• Structural Engineering and Mechanics
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• 제76권4호
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• pp.451-463
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• 2020

In this paper, a new semi-analytical solution for estimating the pull-in parameters of electrically actuated functionally graded (FG) nanobeams is proposed. All the bulk and surface material properties of the FG nanoactuator vary continuously in thickness direction according to power law distribution. Here, the modified couple stress theory (MCST) and Gurtin-Murdoch surface elasticity theory (SET) are jointly employed to capture the size effects of the nanoscale beam in the context of Euler-Bernoulli beam theory. According to the MCST and SET and accounting for the mid-plane stretching, axial residual stress, electrostatic actuation, fringing field, and dispersion (Casimir or/and van der Waals) forces, the nonlinear nonclassical equation of motion and boundary conditions are obtained derived using Hamilton principle. The proposed semi-analytical solution is derived by employing Galerkin method in conjunction with the Particle Swarm Optimization (PSO) method. The proposed solution approach is validated with the available literature. The freestanding behavior of nanoactuators is also investigated. A parametric study is conducted to illustrate the effects of different material and geometrical parameters on the pull-in response of cantilever and doubly-clamped FG nanoactuators. This model and proposed solution are helpful especially in mechanical design of micro/nanoactuators made of FGMs.

• Steel and Composite Structures
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• 제28권2호
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• pp.149-165
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• 2018

Using the modified couple stress theory and Euler-Bernoulli beam theory, this paper studies nonlinear vibration analysis of microbeams resting on the nonlinear orthotropic visco-Pasternak foundation. Using the Hamilton's principle, the set of the governing equations are derived and solved numerically using differential quadrature method (DQM), Newark beta method and arc-length technique for all kind of the boundary conditions. First convergence and accuracy of the presented solution are demonstrated and then effects of radius of gyration, Poisson's ratio, small scale parameters, temperature changes and coefficients of the foundation on the linear and nonlinear natural frequencies and dynamic response of the microbeam are investigated.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 추계학술대회논문집
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• pp.784-789
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• 2000

Equations of motion are derived and solved using the finite element method substructure synthesis for the disk-spindle system with rigid spindle and flexible shaft. The disk is modeled as a flexible spinning disk by Kirchhoff plate theory and von Karman nonlinear strain. The spindle supporting the flexible disk is modeled as a rigid body to consider its complex geometry. The stationary shaft supporting the rotating disk-spindle-bearing system is modeled by Euler beam, and the ball bearings are modeled as the stiffness matrix with 5 degrees of freedom. Developed theory is applied to analyze the vibration characteristics of a 3.5" HDD and a 2.5" HDD, respectively, and modal tests are performed to verify the simulation results. This paper shows that the developed theory can be effectively applied to the rotating disk-spindle system with the spindle of complex shape.

• Advances in aircraft and spacecraft science
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• 제4권3호
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• pp.269-280
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• 2017

The natural vibration analysis of microbeams resting on visco-Pasternak's foundation is presented. The thermoelasticity theory of Green and Naghdi without energy dissipation as well as the classical Euler-Bernoulli's beam theory is used for description of natural frequencies of the microbeam. The generalized thermoelasticity model is used to obtain the free vibration frequencies due to the coupling equations of a simply-supported microbeam resting on the three-parameter viscoelastic foundation. The fundamental frequencies are evaluated in terms of length-to-thickness ratio, width-to-thickness ratio and three foundation parameters. Sample natural frequencies are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak's parameters for future comparisons.

• Structural Engineering and Mechanics
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• 제78권1호
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• pp.103-116
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• 2021

In this work, a model of a functionally graded (FG) nanotube conveying fluid embedded in an elastic medium is developed based on the nonlocal strain gradient theory (NSGT) in conjunction with Euler-Bernoulli beam theory (EBT). The main objective of this research is to investigate the nonlinear vibration and stability analysis of fluid-conveying nanotubes. The governing equations of motion are derived by means of Hamiltonian principle. The analytical expressions of nonlinear frequencies and critical flow velocities for two different types of boundary conditions including pinned-pinned (P-P) and clamped-clamped (C-C) conditions are obtained by employing Galerkin method as well as Hamiltonian Approach (HA). Comparison of the obtained results with the published works show the acceptable accuracy of the current solutions. The effects of the power-law index, the nonlocal and material length scale parameters and the elastic medium on the stability and nonlinear responses of FG nanotubes are thoroughly investigated and discussed.

• Structural Engineering and Mechanics
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• 제61권2호
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• pp.193-207
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• 2017

In this study, the vibration of an electrostatically actuated micro cantilever beam is analyzed in which a viscoelastic layer covers a portion of the micro beam length. This proposed model is considered as the main element of mass and pollutant micro sensors. The nonlinear motion equation is extracted by means of Hamilton principle, considering nonlinear shortening effect for Euler-Bernoulli beam. The non-linear effects of electrostatic excitation, geometry and inertia have been taken into account. The viscoelastic model is assumed as Kelvin-Voigt model. The motion equation is discretized by Galerkin approach. The linear free vibration mode shapes of non-uniform micro beam i.e. the linear mode shape of the system by considering the geometric and inertia effects of viscoelastic layer, have been employed as comparison function in the process of the motion equation discretization. The discretized equation of motion is solved by the use of multiple scale method of perturbation theory and the results are compared with the results of numerical Runge-Kutta approach. The frequency response variations for different lengths and thicknesses of the viscoelastic layer have been founded. The results indicate that if a constant volume of viscoelastic layer is to be deposited on the micro beam for mass or gas sensor applications, then a modified configuration may be found by using the analysis of this paper.

• Steel and Composite Structures
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• 제35권4호
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• pp.555-566
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• 2020

This paper aims to present an analytical methodology to investigate influences of nanoscale and surface energy on buckling stability behavior of perforated nanobeam structural element, for the first time. The surface energy effect is exploited to consider the free energy on the surface of nanobeam by using Gurtin-Murdoch surface elasticity theory. Thin and thick beams are considered by using both classical beam of Euler and first order shear deformation of Timoshenko theories, respectively. Equivalent geometrical constant of regularly squared perforated beam are presented in simplified form. Problem formulation of nanostructure beam including surface energies is derived in detail. Explicit analytical solution for nanoscale beams are developed for both beam theories to evaluate the surface stress effects and size-dependent nanoscale on the critical buckling loads. The closed form solution is confirmed and proven by comparing the obtained results with previous works. Parametric studies are achieved to demonstrate impacts of beam filling ratio, the number of hole rows, surface material characteristics, beam slenderness ratio, boundary conditions as well as loading conditions on the non-classical buckling of perforated nanobeams in incidence of surface effects. It is found that, the surface residual stress has more significant effect on the critical buckling loads with the corresponding effect of the surface elasticity. The proposed model can be used as benchmarks in designing, analysis and manufacturing of perforated nanobeams.

• Advances in aircraft and spacecraft science
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• 제11권1호
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• 대한조선학회논문집
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• 제38권3호
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• pp.41-46
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• 2001

최근에 선박이 대형화되는 추세에 힘입어 조선소는 광폭천흘수선, 초대형 원유운반선 및 초대형 컨테이너선 등을 건조하고 있다. 이와 같은 선박은 상대적으로 다른 선박에 비해 강성이 작기 때문에 파랑 중에서 유탄성 운동을 하게 되고, 입사하는 파고가 작은 경우에도 선체의 2절 모드의 진동에 의해 선체의 갑판이 피로 파괴되는 경우가 종종 발생하는 것으로 알려져 있다. 본 논문에서 전진하는 선박의 유체 압력을 계산하기 위해 적분방정식은 3차원 소오스 분포법을 사용하고, 그린함수는 전진하면서 동요하는 형태를 이용하였다. 방사문제는 선박을 여러 개의 단면으로 나누어 단면간의 간섭효과를 고려하여 heave 및 pitch 강제동요와 관련된 부가질량 및 조파 감쇠계수를 계산하였고, 파강제력은 각 단면에서 선행해에 의한 힘만 고려하였다. 선박의 각 단면의 수직운동은 선박에 대한 운동방정식을 이용하고 강성행렬은 오일러 보 이론에 의해 산정되었다. 계산은 Esso-Osaka 선박을 모델로 도입하여 입사하는 파도의 주파수가 변함에 따른 선박의 각 단면에 대한 운동, 굽힘 모우멘트를 계산하였다.

• Structural Engineering and Mechanics
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• 제61권5호
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• pp.617-624
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• 2017

Piezoelectric nanobeams are used in several nano electromechanical systems. The first step in designing these systems is conducting a vibration analysis. In this research, the free vibration of a piezoelectric nanobeam is analyzed by using the nonlocal elasticity theory. The nanobeam is modeled based on Euler-Bernoulli beam theory. Hamilton's principle is used to derive the equations of motion and also the boundary conditions of the system. The obtained equations of motion are solved by using both Galerkin and the Differential Quadrature (DQ) methods. The clamped-clamped and cantilever boundary conditions are analyzed and the effects of the applied voltage and nonlocal parameter on the natural frequencies and mode shapes are studied. The results show the success of Galerkin method in determining the natural frequencies. The results also show the influence of the nonlocal parameter on the natural frequencies. Increasing a positive voltage decreases the natural frequencies, while increasing a negative voltage increases them. It is also concluded that for the clamped parts of the beam and also other parts that encounter higher values of stress during free vibrations of the beam, anti-nodes in voltage mode shapes are observed. On the contrary, in the parts of the beam that the values of the induced stress are low, the values of the amplitude of the voltage mode shape are not significant. The obtained results and especially the mode shapes can be used in future studies on the forced vibrations of piezoelectric nanobeams based on Galerkin method.