• Steel and Composite Structures
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• v.24 no.1
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• pp.65-77
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• 2017

The purpose of this research is to study the nonlinear free vibration and post-buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams resting on a nonlinear elastic foundation. Uniformly and functionally graded distributions of single walled carbon nanotubes as reinforcing phase are considered in the polymeric matrix. The modified form of rule of mixture is used to estimate the material properties of CNTRC beams. The governing equations are derived employing Euler-Bernoulli beam theory along with energy method and Hamilton's principle. Applying von $K\acute{a}rm\acute{a}n's$ strain-displacement assumptions, the geometric nonlinearity is taken into consideration. The developed governing equations with quadratic and cubic nonlinearities are solved using variational iteration method (VIM) and the analytical expressions and numerical results are obtained for vibration and stability analysis of nanocomposite beams. The presented comparative results are indicative for the reliability, accuracy and fast convergence rate of the solution. Eventually, the effects of different parameters, such as foundation stiffness, volume fraction and distributions of carbon nanotubes, slenderness ratio, vibration amplitude, coefficients of elastic foundation and boundary conditions on the nonlinear frequencies, vibration response and post-buckling loads of FG-CNTRC beams are examined. The developed analytical solution provides direct insight into parametric studies of particular parameters of the problem.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.10
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• pp.3186-3198
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• 1996

When a robot is to have contact with its enviornment, such as a medi-care robot, it would be advantageous for the robot to have a high compliance. For this reason, a robot having not only a flexible link but also an actuator with compliance, is desirable. This paper is concerned with the position and vibration control of 1 degree of freedom flexible robot using a pneumatic artificial muscle actuator. The dynamics of the manipulator assumed to be and Euler-Bernoulli beam are derived on the basis of the linear mathematical modle. Although this pneumatic artifical muscle actuator has many merits for the compliance robot, it is difficult to make an effective control scheme of this system because of ths nonlinearity and uncertainty on the dynamics of the actuator. By designing a controller using .mu.-synthesis, robust performance against measurement noise, various modeling uncertainties on the dynamics of the servo valve, actuator and mainpulator, is achieved. The effectiveness of the proposed control method is illustrated through simulations and experiments.

• Geomechanics and Engineering
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• v.23 no.5
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• pp.405-418
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• 2020

Deep excavation may have impact on the adjacent tunnels. It is obvious that the excavation will adversely affect and even damage the existing tunnels if the induced deformation exceeds the capacity of tunnel structures. It hence creates a high necessity to predict tunnel displacement induced by nearby excavation to ensure the safety of tunnel. In this paper, a simplified method to evaluate the heave of the underlying tunnel induced by adjacent excavation is presented and verified by field measurement results. In the proposed model, the tunnel is represented by a series of short beams connected by tensile springs, compressional springs and shear springs, so that the rotational effect and shearing effect of the joints between lining rings can be captured. The proposed method is compared with the previous modelling methods (e.g., Euler-Bernoulli beam, a series of short beams connected only by shear springs) based on a field measured longitudinal deformation of subway tunnels. Results of these case studies show a reasonable agreement between the predictions and observations.

• Structural Engineering and Mechanics
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• v.30 no.2
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• pp.165-176
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• 2008

In this paper, a new iterative method for solving vehicle-bridge interaction problems is proposed. Iterative methods have advantages over the non-iterative methods in that it is not necessary to update the system matrix for a given wheel location, and the method can be applied for a new type of car or bridge with few or no modifications. In the proposed method, the necessity of system matrices update is eliminated using the equivalent interaction force acting on the bridge, which is obtained iteratively. Ballast stiffness is included in the interaction forces and the geometric compatibility at the contact points are used as convergence criteria. The bridge is considered as an elastic Bernoulli-Euler beam with surface irregularity and ballast stiffness. The moving vehicle is modeled as a multi-axle mass-spring-damper system having many degrees of freedom depending on the number of axles. The pitching effect, which is the interaction effect between the rear and front wheels when a vehicle begins to enter or leave the bridge, is also considered in the formulation including extended ground boundaries having surface irregularity and ballast stiffness. The applicability of the proposed method is illustrated in the numerical studies.

• Smart Structures and Systems
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• v.18 no.5
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• pp.1029-1062
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• 2016

In this research, the nonlinear free vibration analysis of boron-nitride micro ribbon (BNMR) on the Pasternak elastic foundation under electrical, mechanical and thermal loadings using modified strain gradient theory (MSGT) is studied. Employing the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear geometry theory, the nonlinear equations of motion for the graphene micro ribbon (GMR) using Euler-Bernoulli beam model with considering attached mass and size effects based on Hamilton's principle is obtained. These equations are converted into the nonlinear ordinary differential equations by elimination of the time variable using Kantorovich time-averaging method. To determine nonlinear frequency of GMR under various boundary conditions, and considering mass effect, differential quadrature element method (DQEM) is used. Based on modified strain MSGT, the results of the current model are compared with the obtained results by classical and modified couple stress theories (CT and MCST). Furthermore, the effect of various parameters such as material length scale parameter, attached mass, temperature change, piezoelectric coefficient, two parameters of elastic foundations on the natural frequencies of BNMR is investigated. The results show that for all boundary conditions, by increasing the mass intensity in a fixed position, the linear and nonlinear natural frequency of the GMR reduces. In addition, with increasing of material length scale parameter, the frequency ratio decreases. This results can be used to design and control nano/micro devices and nano electronics to avoid resonance phenomenon.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.171-180
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• 2017

Static and dynamic instability of a viscoelastic carbon nanotube (CNT) embedded on a thermo-elastic foundation are investigated, in this research. The CNT is modeled based on Euler-Bernoulli beam (EBB) and nonlocal small scale elasticity theory is utilized to analyze the structure. Governing equations of the system are derived using Hamilton's principle and differential quadrature (DQ) method is applied to solve the partial differential equations. The effects of variable axial load and diverse boundary conditions on static/vibration instability are studied. To verify the result of the DQ method, the Galerkin weighted residual approach is used for the instability analysis. It is observed appropriate agreement for results of two different solution methods and satisfactory accuracy with those obtained in prior studies. The results of this work could be useful for engineers and designers in order to produce and design nano/micro structures in thermo-elastic medium.

• Smart Structures and Systems
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• v.21 no.5
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• pp.677-686
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• 2018

The structural responses are often used to identify the structural local damages. However, it is usually difficult to gain the responses of the track, as the sensors cannot be installed on the track directly. The vehicles running on a track excite track vibration and can also serve as response receivers because the vehicle dynamic response contains the vibration information of the track. A damage identification method using the vehicle responses and sensitivity analysis is proposed for the vehicle-track coupling system in this paper. Different from most damage identification methods of vehicle-track coupling system, which require the structural responses, only the vehicle responses are required in the proposed method. The local damages are identified by a sensitivity-based model updating process. In the vehicle-track coupling system, the track is modeled as a discrete point supported Euler-Bernoulli beam, and two vehicle models are proposed to investigate the accuracy and efficiency of damage identification. The measured track irregularity is considered in the calculation of vehicle dynamic responses. The measurement noises are also considered to study their effects to the damage identification results. The identified results demonstrate that the proposed method is capable to identify the local damages of the track accurately in different noise levels with only the vehicle responses.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.2
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• pp.177-184
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• 2008

The dynamic stability of elastically restrained cantilever pipe conveying fluid with crack is investigated in this paper. The pipe, which is fixed at one end, is assumed to rest on an intermediate spring support. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by the energy expressions using extended Hamilton's Principle. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influence of a crack severity and position, mass ratio and the velocity of fluid flow on the stability of a cantilever pipe by the numerical method are studied. Also, the critical flow velocity for the flutter and divergence due to variation in the support location and the stiffness of the spring support is presented. The stability maps of the pipe system are obtained as a function of mass ratios and effect of crack.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.5 s.98
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• pp.586-594
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• 2005

In this paper, we studied about the effects of the rotating cantilever pipe conveying fluid with a moving mass. The influences of a rotating angular velocity, the velocity of fluid flow and moving mass on the dynamic behavior of a cantilever pipe have been studied by the numerical method. The equation of motion is derived by using the Lagrange's equation. The cantilever pipe is modeled by the Euler-Bernoulli beam theory. When the velocity of a moving mass is constant, the lateral tip-displacement of a cantilever pipe is proportional to the moving mass and the angular velocity. In the steady state, the lateral tip-displacement of a cantilever pipe is more sensitive to the velocity of fluid than the angular velocity, and the axial deflection of a cantilever pipe is more sensitive to the effect of a angular velocity. Totally, as the moving mass is increased, the frequency of a cantilever pipe is decreased in steady state.

• Geomechanics and Engineering
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• v.1 no.2
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• pp.121-142
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• 2009

The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the $LDL^T$ decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major's method for dynamic analysis of machine supporting structures is modified and the plane frames are replaced with springs of exact dynamic stiffness and dynamically flexible longitudinal frames. Results of the analysis are compared with exact values. The possible simplifications that could be introduced for a typical machine induced excitation on a framed structure are illustrated and the developed program is modified to account for dynamic constraint equations with a master slave degree of freedom (DOF) option.