• Wind and Structures
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• v.21 no.3
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• pp.273-287
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• 2015

In this paper, a free vibration analysis of functionally graded beam made of porous material is presented. The material properties are supposed to vary along the thickness direction of the beam according to the rule of mixture, which is modified to approximate the material properties with the porosity phases. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Geomechanics and Engineering
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• v.9 no.3
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• pp.361-372
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• 2015

In this paper, a refined exponential shear deformation theory for free vibration analysis of functionally graded beam with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Journal of the Korea Society for Simulation
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• v.7 no.2
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• pp.105-114
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• 1998

Using finite elements, a simulation is prformed for the pipe systems to investigate free vibrational characteristics, that is natural frequencies, considering the intial tension due to the velocity and the pressure of the inside fluid flow. To confirm the program developed in this study, the results are compared with the results of commercial software ANSYS. When the initial tension is neglected in curved pipes, the natural frequencies are reduced as flow velocity increases, and the rapid decreases of the natural frequencies took place. However, when the initial tension is taken into account, the natural frequencies are not changed with the change of the flow velocity. In free vibrational simulation of pipe systems, it is necessary to calculate the initial state force due to the velocity and the pressure of the fluid flow from the equilibrium first, then the force should be included in the equation of motion of the systems to get more accurate natural frequencies.

• Structural Engineering and Mechanics
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• v.34 no.5
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• pp.549-561
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• 2010

In this paper, free vibration analyses of a parallel placed twin pipe system simulated by simply supported-simply supported and fixed-fixed Euler-Bernoulli beams resting on Winkler elastic soil are presented. The motion of the system is described by a homogenous set of two partial differential equations, which is solved by a simulation method called the Differential Transform Method (DTM). Free vibrations of an elastically connected twin pipe system are realized by synchronous and asynchronous deflections. The results of the presented theoretical analyses for simply supported Euler-Bernoulli beams are compared with existing ones in open literature and very good agreement is demonstrated.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.6
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• pp.57-65
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• 1994

A collision-free path planning algorithm between an articulated robot and polyhedral obstacles using configuration space is presented. In configuration space, a robot is treated as a point and obstacles are treated as grown forbidden regions. Hence path planning problem is transformed into moving a point from start position to goal position without entering forbidden regions. For mapping to 3D joint space, slice projection method is used for first revolute joint and inverse kinematics is used for second and third revolute joint considering kinematic characteristics of industrial robot. Also, three projected 2D joint spaces are used in search of collision-free path. A proper example is provided to illustrate the proposed algorithm.

• Journal of the Korean Society for Precision Engineering
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• v.3 no.2
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• pp.28-38
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• 1986

An analytical and experimental investigation is made to the dynamic responese of a cantilever with a tip mass that models some of the basic phenomena involved in the response of a flexible manipulator with a tip mass on its free end under the given rotating motion. The system equation is derived from the Hamilton's principle on the basis of the Euler-Bernoulli hypothesis and an approximate solution is obtained from model analysis using Galerkin's method for the vibation response of the system subjected to a sudden stop after an impulsive rotation. Experiment was performed to verify the validity of the theoretical analysis. Results are given for the vibration amplitude of the free end with respect to tip mass ratio, non-dimensionalized rotating velocity, rotating angle and non- dimensionalized hub length. The rotating condition to minimize the vibration amplitude of the free end can be determined for the given basic paramenters.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.6 s.123
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• pp.531-538
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• 2007

A new method for free nitration analysis using series functions is proposed to obtain the eigenvalues of arbitrarily shaped, polygonal plates with clamped edges. Since a general solution used in the method satisfies the equation of motion for the transverse vibration of a plate, the method offers very accurate eigenvalues, compared to FEM or BEM results. In addition, the method can minimize the amount of numerical calculation because it has the advantage of not needing to divide the plate of interest. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM (NASTRAN) or another analytical method.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.37-52
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• 2020

This paper investigates the free and forced longitudinal vibration of a double nanorod system using doublet mechanics theory. The doublet mechanics theory is a multiscale theory spanning between lattice dynamics and continuum mechanics. Equations of motion and boundary conditions for the double nanorod system are obtained using Hamilton's principle. Clamped-clamped and clamped-free boundary conditions are considered. Frequencies and dynamic displacements are determined to demonstrate the effects of length scale parameter of considered material and geometry of the nanorods. It is shown that frequencies obtained by the doublet mechanics theory are bounded from above (van Hove singularity) and unlike classical elasticity theory doublet mechanics theory predicts finite number of modes depending on the length of the nanotube. The present doublet mechanics results have been compared to molecular dynamics, experimental and nonlocal theory results and good agreement is observed between the present and other mentioned results. The difference between wave frequencies of graphite is less than 10% between doublet mechanics and experimental results near to the end of the first Brillouin zone.

• Steel and Composite Structures
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• v.33 no.4
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• pp.473-487
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• 2019

A shear-deformable finite element model (FEM) with five nodes and thirteen degrees of freedom (DOFs) for free vibrations of laminated composite beams with arbitrary lay-up is presented. This model can be capable of considering the elastic couplings among the extensional, bending and torsional deformations, and the Poisson's effect. Lagrange's principle is employed in derivation of the equations of motion, and thus the element matrices are obtained. Comparisons of the present element's results with those in experiment, available literature and the 3D finite element analysis software (ANSYS(R)) are made to show its accuracy. Some further results are given as referencing for the future studies in vibrations of laminated composite beamst.

• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.97-112
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• 2019

Using the classical, first order and third order shear deformation plates theories the motion equations of an undrained porous FG circular plate which is located on visco-Pasternak elastic foundation have been derived and used for free vibration analysis thereof. Strains are related to displacements by Sanders relationship. Fluid has saturated the pores whose distribution varies through the thickness according to three physically probable given functions. The equations are discretized and numerically solved by the generalized differential quadrature method. The effect of porosity, pores distribution, fluid compressibility, viscoelastic foundation and aspect ratio of the plate on its vibration has been considered.