• Coupled systems mechanics
• /
• 제7권3호
• /
• pp.321-331
• /
• 2018

When a cantilever beam with a lumped mass at its free end undergoes free transverse vibration, internal axial forces are produced in the beam. Such internal axial forces have an effect on free transverse vibration of the beam. This effect is studied in this paper. The equations of motion for the beam in terms of the generalized coordinates including the effect are derived. The method for determining free transverse vibration of the beam including the effect is presented. In numerical simulations, the results of free transverse vibration of the free end of the beam including and not including the effect are obtained. Based on comparison between the results obtained, the conclusions concerning the effect are given.

• 소음진동
• /
• 제9권5호
• /
• pp.1019-1028
• /
• 1999

Free vibration characteristics of cantilevered laminated composite beams with a transverse non0propagating open carck 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 open crack is modelled as an equivalent rotational spring whose spring constant is calculated on the basis of fracture mechanics of composite material structures. Governing equations of a composite beam with a open crack are derived via Hamilton's Principle and Timoshenko beam theory encompassing transverse shear and rotary inertia effect. the effects of various parameters such as the ply angle, fiber volume fraction, crack depth, crack position and transverse shear on the free vibration characteristics of the beam with a crack is highlighted. The numerical results show that the natural frequencies obtained from Timoshenko beam theory are always lower than those from Euler beam theory. The presence of intrinsic cracks in anisotropic composite beams modifies the flexibility and in turn free vibration characteristics of the structures. It is revealed that non-destructive crack detection is possible by analyzing the free vibration responses of a cracked beam.

• 한국지반공학회:학술대회논문집
• /
• 한국지반공학회 2006년도 춘계 학술발표회 논문집
• /
• pp.1340-1347
• /
• 2006

Dynamic response of buried pipelines both in the axial and the transverse directions on concrete pipe and steel pipe, FRP pipe were investigated through a free vibration analysis. End boundary conditions considered herein consist of free ends, fixed ends, and fixed-free ends in the axial and the transverse direction. Guided ends, simply supported ends, and supported-guided ends were added to the transverse direction. The buried pipeline was regarded as a beam on an elastic foundation and the ground displacement of sinusoidal wave was applied to it. Natural frequencies and mode shapes were determined according to end boundary conditions. In addition, the effects of parameters on the natural frequency were evaluated. The natural frequency is affected most significantly by the soil stiffness and the length of the buried pipelines. The natural frequency increases as the soil stiffness increases while it decreases as the length of the buried pipeline increases. Such behavior appears to be dominant in the axial direction rather than in the transverse direction of the buried pipelines.

• 한국군사과학기술학회지
• /
• 제5권2호
• /
• pp.217-227
• /
• 2002

Theoretical and experimental free vibration characteristics of cantilevered laminated composite beams with single or multiple transverse non-propagating open cracks are investigated. The presence of intrinsic cracks in beams modifies the flexibility and in turn free vibration characteristics of the structures, and 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. Also the experimental results are well coincide with the numerical results in the decrease of natural frequencies and the transformation of mode shapes because of intrinsic cracks in the composite or aluminum beams. It is revealed that non-destructive crack detection(NDT) or vibration based inspection(VBI) is possible by analyzing the free vibration responses of cracked composite beams.

• 한국복합재료학회:학술대회논문집
• /
• 한국복합재료학회 1999년도 추계학술발표대회 논문집
• /
• pp.5-14
• /
• 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.

• Interaction and multiscale mechanics
• /
• 제2권3호
• /
• pp.223-233
• /
• 2009

This paper presents a new nonlocal stress variational principle approach for the transverse free vibration of an Euler-Bernoulli cantilever nanobeam with an initial axial tension at its free end. The effects of a nanoscale at molecular level unavailable in classical mechanics are investigated and discussed. A sixth-order partial differential governing equation for transverse free vibration is derived via variational principle with nonlocal elastic stress field theory. Analytical solutions for natural frequencies and transverse vibration modes are determined by applying a numerical analysis. Examples conclude that nonlocal stress effect tends to significantly increase stiffness and natural frequencies of a nanobeam. The relationship between natural frequency and nanoscale is also presented and its significance on stiffness enhancement with respect to the classical elasticity theory is discussed in detail. The effect of an initial axial tension, which also tends to enhance the nanobeam stiffness, is also concluded. The model and approach show potential extension to studies in carbon nanotube and the new result is useful for future comparison.

• 한국지반공학회:학술대회논문집
• /
• 한국지반공학회 2005년도 춘계 학술발표회 논문집
• /
• pp.1148-1158
• /
• 2005

This work reports results of our study on the dynamic responses of the buried pipelines both along the axial and the transverse directions under various boundary end conditions. We have considered three cases, i.e., the free ends, the fixed ends, and the fixed-free ends. We have studied the seismic responses of the buried pipelines with the various boundary end conditions both along the axial and the transverse direction. We have considered three cases, i.e., the free ends, the fixed ends, and the fixed-free ends for the axial direction, and three more cases including the guided ends, the simply supported ends, and the supported-guided ends for the transverse direction. The buried pipelines are modeled as beams on elastic foundation while the seismic waves as a ground displacement in the form of a sinusoidal wave. The natural frequency and its mode, and the effect of parameters have been interpreted in terms of free vibration. The natural frequency varies most significantly by the soil stiffness and the length of the buried pipelines in the case of free vibration, which increases with increasing soil stiffness and decreases with increasing length of the buried pipeline. Such a behavior appears most prominently along the axial rather than the transverse direction of the buried pipelines. The resulting frequencies and the mode shapes obtained from the free vibration for the various boundary end conditions of the pipelines have been utilized to derive the mathematical formulae for the displacements and the strains along the axial direction, and the displacements and the bending strains along the transverse direction in case of the forced vibration. The negligibly small difference of 6.2% between our result and that of Ogawa et. al. (2001) for the axial strain with a one second period confirms the accuracy of our approach in this study.

• 한국소음진동공학회논문집
• /
• 제20권5호
• /
• pp.492-501
• /
• 2010

Equations of motion of thin-walled composite H-type cross-section beams incorporating a number of nonclassical effects of transverse shear and primary and secondary warping, and anisotropy of constituent materials are derived. The vibrational characteristics of a composite thin-walled beam exhibiting the circumferentially asymmetric stiffness system(CAS) and the circumferentially uniform stiffness system(CUS) are exploited in connection with the bending-transverse shear coupling and the bending-twist coupling resulting from directional properties of fiber reinforced composite materials.

• Wind and Structures
• /
• 제25권4호
• /
• pp.329-342
• /
• 2017

This work presents a static and free vibration analysis of functionally graded metal-ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. A new displacement field containing integrals is proposed which involves only three variables. Based on the suggested theory, the equations of motion are derived from Hamilton's principle. This theory involves only three unknown functions and accounts for parabolic distribution of transverse shear stress. In addition, the transverse shear stresses are vanished at the top and bottom surfaces of the beam. The Navier solution technique is adopted to derive analytical solutions for simply supported beams. The accuracy and effectiveness of proposed model are verified by comparison with previous research. A detailed numerical study is carried out to examine the influence of the deflections, stresses and natural frequencies on the bending and free vibration responses of functionally graded beams.

• Wind and Structures
• /
• 제24권4호
• /
• pp.307-331
• /
• 2017

Free transverse vibration of shear deformable super-elliptical plates with uniform thickness was studied based on Mindlin plate theory using finite element method. Quadrilateral isoparametric elements were used in the paper. Sensitivity analysis was made to determine the influence of the thickness, the aspect ratio, and the shape of the plate on the natural frequency. Accuracy of the results computed in the current study was validated by comparing them with the solutions available in the literature. The results reveal that the frequencies of clamped super-elliptical plates lie in the range bounded by elliptical and rectangular plates irrespective of the aspect ratio, and furthermore, the frequency decreases if the super-elliptical power increases. A similar trend was observed for simply supported plates with high aspect ratio. The free vibration response for the first and the second symmetric-antisymmetric (SA) modes were found to be different for high aspect ratio. The results reveal that using insufficient number of degrees of freedom results in finding a totally different relation between the super-elliptical power and the frequency.