• Geomechanics and Engineering
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• v.1 no.2
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• pp.121-142
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• 2009

The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the $LDL^T$ decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major's method for dynamic analysis of machine supporting structures is modified and the plane frames are replaced with springs of exact dynamic stiffness and dynamically flexible longitudinal frames. Results of the analysis are compared with exact values. The possible simplifications that could be introduced for a typical machine induced excitation on a framed structure are illustrated and the developed program is modified to account for dynamic constraint equations with a master slave degree of freedom (DOF) option.

• Structural Engineering and Mechanics
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• v.57 no.1
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• pp.141-159
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• 2016

Bearing joint dynamic parameter identification is crucial in modeling the high speed spindles for machining centers used to predict the stability and natural frequencies of high speed spindles. In this paper, a hybrid method is proposed to identify the dynamic stiffness of bearing joint for the high speed spindles. The hybrid method refers to the analytical approach and experimental method. The support stiffness of spindle shaft can be obtained by adopting receptance coupling substructure analysis method, which consists of series connected bearing and joint stiffness. The bearing stiffness is calculated based on the Hertz contact theory. According to the proposed series stiffness equation, the stiffness of bearing joint can be separated from the composite stiffness. Then, one can obtain the bearing joint stiffness fitting formulas and its variation law under different preload. An experimental set-up with variable preload spindle is developed and the experiment is provided for the validation of presented bearing joint stiffness identification method. The results show that the bearing joint significantly cuts down the support stiffness of the spindles, which can seriously affects the dynamic characteristic of the high speed spindles.

• Structural Engineering and Mechanics
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• v.13 no.4
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• pp.437-453
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• 2002

In this paper, dynamic stiffness and flexibility for circular membranes are analytically derived using an efficient mixed-part dual boundary element method (BEM). We employ three approaches, the complex-valued BEM, the real-part and imaginary-part BEM, to determine the dynamic stiffness and flexibility. In the analytical formulation, the continuous system for a circular membrane is transformed into a discrete system with a circulant matrix. Based on the properties of the circulant, the analytical solutions for the dynamic stiffness and flexibility are derived. In deriving the stiffness and flexibility, the spurious resonance is cancelled out. Numerical aspects are discussed and emphasized. The problem of numerical instability due to division by zero is avoided by choosing additional constraints from the information of real and imaginary parts in the dual formulation. For the overdetermined system, the least squares method is considered to determine the dynamic stiffness and flexibility. A general purpose program has been developed to test several examples including circular and square cases.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.945-949
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• 2002

This part of specifies the method for determining the dynamic stiffness of resilient materials used under floating floors. Dynamic stiffness is one of the parameters that determine the sound insulation of such floors in dwellings. This part applies to the determination of dynamic stiffness per unit area of resilient materials with smooth surfaces used in a continuous layer under floating floors in dwellings

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.11
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• pp.1244-1248
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• 2009

Although rubber components are extensively used in mechanic parts. There are still a lot of difficulties in designing the rubber components applied in complex shapes and preloaded states because of the complicated material properties. One of the most important parameters for more detailed and accurate mechanical analysis during the development stages is the dynamic characteristics of the rubber components. It is well known that the dynamic properties of rubber are dependent on frequency as well as static preload. Consequently, a large number of experiments have to be conducted to identify the dynamic stiffness of a rubber bush considering the various applied conditions. In this paper, an efficient experimental method is suggested, which estimates the dynamic stiffness of a rubber bush using rubber material test and static stiffness of the bush. This method is capable of predicting the dynamic stiffness of a rubber bush under various load conditions from minimized test data.

• Journal of KSNVE
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• v.8 no.2
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• pp.361-368
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• 1998

Complex and large lattice type structures are frequently used in design of bridge, tower, crane and aerospace structures. In general, in order to analyze these structures we have used the finite element method(FEM). This method is the most widely used and powerful tool for structural analysis. However, it is necessary to use a large amount of computer memory and computation time because the FEM resuires many degrees of freedom for solving dynamic problems exactly for these complex and large structures. For overcoming this problem, the authors developed the transfer stiffness coefficient method(TSCM). This method is based on the concept of the transfer of the nodal dynamic stiffness coefficient which is related to force and displacement vector at each node. In this paper, the authors formulate vibration analysis algorithm for a complex and large lattice type structure using the transfer of the nodal dynamic stiffness coefficient. And we confirmed the validity of TSCM through numerical computational and experimental results for a lattice type structure.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.10a
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• pp.190-195
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• 1997

Recently it is increased by degrees to construct complex or large lattice type structures such as bridges, towers, cranes, and structures that can be used for space technology. In general, in order to analyze, these structures we have used the finite element method(FEM). In this method, however, it is necessary to use a large amount of computer memory and computation time because the FEM requires many degrees of freedom for solving dynamic problems for these structures. For overcoming this problem, the authors have developed the transfer dynamic stiffness coefficient method(TDSCM). This method is based on the concepts of the transfer and the synthesis of the dynamic stiffness coefficient which is related to force and displacement vector at each node. In this paper, the authors formulate vibration analysis algorithm for a complex and large lattice type structure using the transfer of the dynamic stiffness coefficient. And the validity of TDSCM demonstrated through numerical computational and experimental results.

• Journal of the Korea Institute of Military Science and Technology
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• v.10 no.3
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• pp.181-188
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• 2007

This paper presents a torque control method of a hydraulic actuation system for measuring the dynamic stiffness of missile fin actuators. We propose a new control technique called Dual Dynamic Torque Feedback Control(DDTFC), which improves the stability of the torque control system and enables fast tracking of torque command. The developed control scheme is derived from the physical understanding based on mathematical modelling and analysis. The dynamics of hydraulic torque control servo-system is unravelled via physics-based modelling and nonparametric system identification. In order to verify the effectiveness of the method, the experiment is carried out with a test equipment for measuring the dynamic stiffness. The experiment and simulation results show that DDTFC gives stability improvement.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.392.1-392
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• 2002

This part of specifies the method for determining the dynamic stiffness of resilient materials used under floating floors. Dynamic stillness is one of the parameters that determine the sound insulation of such floors in dwellings. This part applies to the determination of dynamic stiffness per unit area of resilient materials with smooth surfaces used in a continuous layer under floating floors in dwellings.

• Interaction and multiscale mechanics
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• v.5 no.4
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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.