• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.478-487
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• 1991

In this study, dynamic stability of discontinuous free Timoshenko beam, barring a concentrated mass, under constant follower force is considered. Governing differential equations are derived based on the extended Hamilton's principle and finite element method is applied for numerical analysis. Conclusions of the study are as follows : (1) Without force direction control, (i) the critical follower force at instability is increased with concentrated mass regardless of discontinuity. (ii) the minimum critical follower force is located in the vicinity of discontinuity position .xi.$_{d}$=0.75. (iii) at mass location .mu. .leq.0.5 the force at instability is decreased as magnitude of concentrated mass is increased but, at .mu. .geq. 0.5 the force is increased as the mass is increased. (2) With force direction control, (i) shear deformation parameter S contributes insignificantly to the force at instability when S>10$^{[-993]}$ (ii) maximum critical follower force can be obtained for the discontinuity location .xi.$_{d}$=0.25. (iii) the critical follower force is increased as magnitude of concentrated mass .alpha. is increased at mass location .mu. .geq.0.4, but is increased, .mu ..leq.0.4.4.

• Geomechanics and Engineering
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• v.23 no.3
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• pp.275-287
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• 2020

Rectangular barrettes have been increasingly used as foundations for many infrastructure projects, but the vertical vibration of a barrette has been rarely addressed theoretically. This paper presents an analysis method of dynamic response for a rectangular barrette subjected to a time-harmonic vertical force with the aid of a modified Vlasov foundation model in multilayered viscoelastic soil. The barrette-soil system is modeled as a continuum, the vertical continuous displacement model for the barrette and soil is proposed. The governing equations of the barrette-soil system and the boundary conditions are obtained and the vertical shaft resistance of barrette is established by employing Hamilton's principle for the system and thin layer element, respectively. The physical meaning of the governing equations and shaft resistance is interpreted. The iterative solution algorithm flow is proposed to obtain the dynamic response of barrette. Good agreement of the analysis and comparison confirms the correctness of the present solution. A parametric study is further used to demonstrate the effects of cross section aspect ratio of barrettes, depth of soil column, and module ratio of substratum to the upper soil layers on the complex barrette-head stiffness and the resistance stiffness.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.2
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• pp.217-224
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• 2016

In this study, a transfer matrix method (TMM) for a twisted uniform beam considering the effect of rotary inertia is developed, and the differential equation and the displacements and forces are derived from Hamilton's principle. The particular transfer matrix is derived by applying the distributed mass and transcendental function while using a local coordinate system. In addition, the results obtained from this method are independent for a number of subdivided elements, and this method can determine the exact solutions for the free vibration characteristics of a twisted uniform Rayleigh beam. To validate the accuracy of the proposed TMM, the computed results are compared with those reported in the existing literature, and the comparison results indicate notably good agreement. In addition, the method is used to investigate the effects of rotary inertia for a twisted beam.

• Geomechanics and Engineering
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• v.16 no.1
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• pp.1-9
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• 2018

In this paper an efficient and simple refined shear deformation theory is presented for the free vibration of Functionally Graded Plates Under Various Boundary Conditions. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. The plates are considered of the type having two opposite sides simply-supported, and the two other sides having combinations of simply-supported, clamped, and free boundary conditions. The mechanical properties of functionally graded material are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived using Hamilton's principle. The results of this theory are compared with those of other shear deformation theories. Various numerical results including the effect of boundary conditions, power-law index, plate aspect ratio, and side-to-thickness ratio on the free vibration of FGM plates are presented.

• Proceedings of the Korean Society For Composite Materials Conference
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• 1999.11a
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• pp.5-14
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• 1999

Free vibration characteristics of a cantilevered laminated composite beam with multiple non-propagating transverse open cracks are investigated. In the present analysis a special ply-angle distribution referred to as asymmetric stiffness configuration inducing the elastic coupling between chord-wise bending and extension is considered. The multiple open cracks are modelled as equivalent rotational springs whose spring constants are calculated based on the fracture mechanics of composite material structures. Governing equations of a composite beam with open cracks are derived via Hamilton's Principle and Timoshenko beam theory encompassing transverse shear and rotary inertia effect is adopted. The effects of various parameters such as the ply angle, fiber volume fraction, crack numbers, crack positions and crack depthes on the free vibration characteristics of the beam with multiple cracks are highlighted. The numerical results show that the existence of the multiple cracks in an anisotropic composite beam affects the free vibration characteristics in a more complex fashion compared with the beam with a single crack.

• Nuclear Engineering and Technology
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• v.23 no.3
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• pp.306-315
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• 1991

This paper considered the out-of-plane motion of the piping system conveying fluid through the elbow connecting two straight pipes. The extended Hamilton's principle is used to derive equations of motion. It is found that dynamic instability does not exist for the clamped-clamped, clamped-pinned and pinned-pinned boundary conditions. The frequency equations for each boundary conditions are solved numerically to find the natural frequencies. The effects of fluid velocity and Coriolis force on the natural frequencies of piping system are investigated. It is shown that buckling-type instability may occur at certain critical velocities and fluid pressures. Equivalent critical velocity, which is defined as a function of flow velocity and fluid pressure, are calculated for various boundary conditions.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.161-169
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• 2017

In this paper, using consistent couple stress theory and Hamilton's principle, the free vibration analysis of Euler-Bernoulli nano-beams made of bi-directional functionally graded materials (BDFGMs) with small scale effects are investigated. To the best of the researchers' knowledge, in the literature, there is no study carried out into consistent couple-stress theory for free vibration analysis of BDFGM nanostructures with arbitrary functions. In addition, in order to obtain small scale effects, the consistent couple-stress theory is also applied. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in both axial and thickness directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of Hamilton principle. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of BDFG nano-beam. At the end, some numerical results are presented to study the effects of material length scale parameter, and inhomogeneity constant on natural frequency.

• Journal of Mechanical Science and Technology
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• v.16 no.4
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• pp.512-521
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• 2002

The flap-lag-torsion coupled aeroelastic behavior of a hingeless rotor blade with composite flexures in hovering flight has been investigated by using the finite element method. The quasisteady strip theory with dynamic inflow effects is used to obtain the aerodynamic loads acting on the blade. The governing differential equations of motion undergoing moderately large displacements and rotations are derived using the Hamilton's principle. The flexures used in the present model are composed of two composite plates which are rigidly attached together. The lead-lag flexure is located inboard of the flap flexure. A mixed warping model that combines the St. Versant torsion and the Vlasov torsion is developed to describe the twist behavior of the composite flexure. Numerical simulations are carried out to correlate the present results with experimental test data and also to identify the effects of structural couplings of the composite flexures on the aeroelastic stability of the blade. The prediction results agree well with other experimental data. The effects of elastic couplings such as pitch-flap, pitch-lag, and flap-lag couplings on the stability behavior of the composite blades are also investigated.

• Wind and Structures
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• v.29 no.6
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• pp.371-387
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• 2019

In the present paper, a simple refined nth-higher-order shear deformation theory is applied for the free vibration analysis of laminated composite plates. The proposed displacement field is based on a novel kinematic in which include the undetermined integral terms and contains only four unknowns, as against five or more in case of other higher-order theories. The present theory accounts for adequate distribution of the transverse shear strains through the plate thickness and satisfies the shear stress-free boundary conditions on the top and bottom surfaces of the plate, therefore, it does not require problem dependent shear correction factor. The governing equations of motion are derived from Hamilton's principle and solved via Navier-type to obtain closed form solutions. The numerical results of non-dimensional natural frequencies obtained by using the present theory are presented and compared with those of other theories available in the literature to verify the validity of present solutions. It can be concluded that the present refined theory is accurate and efficient in predicting the natural frequencies of isotropic, orthotropic and laminated composite plates.

• Computers and Concrete
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• v.26 no.1
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• pp.31-52
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• 2020

This paper investigates the size dependent effect on the vibration analysis of a porous nanocomposite viscoelastic plate reinforced by functionally graded-single walled carbon nanotubes (FG-SWCNTs) by considering nonlocal strain gradient theory. Therefore, using energy method and Hamilton's principle, the equations of motion are derived. In this article, the effects of nonlocal parameter, aspect ratio, strain gradient parameter, volume fraction of carbon nanotubes (CNTs), damping coefficient, porosity coefficient, and temperature change on the natural frequency are perused. The innovation of this paper is to compare the effectiveness of each mentioned parameters individually on the free vibrations of this plate and to represent the appropriate value for each parameter to achieve an ideal nanocomposite plate that minimizes vibration. The results are verified with those referenced in the paper. The results illustrate that the effect of damping coefficient on the increase of natural frequency is significantly higher than the other parameters effect, and the effects of the strain gradient parameter and nonlocal parameter on the natural frequency increase are less than damping coefficient effect, respectively. Furthermore, the results indicate that the natural frequency decreases with a rise in the nonlocal parameter, aspect ratio and temperature change. Also, the natural frequency increases with a rise in the strain gradient parameter and CNTs volume fraction. This study can be used for optimizing the industrial and medical designs, such as automotive industry, aerospace engineering and water purification system, by considering ideal properties for the nanocomposite plate.