• Structural Engineering and Mechanics
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• v.22 no.6
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• pp.701-717
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• 2006

In the existing reports regarding free transverse vibrations of the Euler-Bernoulli beams, most of them studied a uniform beam carrying various concentrated elements (such as point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, ${\ldots}$, etc.) or a stepped beam with one to three step changes in cross-sections but without any attachments. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of the multiple-step Euler-Bernoulli beams carrying a number of lumped masses and rotary inertias. First, the coefficient matrices for an intermediate lumped mass (and rotary inertia), left-end support and right-end support of a multiple-step beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions, respectively. The effects of distribution of lumped masses and rotary inertias on the dynamic characteristics of the multiple-step beam are also studied.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.394.1-394
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• 2002

The purpose of this paper is to investigate the natural frequencies and mode shapes of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass of rotatory inertia at the other end. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. (omitted)

• Journal of the Earthquake Engineering Society of Korea
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• v.22 no.6
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• pp.345-352
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• 2018

It is inevitable to use the distinct element method in the analysis of structural dynamics for stacked stone pagoda system. However, the experimental verification of analytical results produced by the discrete element method is not sufficient yet, and the theory of distinct element method is not universal in Korea. This study introduces how to model the stacked stone pagoda system using the distinct element method, and draws some considerations in the seismic analysis procedures. First, the rocking mode and sliding mode are locally mixed in the seismic responses. Second, the vertical stiffness and the horizontal stiffness on the friction surface have the greatest influence on the seismic behavior. Third, the complete seismic analysis of stacked stone pagoda system requires a set of the horizontal, vertical, and rotational velocity time histories of the ground. However, earthquake data monitored in Korea are limited to acceleration and velocity signals in some areas.

• Journal of KSNVE
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• v.6 no.3
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• pp.287-296
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• 1996

A virtual work form of flexible multibody dynamic formulation with rotary inertia has been derived. For the analysis of large flexible multibody systems, deformation modal coordinates have been employed to represent coupled motion between gross and vibrational motion. For the efficient evaluation of the entries in the mass matrix, a flexible body has been treated as a collection of mass points. The rotary inertia was generated from the consistent mass matrix in a finite element model. Deformation mode shapes were obtained from finite element analysis. Bending and twisting vibration analyses of a cantilever have been carried out to see rotary inertia effects. A space flexible robot simulation has been also carried out to show effectiveness of the proposed formulation. This formulation is effective to the model that consists of beam, plate, or shell element that contains rotational degree of freedom at the nodal point. It is also effective to the flexible body model to which a large lumped rotary inertia is attached.

• Steel and Composite Structures
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• v.6 no.6
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• pp.513-529
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• 2006

This paper deals with the dynamic behaviour of cold-formed steel hollow frames with different connection stiffnesses. An analytical model of a semi-rigid frame was developed to study the influence of connection stiffnesses on the fundamental frequency and dynamic response of the frames. The flexibilities of the connections are modeled by rotational springs. Neglect of semi-rigidity leads to an artificial stiffening of frames resulting in shorter fundamental period, which in turn results in a significant error in the evaluation of dynamic loads. In the seismic design of structures, of all the principal modes, the fundamental mode of translational vibration is the most critical. Hence, experiments were conducted to study the influence of the connection stiffnesses on the fundamental mode of translational vibration of the steel hollow frames. From the experimental study it was found that the fundamental frequency of the frames lie in the semi-rigid region. From the theoretical investigation it was found that the flexibly connected frames subjected to lateral loads exhibit larger deflection as compared to rigidly connected frames.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.348-353
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• 1995

When cantilever beams rotate, their bending stiffnesses change due to the stretching caused by centrifugal inertia forces. Such phenomena result in variations of natural frequencies and mode shapes associated with constant speed rotational motions of the beams. These variations are important in many practical applications such as helicopter blades, turbomachines, and space structures. This paper presents the formulation of a set of linear equations governing the flapwise bending vibration of rotating cantilever beams. These equations can be used to provide accurate predictions of the variations of natural frequencies and mode shapes due to rotation.

• Computational Structural Engineering
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• v.1 no.2
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• pp.83-90
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• 1988

The present work is concerned with the improvement of finite element for the analysis of plate bending structures. The element formulation is based upon Mindlin plate concept. The displacement field of this element is formed by adding nonconforming modes to two rotational displacement components of a 'heterosis plate element. The element has the requisite numbers of zero eigenvalues associated with rigid body modes to avoid the spurious zero energy mode. It is shown that the results obtained by the element converged to the exact solutions very rapidly as the mesh is refined and exhibited reliable solutions through numerical studies for standard benchmark problems. This element is shown to overcome the shear locking problem completely in very thin plate situation even for irregular meshes.

• Journal of KSNVE
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• v.8 no.3
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• pp.477-484
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• 1998

An analytical procedure on the base of the substructure synthesis and assumed modes method is developed to investigate the flexibility effect of bladed disk assembly on vibrational modes of flexible rotor system. In modeling the system, Coriolis forces, gyroscopic moments, and centrifugal stiffening effects are taken into account. The coupled vibrations between the shaft and bladed disk are then extensively investigated through the numerical simulation of simplified models, with varying the shaft rotational speed and the prewist and stagger angles of the blade. It is found that the Coriolis and inertia forces and the inertia torque, which are induced by the one nodal diameter modes of the bladed disk and vary depending upon the stagger and prewist angles, lead to the coupled motions of the shaft and the bladed disk.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.623-628
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• 2004

In this study, the assumed-mode method using characteristic polynomials of Timoshenko beam is applied for the free vibration analysis of rectangular stiffened plates. The polynomial is derived considering the rotational constraint along the boundary edges of plate and the orthogonal relation of Timoshenko beam functions, which enables to simplify the free vibration analysis of plate structure having various boundary conditions. To verify the validity and effectiveness of the adopted method, numerical analysis for cross-stiffened plates were carried out and its results were compared with those obtained by the general purpose FEA software.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.1-13
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• 1996

The measurement of radial directional natural frequency ina passenger car tire rotating under the load is studied. In order to obtain theoretical matural frequency and mode shape, the ploane vibration of a tire is modeled to that of circular beam. By esing the Tieking method based on Hamiltons's principle, theoretical results are determined by considering tension horce due to tire inflation pressure, retational velocity and tangential, radial stiffness. Radial directional modal parameters varying with the inflation pressure, load, rotational velocity are experimentally determined by using frequency response function method. The results show that experimental conditions canbe considered as the parameters which shift the natural frequency.