• Structural Engineering and Mechanics
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• v.10 no.3
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• pp.197-209
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• 2000

The effects of weight and axial inertia of a beam are taken into account for studying the nonlinear vibration of the Timoshenko beam due to external loads. The combination of Galerkins method and Runge-Kutta method are employed to obtain the dynamic responses of the beam. A concentrated force and a two-axle vehicle traversing on the beam are taken as two examples to investigate the response characteristics of the beam. Results show that the effect of axial inertia of the beam increases the fundamental period of the beam. Further, both the dynamic deflection and the dynamic moment of the beam obtained with including the effect of axial inertia of the beam are greater than those of the beam without including that effect of the beam.

• Structural Monitoring and Maintenance
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• v.4 no.2
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• pp.153-173
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• 2017

An improved method is presented to estimate the axial force of a bar member with vibrational measurements based on modified Timoshenko beam theory. Bending stiffness effects, rotational inertia, shear deformation, rotational inertia caused by shear deformation are all taken into account. Axial forces are estimated with certain natural frequency and corresponding mode shape, which are acquired from dynamic tests with five accelerometers. In the paper, modified Timoshenko beam theory is first presented with the inclusion of axial force and rotational inertia effects. Consistent mass and stiffness matrices for the modified Timoshenko beam theory are derived and then used in finite element simulations to investigate force identification accuracy under different boundary conditions and the influence of critical axial force ratio. The deformation coefficient which accounts for rotational inertia effects of the shearing deformation is discussed, and the relationship between the changing wave speed and the frequency is comprehensively examined to improve accuracy of the deformation coefficient. Finally, dynamic tests are conducted in our laboratory to identify progressive axial forces of a steel plate and a truss structure respectively. And the axial forces identified by the proposed method are in good agreement with the forces measured by FBG sensors and strain gauges. A significant advantage of this axial force identification method is that no assumption on boundary conditions is needed and excellent force identification accuracy can be achieved.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.7
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• pp.665-673
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• 2011

Simplified formulae for axial and bending natural frequencies of a bellows are developed using an equivalent thin-walled pipe model. The axial and bending stiffness of bellows is determined using lumped transfer matrix method. Transfer matrix method which includes the rotary inertia is used to calculate the natural frequencies for axial and lateral vibration. The result from the simplified formula are verified by those from as experiment result and a finite element analysis. This comparisons show good agreement with the each other.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.6
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• pp.580-586
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• 2011

This paper addresses the effect of transverse shear deformation and rotary inertia on the natural frequency of beams under axial loads. It has been reported in the author's paper using a finite element analysis that the Timoshenko effect in a rotating disk deceases and then increases again with increasing rotation speed. To validate the phenomenon, the simply-supported beams under uniform tension are selected in this study since they have exact solutions in vibration problem. The results show that the axial tension in beams would not make the Timoshenko effect decrease monotonically but could make the effect increase again unlike the results reported in the other studies for beams.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.10a
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• pp.204-208
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• 2001

Position control of the electro-hydraulic servo indexing system in a flexible forging machine was investigated Flexible forging machine forges an axial type workpiece in the radial direction as well as in the axial direction. The role of the indexing system is to rotate a workpiece fast and accurately to a desired position for continuous shaping. Since the inertia of a workpiece changes during each forging step, a control technique which is robust to inertia variation should be adopted to the position control of the workpiece. In this study, time delayed control technique is applied to the servo system. Time delayed control method does not depend on estimation of specific parameters. Rather, it depends on the direct estimation of a function representing the effect of uncertainties. Direct estimation is accomplished using time delay and the gathered information is used to cancel the unknown dynamics is accomplished using disturbances simultaneously. Experimental result show that the time delayed controller is robust to inertia variation of the load, and satisfactory performance on the sposition accuracy is obtained compared to the contentional feedback control.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.942-947
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• 2004

The differential equations governing free, in-plane vibrations of stepped non-circuiar arches are derived as nondimensional forms including the effects of rotatory inertia, shear deformation and axial deformation. The governing equations are solved numerically to obtain frequencies and mode shapes. The lowest four natural frequencies and mode shapes are calculated for the stepped parabolic arches with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. A wide range of arch rise to span length ratios, slenderness ratios, section ratios, and discontinuous sector ratios are considered. The effect of rotatory inertia and shear deformation on natural frequencies is reported. Typical mode shapes of vibrating arches are also presented.

• Steel and Composite Structures
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• v.28 no.6
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• pp.749-758
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• 2018

Free axial vibration of axially functionally graded (AFG) nanorods is studied by focusing on the inertia of lateral motions and shear stiffness effects. To this end, Bishop's theory considering the inertia of the lateral motions and shear stiffness effects and the nonlocal theory considering the small scale effect are used. The material properties are assumed to change continuously through the length of the AFG nanorod according to a power-law distribution. Then, nonlocal governing equation of motion and boundary conditions are derived by implementing the Hamilton's principle. The governing equation is solved using the harmonic differential quadrature method (HDQM), After that, the first five axial natural frequencies of the AFG nanorod with clamped-clamped end condition are obtained. In the next step, effects of various parameters like the length of the AFG nanorod, the diameter of the AFG nanorod, material properties, and the nonlocal parameter value on natural frequencies are investigated. Results of the present study can be useful in more accurate design of nano-electro-mechanical systems in which nanotubes are used.

• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.537-573
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• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• Journal of Advanced Marine Engineering and Technology
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• v.29 no.8
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• pp.891-898
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• 2005

Inertia welding is a solid-state welding process in which butt welds in materials are made in bar and in ring form at the joint race, and energy required lot welding is obtained from a rotating flywheel. The stored energy is converted to frictional heat at the interface under axial load. The quality of the welded joint depends on many parameters, including axial force, initial revolution speed and energy amount of upset. working time, and residual stresses in the joint. Inertia welding was conducted to make the large exhaust valve spindle for low speed marine diesel engine. superalloy Nimonic 80A for valve head of 540mm and high alloy SNCrW for valve stem of 115mm. Due to different material characteristics such as, thermal conductivity and flow stress. on the two sides of the weld interface, modeling is crucial in determining the optimal weld geometry and Parameters. FE simulation was performed by the commercial code DEFORM-2D. A good agreement between the Predicted and actual welded shape is observed. It is expected that modeling will significantly reduce the number of experimental trials needed to determine the weld parameters. especially for welds for which are very expensive materials or large shaft. Many kinds of tests, including macro and microstructure observation, chemical composition tensile , hardness and fatigue test , are conducted to evaluate the qualify of welded joints. Based on the results of the tests it can be concluded that the inertia welding joints of the superalloy exhaust valve spindle are better properties than the material specification of SNCrW.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2007.05a
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• pp.401-404
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• 2007

Inertia welding is a solid-state welding process in which butt welds in materials are made in bar and in ring form at the joint face, and energy required for welding is obtained from a rotating flywheel. The stored energy is converted to frictional heat at the interface under axial load. The quality of the welded joint depends on many parameters, including axial force, initial revolution speed and energy, amount of upset, working time, and residual stresses in the joint. Inertia welding was conducted to make the large rotor shaft for low speed marine diesel engine, alloy steel for shaft of 140mm. Due to different material characteristics, such as, thermal conductivity and flow stress, on the two sides of the weld interface, modeling is crucial in determining the optimal weld geometry and parameters. FE simulation was performed by the commercial code DEFORM-2D. A good agreement between the predicted and actual welded shape is observed. It is expected that modeling will significantly reduce the number of experimental trials needed to determine the weld parameters.