• 한국소음진동공학회논문집
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• 제20권5호
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• pp.453-459
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• 2010

In this paper, the purpose is to investigate the stability of cracked cantilever T-beams subjected to axial force. In addition, an analysis of the natural frequency of a cracked beams as crack position, crack depth and tip mass is investigated. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by the energy expressions using extended Hamilton's Principle. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The results of this study will contribute to the safety test and stability estimation of structures of a cracked T-beams subjected to axial force.

• 한국기계가공학회지
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• 제9권3호
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• pp.49-55
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• 2010

In this paper, the stability of cracked cantilever T-beams subjected to subtangential follower force is investigated. Also, the effect of subtangential coefficient and crack on the natural frequency of T-beams is presented. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by the energy expressions using extended Hamilton's Principle. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The values of critical follower force and the stability maps of cantilever T-beams are obtained according to the subtangential coefficient and crack severity. The results of this study will contribute to the safety testing and the stability estimation of cracked T-beams subjected to follower force.

• 한국기계가공학회지
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• 제9권6호
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• pp.78-86
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• 2010

This paper aims to investigate the natural frequency of a cracked cantilever L-beams with a coupled bending and torsional vibrations. In addition, a theoretical method for detection of the crack position and size in a cantilever L-beams is presented based on natural frequencies. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using extended Hamilton's Principle. The dynamic transfer matrix method is used for calculation of a exact natural frequencies of L-beams. In order to detect the crack of L-beams, the effect of spring coefficients for bending moment and torsional force is included. In this study, the differences between the actual data and predicted positions and sizes of crack are less than 0.5% and 6.7% respectively.

• Advances in nano research
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• 제6권3호
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• pp.201-217
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• 2018

In the present research, wave propagation characteristics of a rotating FG nanobeam undergoing rotation is studied based on nonlocal strain gradient theory. Material properties of nanobeam are assumed to change gradually across the thickness of nanobeam according to Mori-Tanaka distribution model. The governing partial differential equations are derived for the rotating FG nanobeam by applying the Hamilton's principle in the framework of Euler-Bernoulli beam model. An analytical solution is applied to obtain wave frequencies, phase velocities and escape frequencies. It is observed that wave dispersion characteristics of rotating FG nanobeams are extremely influenced by angular velocity, wave number, nonlocal parameter, length scale parameter, temperature change and material graduation.

• Structural Engineering and Mechanics
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• 제64권6권
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• pp.723-730
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• 2017

This paper studies on dynamic and stability behavior of a clamped-elastically restrained nanobeam under the action of a nonconservative force with an emphasis on the influence of surface properties on divergence and flutter instability. Using the Euler-Bernoulli beam theory incorporating surface effects, a governing equation for a clamped-elastically restrained nanobeam is derived according to Hamilton's principle. The characteristic equation is obtained explicitly and the force-frequency interaction curves are displayed to show the influence of the surface effects, spring stiffness of the elastic restraint end on critical loads including divergence and flutter loads. Divergence and flutter instability transition is analyzed. Euler buckling and stability of Beck's column are some special cases of the present at macroscale.

• Interaction and multiscale mechanics
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• 제5권4호
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• pp.385-397
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• 2012

In this paper the dynamic stiffness matrix method was used for the free vibration analysis of axially moving micro beam with constant velocity. The extended Hamilton's principle was employed to derive the governing differential equation of the problem using the modified couple stress theory. The dynamic stiffness matrix of the moving micro beam was evaluated using appropriate expressions of the shear force and bending moment according to the Euler-Bernoulli beam theory. The effects of the beam size and axial velocity on the dynamic characteristic of the moving beam were investigated. The natural frequencies and critical velocity of the axially moving micro beam were also computed for two different end conditions.

• 동력기계공학회지
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• 제10권2호
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• pp.68-74
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• 2006

In the development of new automobiles, the efforts to reduce environmental problems like air pollution have been risen. Blowby gas consists of about $20{\sim}35%$ of total amount of Hydrocarbon (HC), one of dangerous pollutants issuing from automobiles. A PCV valve is a very small component in an automotive engine but it is a very important part. Because that a PCV valve is used to control blowby gas and to recirculate it into a manifold automatically. Although it has very simple operating principle, designing a PCV valve is so difficult due to interaction between fluid and solid. In this study, our purpose is to develop a design program for a PCV valve and to verify its efficiency. Both Bernoulli equation and 4th order Runge-Kutta method were adopted to predict spool displacements and flow patterns. Comparing with experiments, it was found that both spool diameters and displacements were predicted well, however, flow rates showed a little differences because of the assumption of non viscous flow.

• 한국소음진동공학회논문집
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• 제17권11호
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• pp.1119-1126
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• 2007

In this paper, the dynamic stability of a cracked cantilever pipe conveying fluid with tip mass is investigated. The pipe is modelled by the Euler-Bernoulli beam theory in which rotatory inertia and shear deformation effects are ignored. 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 the crack severity, the position of crack, the mass ratio, and a tip mass on the stability of a cantilever pipe conveying fluid are studied by the numerical method. Besides, the critical flow velocity and the stability maps of the pipe system as a function of mass ratios($\beta$) for the changing each parameter are obtained.

• 한국정밀공학회지
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• 제28권8호
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• pp.951-958
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• 2011

In this paper, the purpose is to investigate the vibration characteristics and the design of resonance avoidance of the unmanned helicopter master. Based on the Euler-Bernoulli beam theory for helicopter master, the equation of motion is derived by using extended Hamilton's principle. It was studied about the natural frequency of helicopter master as the design variances(tip mass, length and diameter of master). Also, it was compared the theoretical results for natural frequency with the results of FE analysis. The results of this study showed the vibration characteristics of helicopter master for the design of resonance avoidance.

• Advances in materials Research
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• 제6권2호
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• pp.93-128
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• 2017

In this paper, thermal vibration behavior of nanoscale beams made of functionally graded (FG) materials subjected to various types of thermal loading are investigated. A Reddy shear deformation beam theory which captures both the microstructural and shear deformation effects without the need for any shear correction factors is employed. Material properties of FG nanobeam are assumed to be temperature-dependent and vary gradually along the thickness according to the power-law form. The influence of small scale is captured based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. The comparison of the obtained results is conducted with those of nonlocal Euler-Bernoulli beam theory and it is demonstrated that the proposed modeling predict correctly the vibration responses of FG nanobeams. The effects of nonlocal parameter, material graduation, mode number, slenderness ratio and thermal loading on vibration behavior of the nanobeams are studied in detail.