to obtain the small- and large-amplitude frequencies of FG-CNTRC curved pipes rested on a nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of CNT distribution pattern, the CNT volume fraction, thermal environment, nonlinear foundation stiffness, and geometrical parameters on the fundamental linear and nonlinear frequencies of the curved nanocomposite pipe.

• Advances in nano research
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• 제16권5호
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• pp.473-487
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• 2024

The current study employs the nonlocal Timoshenko beam (NTB) theory and von-Kármán's geometric nonlinearity to develop a non-classic beam model for evaluating the nonlinear free vibration of bi-directional functionally-graded (BFG) nanobeams. In order to avoid the stretching-bending coupling in the equations of motion, the problem is formulated based on the physical middle surface. The governing equations of motion and the relevant boundary conditions have been determined using Hamilton's principle, followed by discretization using the differential quadrature method (DQM). To determine the frequencies of nonlinear vibrations in the BFG nanobeams, a direct iterative algorithm is used for solving the discretized underlying equations. The model verification is conducted by making a comparison between the obtained results and benchmark results reported in prior studies. In the present work, the effects of amplitude ratio, nanobeam length, material distribution, nonlocality, and boundary conditions are examined on the nonlinear frequency of BFG nanobeams through a parametric study. As a main result, it is observed that the nonlinear vibration frequencies are greater than the linear vibration frequencies for the same amplitude of the nonlinear oscillator. The study finds that the difference between the dimensionless linear frequency and the nonlinear frequency is smaller for CC nanobeams compared to SS nanobeams, particularly within the α range of 0 to 1.5, where the impact of geometric nonlinearity on CC nanobeams can be disregarded. Furthermore, the nonlinear frequency ratio exhibits an increasing trend as the parameter µ is incremented, with a diminishing dependency on nanobeam length (L). Additionally, it is established that as the nanobeam length increases, a critical point is reached at which a sharp rise in the nonlinear frequency ratio occurs, particularly within the nanobeam length range of 10 nm to 30 nm. These findings collectively contribute to a comprehensive understanding of the nonlinear vibration behavior of BFG nanobeams in relation to various parameters.

• 한국해양환경ㆍ에너지학회지
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• 제6권2호
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• pp.54-62
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• 2003

해저배관은 지반쇄굴로 인하여 일부분이 노출되어 자유경간이 형성될 수 있다. 자유경간이 형성되면 환경하중 및 와동유기진동에 의해서 안정성을 잃을 수 있다. 본 연구에서는 해저배관의 안정성을 위협하는 중요 요소인 자유경간의 정적 및 동적 경간을 결정하는 방법을 제시한다. 자유경간 해석에서는 해저배관에 작용하는 압축력 효과를 고려하였으며 토양의 종류에 따라 경계조건을 일반화시켰다. 자유경간 양단의 해저지반은 탄성기초로 간주하였으며, 이들 선형 및 회전 스프링으로 치환하여 경계조건을 일반화시켰다. 정적 및 동적 자유경간의 길이를 산정 할 수 있는 무차원화 된 곡선을 구하였다. 예제해석을 수행하여 그 적용방법을 소개하였다. 본 연구결과는 자유경간을 갖는 해저배관의 설계에 유용하게 적용될 수 있다.