• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1995년도 추계학술대회논문집; 한국종합전시장, 24 Nov. 1995
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• pp.185-190
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• 1995

In recent years, many researcher have been interested in the stability of a thin beam. Among them, Pai and Nayfeh[1] had investigated the nonplanar motion of the cantilever beam under lateral base excitation and chaotic motion, but this study is associated with internal resonance, i.e. one to one resonance. Also Cusumano[2] had made an experiment on a thin beam, called Elastica, under bending loads. In this experiment, he had shown that there exists out-of-plane motion, involving the bending and the torsional mode. Pak et al.[3] verified the validity of Cusumano's experimental works theoretically and defined the existence of Non-Local Mode(NLM), which is came out due to the instability of torsional mode and the corresponding aspect of motions by using the Normal Modes. Lee[4] studied on a thin beam under bending loads and investigated the routes to chaos by using forcing amplitude as a control parameter. In this paper, we are interested in the motion of a thin beam under torsional loads. Here the form of force based on the natural forcing function is used. Consequently, it is found that small torsional loads result in instability and in case that the forcing amplitude is increasing gradually, the motion appears in the form of dynamic double potential well, finally leads to complex motion. This phenomenon is investigated through the poincare map and time response. We also check that Harmonic Balance Method(H.B.M.) is a suitable tool to calculate the bifurcated modes.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.221-226
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• 2005

In this paper, a dynamic model for the rotor shaft-coupling-blade system is developed. The blades are attached to a disk and driven by an electric motor shaft which is flexible in torsion. We assumed that the shaft torsional flexibility is lumped in the flexible coupling which is usually adopted in rotor systems. The Lagrangian approach with the small deformation theory for both blade-bending and shaft-torsional deformations is employed for developing the equation of the motion. The assumed modes method is used for estimating the blade transverse deflection. The numerical results highlight the effects of both structural damping of the system and the torsional stiffness of the flexible coupling to the dynamic response of the blade. The results showed strong coupling between the blade bending and shaft torsional vibrations in the form of inertial nonlinearif, stiffness hardening and softening.

• 한국소음진동공학회논문집
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• 제15권9호
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• pp.1023-1029
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• 2005

In this paper, a dynamic model for the rotor shaft-coupling-blade system was developed. The blades are attached to a disk and driven by an electric motor shaft which is flexible in torsion. We assumed that the shaft torsional flexibility was lumped in the flexible coupling which is usually adopted in rotor systems. The Lagrangian approach with the small deformation theory for both blade-bending and shaft-torsional deformations was employed for developing the equation of the motion. The Assumed Modes Method was used for estimating the blade transverse deflection. The numerical results highlight the effects of both structural damping of the system and the torsional stiffness of the flexible coupling to the dynamic response of the blade. The results showed strong coupling between the blade bending and shaft torsional vibrations in the form of inertial nonlinearity, stiffness hardening and softening.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 추계학술대회 논문집
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• pp.730-735
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• 2013

This paper contains various vibration analysis of multi-stage shaft shape such as the bending, torsional and axial vibration. The shaft system is modeled as Timoshenko beam with the transverse shear and rotary inertia effect and the equation of motion is derived by Hamilton's principle with considering clamped-free boundary condition. Then, eigenvalue problem of discrete equation of motion for multi-stage shaft model is solved and got results of the natural frequency through the numerical analysis. Obtained numerical analysis results through Matlab program were compared with those of FEM analysis to verify the results. This study suggests that design of shaft system be consider torsional and axial vibration as well as bending vibration.

• 한국기계가공학회지
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• 제10권4호
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• pp.8-15
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• 2011

In this paper, the influence of a crack on the natural frequency of cracked cantilever L-shaped beam with coupled bending and torsional vibrations by analytically and experimentally is analyzed. The L-shaped beam with a crack is modeled by Hamilton's principle with consideration of bending and torsional energy. The two coupled governing differential equations are reduced to one sixth-order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first, second and third mode of fracture and to be always opened during the vibrations. The theoretical results are validated by a comparison with experimental measurements. The maximal difference between the theoretical results and experimental measurements of the natural frequency is less than 7.5% in the second vibration mode.

• Structural Engineering and Mechanics
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• 제90권4호
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• pp.325-343
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• 2024

Triple-tower double-cable suspension bridges have increased confinement stiffness imposed by the main cable on the middle tower, which has bright application prospects. However, vertical bending and torsional vibrations of the double-cable and the girder are coupled in such bridges due to the hangers. In particular, the bending vibration of the towers in the longitudinal direction and torsional vibrations about the vertical axis influence the vertical bending and torsional vibrations of the stiffening girders, respectively. The conventional analytical algorithm for assessing the dynamic features of the suspension bridge is not directly applicable to this type of bridge. This study attempts to mitigate this problem by introducing an analytical algorithm for solving the triple-tower double-cable suspension bridge's natural frequencies and mode shapes. D'Alembert's principle is employed to construct the differential equations of the vertical bending and torsional vibrations of the stiffening girder continuum in each span. Vibrations of stiffening girders in each span are interrelated via the vibrations of the main cables and the bridge towers. On this basis, the natural frequencies and mode shapes are derived by separating variables. The proposed algorithm is then applied to an engineering example. The natural frequencies and mode shapes of vertical bending and torsional vibrations derived by the analytical algorithm agreed well with calculations via the finite element method. The fundamental frequency of vertical bending and first- and second-order torsion frequencies of double-cable suspension bridges are much higher than those of single-cable suspension bridges. The analytical algorithm has high computational efficiency and calculation accuracy, which can provide a reference for selecting appropriate structural parameters to meet the requirements of dynamics during the preliminary design.

• Structural Engineering and Mechanics
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• 제30권5호
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• pp.603-617
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• 2008

Three dimensional coupled bending-torsion dynamic vibrations of thin-walled open section beam subjected to moving vehicle are investigated by transfer matrix method. Through adopting the idea of Newmark-${\beta}$ method, the partial differential equations of structural vibration can be transformed to the differential equations. Then, those differential equations are solved by transfer matrix method. An iterative scheme is proposed to deal with the coupled bending-torsion terms in the governing vibration equations. The accuracy of the presented method is verified through two numerical examples. Finally, with different eccentricities of vehicle, the torsional vibration of thin-walled open section beam and vertical and rolling vibration of truck body are investigated. It can be concluded from the numerical results that the torsional vibration of beam and rolling vibration of vehicle increase with the eccentricity of vehicle. Moreover, it can be observed that the torsional vibration of thin-walled open section beam may have a significant nonlinear influence on vertical vibration of truck body.

• Structural Engineering and Mechanics
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• 제65권4호
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• pp.381-388
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• 2018

Dynamic behaviour of beam carrying masses has attracted attention of many researchers and engineers. Many studies on the analytical solution of beam with concentric tip mass have been published. However, there are limited works on vibration analysis of beam with an eccentric three dimensional object. In this case, bending and torsional deformations of beam are coupled due to the boundary conditions. Analytical solution of equations of motion of the system is complicated and lengthy. Therefore, in this study, Differential Transform Method (DTM) is applied to solve the relevant equations. First, the Timoshenko beam with 3D tip attachment whose centre of gravity is not coincident with beam end point is considered. The beam is assumed to undergo bending in two orthogonal planes and torsional deformation about beam axis. Using Hamilton's principle the equations of motion of the system along with the possible boundary conditions are derived. Later DTM is applied to obtain natural frequencies and mode shapes of the system. According to the relevant literature DTM has not been applied to such a system so far. Moreover, the problem is modelled by Ansys, the well-known finite element method, and impact test is applied to extract experimental modal data. Comparing DTM results with finite element and experimental results it is concluded that the proposed approach produces accurate results.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 춘계학술대회 논문집
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• pp.73-78
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• 2013

In this paper, the vibration for a pickup actuator is described by mathematically analyzing its suspension configuration and motion, confined to lateral and torsional directions of suspensions. In order to prove the accuracy of this result, it is compared to a finite element analysis. Also it is shown that modal frequencies can be modified by changing design parameters in mathematical motion expressions.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.316-323
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• 2003

The gear system is commonly applied in the marine propulsion shafting system using the diesel engine with the power take off/in system and it also is necessary to reduce propeller revolution increasing the propulsion efficiency. The diesel engine has the advantage more than other thermal engines in high thermal efficiency and mobility. But the large vibratory torque which induced by higher combustion pressure is transmitted to these gears. In this paper, the surface durability and bending stress of gear system considering vibratory and transient torque is evaluated by ISO and AGMA regulation. And the influence of these in gear design is investigated with the theoretical analysis and onboard measurement result of torsional vibration.