• Structural Engineering and Mechanics
• /
• v.12 no.3
• /
• pp.267-281
• /
• 2001

Transient and quasi-steady-state vertical vibrations of a multi-span beam steel bridge located on a single-track railway line are considered, induced by a superfast passenger train, moving at speed 120-360 km/h. Matrix dynamic equations of motion of a simplified model of the system are formulated partly in the implicit form. A recurrent-iterative algorithm for solving these equations is presented. Excessive vibrations of the system in the resonant zones are reduced effectively with passive dynamic absorbers, tuned to the first mode of a single bridge span. The dynamic analysis has been performed for a series of types of bridges with span lengths of 10 to 30 m, and with parameters closed to multi-span beam railway bridges erected in the second half of the $20^{th}$ century.

• Structural Engineering and Mechanics
• /
• v.21 no.3
• /
• pp.351-367
• /
• 2005

Multi-span beams carrying multiple point masses are widely used in engineering applications, but the literature for free vibration analysis of such structural systems is much less than that of single-span beams. The complexity of analytical expressions should be one of the main reasons for the last phenomenon. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of a multi-span uniform beam carrying multiple point masses. First, the coefficient matrices for an intermediate pinned support, an intermediate point mass, left-end support and right-end support of a uniform beam are derived. Next, the overall coefficient matrix for the whole structural system is obtained using the numerical assembly technique of the finite element method. Finally, the 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 related eigenfunctions respectively. The effects of in-span pinned supports and point masses on the free vibration characteristics of the beam are also studied.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.23 no.11 s.170
• /
• pp.2058-2066
• /
• 1999

The present paper proposes a new dynamic analysis method for multi-span Timoshenko beam structures supported by joints with damping subject to moving loads. An exact dynamic element matrix method is adopted to model Timoshenko beam structures. A generalized modal analysis method is applied to derive response formulae for beam structures subject to moving loads. The proposed method offers an exact and closed form solution. Two numerical examples are provided for validating and illustrating the proposed method. In the first numerical example, a single span beam with multiple moving loads is considered. A dynamic analysis on a multi-span beam under a moving load is considered as the second example, in which the flexibility and damping of supporting joints are taken into account. The numerical study proves that the proposed method is useful for the vibration analysis of multi-span beam-hype structures by moving loads.

• Structural Engineering and Mechanics
• /
• v.65 no.3
• /
• pp.263-274
• /
• 2018

In this study, we propose a frequency domain spectral element method (SEM) for the vibration analysis of a multi-span beam subjected to a moving point force. This study is an extension of the authors' previous study for a single-span beam subjected to a moving point force, where the two-element model-based SEM was applied. In this study, each span of a multi-span beam is represented by the Timoshenko beam model and the moving point force is transformed into the frequency domain as a series of each stationary point force distributed on the multi-span beam. The span at which a stationary point force is located is represented by two-element model, but all other spans are represented by one-element models. The vibration responses to a moving point force are obtained by superposing all individual vibration responses generated by each stationary point force. The high accuracy and computational efficiency of the proposed SEM are verified by comparing the solutions by SEM with exact analytical solutions by the integral transform method (ITM) as well as the solutions by the finite element method (FEM).

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.23 no.12
• /
• pp.1103-1110
• /
• 2013

Based on the string, Euler beam, and Timoshenko beam theories, the transfer functions of axially translating web system to predict the lateral tracking are introduced in this paper. In addition, total transfer function of a multi-span web handling system is developed by the combination of the transfer functions of each single span. Experiments and computations are carried out and the results obtained for the Timoshenko beam model are compared with those of other models. The comparison indicates that the predictions from the Timoshenko and Euler beam models are quite different from that of the classical string model in both the gain and phase response. The results are expected to help in the development of high fidelity models of web tracking systems within a general computational framework.

• Proceedings of the Korean Society of Agricultural Engineers Conference
• /
• 2000.10a
• /
• pp.315-320
• /
• 2000

An investigation and structural safety analysis was conducted to get the basic data for establishing maintenance strategy of pipe framed greenhouses. The number of greenhouses investigated was 108 in total. Most multi-span greenhouses had narrower width and lower height than the standard 1-2W greenhouse, and most of single-span greenhouses were tunnel type. In multi-span greenhouses, the size and interval of frameworks such as rafter, purline, column, and cross beam were mostly suitable, but frameworks of single-span greenhouses were mostly insufficient.

• Structural Engineering and Mechanics
• /
• v.82 no.1
• /
• pp.41-53
• /
• 2022

We developed an accurate and simple vibration model to calculate the natural frequencies and their corresponding vibration modes for multi-span beam bridges with non-uniform cross-sections. A closed set of characteristic functions of a single-span beam was used to construct the vibration modes of the multi-span bridges, which were considered single-span beams with multiple constraints. To simplify the boundary conditions, the restraints were converted into spring constraints. Then the functional of the total energy has the same form as the penalty method. Compared to the conventional penalty method, the penalty coefficients in the proposed approach can be calculated directly, which can avoid the iteration process and convergence problem. The natural frequencies and corresponding vibration modes were obtained via the minimum total potential energy principle. By using the symmetry of the eigenfunctions or structure, the matrix size can be further reduced, which increases the computational efficiency of the proposed model. The accuracy and efficiency of the proposed approach were validated by the finite element method.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.6 no.4
• /
• pp.323-330
• /
• 1982

The vibration characteristics of continuous span periodically supported beams with moving loads are determined theoretically and experimentally. Moving loads are assumed to travel at constant acceleration with constant magnitude. Analyses by using the Fourier Transform technique are developed to determine the dynamic performance of moving load interacting with multiple and continuous beam. Equation of motion for the moving load is non-dimensionalized. Non-dimensional deflection proflies of continuous beam are presented in detail for the single concentrated moving load with constant acceleration. Experimental moving load and continuous beam models are developed. The maximum deflections at each midpoints 5,7 and 9 span beam are measured and their non-dimensional maximum deflections are presented. The non-dimensional maximum deflection of continuous beam is compared with measured maximum deflection of 9 span beam and found to agree reasonably well. The deflection of continuous beam due to moving load with acceleration is strongly influenced in the resonance region.

• Structural Engineering and Mechanics
• /
• v.51 no.6
• /
• pp.1037-1046
• /
• 2014

Most existing damage detection methods based on curvature should investigate the indicator value changes between the intact and damaged state. However, the 'footprint' in the intact state is usually not available for most actual beams. Therefore, a new damage localization indicator called Difference of Nearby Difference Curvature Indicator (DNDCI) was introduced for single-span beams. This indicator does not require prior information of the intact beam and is sensitive to the damage occurs on or nearby the measuring points. Practical and detailed application method of DNDCI has been proposed. Besides the idealized simply supported beams, it was validated by example that DNDCI is also applicable to the actual single-span beams supported by bearings.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2006.11a
• /
• pp.313-316
• /
• 2006

Externally prestressed structures have many advantages such as easy prestressing control and visible maintenance. Flexural strength of externally prestressed concrete members can be calculated by analysis of internal indeterminacy, which is different from internally prestressed concrete members. However, it needs nonlinear analysis considering member stiffness at strength limit state. Thus most of design codes proposed approximate methods which are empirical, based on test results. To reduce difference between accurate analysis and approximate design methods, many experiments and studies are continued. Since most of the experiments are single span beams. In order to adapt of continuous beam it needs further investigation for the continuous beam. In this study, we carried out externally prestressed 2-span concrete beam test to find out the flexural behavior and strength of externally prestressed concrete members.