• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.4
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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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• v.90 no.4
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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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.2
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• pp.169-177
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• 2011

In this paper, the natural frequency of a cracked cantilever L-beams with a coupled bending and torsional vibrations is investigate by theory and experiment. In addition, a method for detection of crack in a cantilever L-beams is presented based on natural frequency measurements. The governing differential equations of a cracked L-beam are derived via Hamilton's principle. The two coupled governing differential equations are reduced to one sixth order ordinary differential equation in terms of the flexural displacement. Futher, the dynamic transfer matrix method is used for calculation of a exact natural frequencies of L-beams. The crack is assumed to be in the first mode of fracture and to be always opened during vibrations. In this study, the differences between the actual and predicted positions and sizes of crack are less than about 10 % and 39.5 % respectively.

• Structural Engineering and Mechanics
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• v.76 no.3
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• pp.293-310
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• 2020

This study derives the differential equations of free vertical bending and torsional vibrations for two- and three-pylon suspension bridges using d'Alembert's principle. The respective algorithms for natural vibration frequency and vibration mode are established through the separation of variables. In the case of the three-pylon suspension bridge, the effect of the along-bridge bending vibration of the middle pylon on the vertical bending vibration of the entire bridge is considered. The impact of torsional vibration of the middle pylon about the vertical axis on the torsional vibration of the entire bridge is also analyzed in detail. The feasibility of the proposed method is verified by two engineering examples. A comparative analysis of the results obtained via the proposed and more intricate finite element methods confirmed the former feasibility. Finally, the middle pylon stiffness effect on the vibration frequency of the three-pylon suspension bridge is discussed. It is found that the vibration frequencies of the first- and third-order vertical bending and torsional modes both increase with the middle pylon stiffness. However, the increase amplitudes of third-order bending and torsional modes are relatively small with the middle pylon stiffness increase. Moreover, the second-order bending and torsional frequencies do not change with the middle pylon stiffness.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.12
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• pp.109-119
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• 1995

A driveline incorporating universal joints when driving through an angle can excite various components in a vehicle with second order excitation of torsional and bending vibrations, being transmitted either audibly(noise), or physically(vibration). For a certain range of vehicle dpeed noises can be radiated from the cab wall, in which resonances occur by the excitations transmitted from the driveline as a vibration source. In this paper, the excitation mechanism of cab noises is studied especially for the vehicle speed range of 65 .approx. 75 km/h through the simulation for torsional vibrations of the driveline and for bending vibrations of the cab of an 11 Ton grade Cargo Truck, and verified additionally by vibration and noise measurements. As a result, it is found that the uncomfortable noises in the cab are caused mainly by the abrupt increase of the joint angle of driveline near the axle differential resulted from the excessive clearance alignment of the leaf spring gate.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1159-1164
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• 2006

Torsional vibration is an important vibration mode when shafts, cylinders and pipes are considered. However, the modal testing of torsional vibrations is not an easy job to carry out because of the lack of proper transducers. This work presents a new torsional vibration transducer based on the magnetostrictive principle and its application to torsional modal testing. The transducer is so designed as to generate/measure only torsional vibrations excluding other vibration modes such as longitudinal and bending vibrations. The transducer is composed of ferromagnetic patches bonded to a test structure, permanent magnets, and a solenoid. Though patches and magnets are bonded to a structure, torsional vibrations are generated and measured wirelessly by a solenoid encircling a test structure. The proposed transducer works even at considerably high frequencies, say, tens of kilohertz. Furthermore, the transducer can be manufactured at a low price. To check the performance of the proposed method, the torsional modal testing on a hollow aluminum shaft was conducted. The results, such as eigenfrequencies, obtained by the proposed transducer agreed favorably with theoretical results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.8 s.113
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• pp.879-885
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• 2006

Torsional vibration is an important vibration mode when shafts, cylinders and pipes are considered. However, the modal testing of torsional vibrations is not an easy task to carry out because of the lack of proper transducers. This work presents a new torsional vibration transducer based on the magnetostrictive principle and its application to torsional modal testing. The transducer is so designed as to generate/measure only torsional vibrations excluding other vibration modes such as longitudinal and bending vibrations. The transducer is composed of ferromagnetic patches bonded to a test structure, permanent magnets, and a solenoid. Though patches and magnets are bonded to a structure, torsional vibrations are generated and measured wirelessly by a solenoid encircling a test structure. The proposed transducer works even at considerably high frequencies, say, tens of kilohertz. Furthermore, the transducer can be manufactured at a low price. To check the performance of the proposed method, the torsional modal testing on a hollow aluminum shaft was conducted. The results, such as eigenfrequencies, obtained by the proposed transducer agreed favorably with theoretical results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.9 s.102
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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.

• Journal of the Korean Society for Precision Engineering
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• v.8 no.4
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• pp.137-145
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• 1991

A universal joint is a connecting device of two hinges which can transmit torque from one shaft to another at fixed or at varying angles of intersection. It has been used properly not only as rotational but also as intermittent motion. For the particular kinematics condition of a universal joint, torsional and bending vibrations are produced excessively in an elastic driveline. In this paper only the torsional vibration behavior of a driveline with universal joints is analyzed numerically with the discrete model and a design method of the dynamic vibration damper is proposed, in order to reduce torsional vibrations especially in resonance region as a result of parametric variation.