• Structural Engineering and Mechanics
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• 제53권3호
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• pp.537-573
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• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• Smart Structures and Systems
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• 제22권1호
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• pp.105-120
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• 2018

In this paper, the nonlinear free and forced vibration responses of sandwich nano-beams with three various functionally graded (FG) patterns of reinforced carbon nanotubes (CNTs) face-sheets are investigated. The sandwich nano-beam is resting on nonlinear Visco-elastic foundation and is subjected to thermal and electrical loads. The nonlinear governing equations of motion are derived for an Euler-Bernoulli beam based on Hamilton principle and von Karman nonlinear relation. To analyze nonlinear vibration, Galerkin's decomposition technique is employed to convert the governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). Furthermore, the Multiple Times Scale (MTS) method is employed to find approximate solution for the nonlinear time, frequency and forced responses of the sandwich nano-beam. Comparison between results of this paper and previous published paper shows that our numerical results are in good agreement with literature. In addition, the nonlinear frequency, force response and nonlinear damping time response is carefully studied. The influences of important parameters such as nonlocal parameter, volume fraction of the CNTs, different patterns of CNTs, length scale parameter, Visco-Pasternak foundation parameter, applied voltage, longitudinal magnetic field and temperature change are investigated on the various responses. One can conclude that frequency of FG-AV pattern is greater than other used patterns.

• Structural Engineering and Mechanics
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• 제81권5호
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• pp.607-616
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• 2022

In this work, the free vibration problem of a rotating Rayleigh beam is solved using the meshless Petrov-Galerkin method which is a truly meshless method. The Rayleigh beam includes rotatory inertia in addition to Euler-Bernoulli beam theory. The radial basis functions, which satisfy the Kronecker delta property, are used for the interpolation. The essential boundary conditions can be easily applied with radial basis functions. The results are obtained using six nodes within a subdomain. The results accurately match with the published literature. Also, the results with Euler-Bernoulli are obtained to compare the change in higher natural frequencies with change in the slenderness ratio (${\sqrt{A_0R^2/I_0}}$). The mass and stiffness matrices are derived where we get two stiffness matrices for the node and boundary respectively. The non-dimensional form is discussed as well.

• Advances in concrete construction
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• 제12권6호
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• pp.491-497
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• 2021

Cell components play vital role within the cell when the cell under goes deformation. These components are microtubules, microfilaments and intermediate filaments. Intermediate filaments are like thread and are of different types. Like microtubules and microfilaments these components also undergo the deformation and their dynamics affected when change occurs within cell. In the present study, bending of intermediate filaments are studied keeping the nonlocal effects under consideration. It is observed that the nonlocal parameter has a great impact on the dynamics of intermediate filaments. This study is made by the application of Euler beam theory.

• Structural Engineering and Mechanics
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• 제65권3호
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• pp.335-342
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• 2018

The transverse free vibration of chiral double-walled carbon nanotube (DWCNTs) embedded in elastic medium is modeled by the non-local elasticity theory and Euler Bernoulli beam model. The governing equations are derived and the solutions of frequency are obtained. According to this study, the vibrational mode number, the small-scale coefficient, the Winkler parameter and chirality of double-walled carbon nanotube on the frequency ratio (xN) of the (DWCNTs) are studied and discussed. The new features of the vibration behavior of (DWCNTs) embedded in an elastic medium and the present solutions can be used for the static and dynamic analyses of double-walled carbon nanotubes.

• Advances in nano research
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• 제15권1호
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• pp.15-23
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• 2023

Dynamics of protein filamentous has been an active area of research since the last few decades as the role of cytoskeletal components, microtubules, intermediate filaments and microfilaments is very important in cell functions. During cell functions, these components undergo the deformations like bending, buckling and vibrations. In the present paper, bending and buckling of microfilaments are studied by using Euler Bernoulli beam theory with nonlocal parametric effects in conjunction. The obtained results show that the nonlocal parametric effects are not ignorable and the applications of nonlocal parameters well agree with the experimental verifications.

• 대한기계학회논문집
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• 제16권8호
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• pp.1513-1518
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• 1992

본 연구에서는 참고문헌 8의 해법을 응용하여 다발 보의 마찰 접촉 문제를 푸는 방법에 대하여 설명한다. 각 보 요소의 변형은 미소변형 및 Bernoulli-Euler이 론을 이용하여 계산하며, 마찰력 계산을 위하여는 Coulomb 마찰 법칙을 이용한다. 보의 종류와 형상 및 보를 묶는 클램프(clamp)의 종류에 따라서 수 많은 종류의 스프 링이 얻어 질 수 있다. 여기에서는 편의상 보 다발이 클램프에 의하여 강하게 묶여 있으며, 그 묶인 점에서는 각 보의 법선 방향(normal direction) 상대 운동은 없는 것 으로 간주한다.

• Structural Engineering and Mechanics
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• 제63권4호
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• pp.471-480
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• 2017

This paper investigates free vibration characteristics of a rotating functionally graded (FG) beam in hygro environments. In the present study, material properties of the FG beam vary continuously through thickness direction according to the power-law which approximates material properties of FG beam. The governing differential equations of motion are derived based on Euler-Bernoulli beam theory and using the Hamilton's principle which solved utilizing a semi-analytical technique called the Differential Transform Method (DTM). In order to verify the competency and accuracy of the current analysis, a comparative study with previous researches are performed and good agreement is observed. Influences of Several important parameters such as power-law exponent, hygro environment, rotational speed and slenderness ratio on natural frequencies are investigated and discussed in detail. It is concluded that these effects play significant role on dynamic behavior of rotating FG beam in the hygro environments. Numerical results are tabulated in several tables and figures that can be serving as benchmarks for future analyses of rotating FG beams in the hygro environments.

• 한국소음진동공학회논문집
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• 제13권7호
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• pp.555-561
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported Euler-Bernoulli beams with the moving masses. The influences of the velocities of moving masses, the distance between the moving masses and a crack have been studied on the dynamic behavior of a simply supported beam system by numerical method. The Presence of crack results In large deflection of beam. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. Totally, as the velocity of the moving masses and the distance between the moving masses are increased, the mid-span deflection of simply supported beam with the crack is decreased.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.1085-1090
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported Euler-Bernoulli beams with the moving masses. The influences of the velocities of moving masses, the distance between the moving masses and a crack have been studied on the dynamic behavior or a simply supported beam system by numerical method. no presence or crack results in large deflection of beam. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. Totally, as the velocity of the moving masses and the distance between the moving masses are increased, the mid-span deflection of simply supported beam with the crack is decreased.