• Proceedings of the KSME Conference
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• 2003.04a
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• pp.491-496
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• 2003

In sensitivity analysis, semi-analytical method(SAM) reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Recently such errors of SAM resulted by the finite difference scheme have been improved by the separation of rigid body mode. But the eigenvalue should be obtained first before the sensitivity analysis is performed and it takes much time in the case that large system is considered. In the present study, by constructing a reduced one from the original system, iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The sensitivity analysis is performed by the eigenvector acquired from the reduced system. The error of SAM caused by difference scheme is alleviated by Von Neumann series approximation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.585-592
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• 2003

Among various sensitivity evaluation techniques, semi-analytical method(SAM) is quite popular since this method is more advantageous than analytical method(AM) and global finite difference method(FDM). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified fur individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, an iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives.

• Journal of Korean Association for Spatial Structures
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• v.19 no.2
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• pp.101-108
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• 2019

In this paper, the characteristic of intrinsic mode function(IMF) and its orthogonalization of ensemble empirical mode decomposition(EEMD), which is often used in the analysis of the non-linear or non-stationary signal, has been studied. In the decomposition process, the orthogonal IMF of EEMD was obtained by applying the Gram-Schmidt(G-S) orthogonalization method, and was compared with the IMF of orthogonal EMD(OEMD). Two signals for comparison analysis are adopted as the analytical test function and El Centro seismic wave. These target signals were compared by calculating the index of orthogonality(IO) and the spectral energy of the IMF. As a result of the analysis, an IMF with a high IO was obtained by GSO method, and the orthogonal EEMD using white noise was decomposed into orthogonal IMF with energy closer to the original signal than conventional OEMD.

• Smart Structures and Systems
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• v.15 no.1
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• pp.1-13
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• 2015

This paper proposes an analytical mode decomposition (AMD) and Hilbert transform method for structural nonlinearity quantification and damage detection under earthquake loads. The measured structural response is first decomposed into several intrinsic mode functions (IMF) using the proposed AMD method. Each IMF is an amplitude modulated-frequency modulated signal with narrow frequency bandwidth. Then, the instantaneous frequencies of the decomposed IMF can be defined with Hilbert transform. However, for a nonlinear structure, the defined instantaneous frequencies from the decomposed IMF are not equal to the instantaneous frequencies of the structure itself. The theoretical derivation in this paper indicates that the instantaneous frequency of the decomposed measured response includes a slowly-varying part which represents the instantaneous frequency of the structure and rapidly-varying part for a nonlinear structure subjected to earthquake excitations. To eliminate the rapidly-varying part effects, the instantaneous frequency is integrated over time duration. Then the degree of nonlinearity index, which represents the damage severity of structure, is defined based on the integrated instantaneous frequency in this paper. A one-story hysteretic nonlinear structure with various earthquake excitations are simulated as numerical examples and the degree of nonlinearity index is obtained. Finally, the degree of nonlinearity index is estimated from the experimental data of a seven-story building under four earthquake excitations. The index values for the building subjected to a low intensity earthquake excitation, two medium intensity earthquake excitations, and a large intensity earthquake excitation are calculated as 12.8%, 23.0%, 23.2%, and 39.5%, respectively.

• Structural Engineering and Mechanics
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• v.25 no.6
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• pp.653-674
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• 2007

This paper discusses the application of piezoelectric sensors used for evaluation of damping ratio of PVC plastics. The development of the mathematical formulation based on the Empirical Mode Decomposition for calculating the damping coefficient and natural frequency of the system is presented. A systematic experimental and analytical investigation was also carried out to demonstrate the integrity of several methods commonly used to evaluate the damping of materials based on a single degree freedom formulation. The influence of the sensors' location was also investigated. Besides the commonly used methods, a newly emerging time-frequency method, namely the Empirical Mode decomposition, is also employed. Mathematical formulations based on the Hilbert-Huang formulation, and a frequency spacing technique were also developed for establishing the natural frequency and damping ratio based on the output voltage of a single piezoelectric sensor. An experimental investigation was also conducted and the results were compared and verified with Finite Element Analysis (FEA), revealing good agreement.

• Computers and Concrete
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• v.12 no.6
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• pp.803-818
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• 2013

In this study, analytical and experimental modal analyses of a scaled bridge model are carried out to extract the dynamic characteristics such as natural frequency, mode shapes and damping ratios. For this purpose, a scaled bridge model is constructed in laboratory conditions. Three dimensional finite element model of the bridge is constituted and dynamic characteristics are determined, analytically. To identify the dynamic characteristics experimentally; Experimental Modal Analyses (ambient and forced vibration tests) are conducted to the bridge model. In the ambient vibration tests, natural excitations are provided and the response of the bridge model is measured. Sensitivity accelerometers are placed to collect signals from the measurements. The signals collected from the tests are processed by Operational Modal Analysis; and the dynamic characteristics of the bridge model are estimated using Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods. In the forced vibration tests, excitation of the bridge model is induced by an impact hammer and the frequency response functions are obtained. From the finite element analyses, a total of 8 natural frequencies are attained between 28.33 and 313.5 Hz. Considering the first eight mode shapes, these modes can be classified into longitudinal, transverse and vertical modes. It is seen that the dynamic characteristics obtained from the ambient and forced vibration tests are close to each other. It can be stated that the both of Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods are very useful to identify the dynamic characteristics of the bridge model. The first eight natural frequencies are obtained from experimental measurements between 25.00-299.5 Hz. In addition, the dynamic characteristics obtained from the finite element analyses have a good correlation with experimental frequencies and mode shapes. The MAC values obtained between 90-100% and 80-100% using experimental results and experimental-analytical results, respectively.

• Smart Structures and Systems
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• v.16 no.5
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• pp.919-935
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• 2015

The Hilbert-Huang transform (HHT) consists of empirical mode decomposition (EMD) and Hilbert spectral analysis. EMD has been successfully applied for identification of mode shapes of structures based on input-output approaches. This paper aims to extend application of EMD for output-only identification of mode shapes of linear structures. In this regard, a new simple and efficient method based on band-pass filtering and EMD is proposed. Having rather accurate estimates of modal frequencies from measured responses, the proposed method is capable to extract the corresponding mode shapes. In order to evaluate the accuracy and performance of the proposed identification method, two case studies are considered. In the first case, the performance of the method is validated through the analysis of simulated responses obtained from an analytical structural model with known dynamical properties. The low-amplitude responses recorded from the UCLA Factor Building during the 2004 Parkfield earthquake are used in the second case to identify the first three mode shapes of the building in three different directions. The results demonstrate the remarkable ability of the proposed method in correct estimation of mode shapes of the linear structures based on rather accurate modal frequencies.

• Structural Engineering and Mechanics
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• v.62 no.1
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• pp.65-77
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• 2017

The free vibration analysis of fluid conveying Timoshenko pipeline with different boundary conditions using Differential Transform Method (DTM) and Adomian Decomposition Method (ADM) has not been investigated by any of the studies in open literature so far. Natural frequencies, modes and critical fluid velocity of the pipelines on different supports are analyzed based on Timoshenko model by using DTM and ADM in this study. At first, the governing differential equations of motion of fluid conveying Timoshenko pipeline in free vibration are derived. Parameter for the nondimensionalized multiplication factor for the fluid velocity is incorporated into the equations of motion in order to investigate its effects on the natural frequencies. For solution, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Timoshenko beam theory. After the analytical solution, the efficient and easy mathematical techniques called DTM and ADM are used to solve the governing differential equations of the motion, respectively. The calculated natural frequencies of fluid conveying Timoshenko pipelines with various combinations of boundary conditions using DTM and ADM are tabulated in several tables and figures and are compared with the results of Analytical Method (ANM) where a very good agreement is observed. Finally, the critical fluid velocities are calculated for different boundary conditions and the first five mode shapes are presented in graphs.

• Nuclear Engineering and Technology
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• v.38 no.4
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• pp.343-352
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• 2006

Convenient analytical tools for evaluation of the aperiodic and the fluctuating instabilities of the passive residual heat removal system (PRHRS) of an integral reactor are developed and results are discussed from the viewpoint of the system design. First, a static model for the aperiodic instability using the system hydraulic loss relation and the downcomer feedwater heating equations is developed. The calculated hydraulic relation between the pressure drop and the feedwater flow rate shows that several static states can exist with various numbers of water-mode feedwater module pipes. It is shown that the most probable state can exist by basic physical reasoning, that there is no flow rate through the steam-mode feedwater module pipes. Second, a dynamic model for the fluctuating instability due to steam generation retardation in the steam generator and the dynamic interaction of two compressible volumes, that is, the steam volume of the main steam pipe lines and the gas volume of the compensating tank is formulated and the D-decomposition method is applied after linearization of the governing equations. The results show that the PRHRS becomes stabilized with a smaller volume compensating tank, a larger volume steam space and higher hydraulic resistance of the path $a_{ct}$. Increasing the operating steam pressure has a stabilizing effect. The analytical model and the results obtained from this study will be utilized for PRHRS performance improvement.

• Structural Engineering and Mechanics
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• v.75 no.3
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• pp.377-387
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• 2020

Modern long-span floor system typically possesses low damping and low natural frequency, presenting a potential vibration sensitivity problem induced by human activities. Field test and numerical analysis methods are available to study this kind of problems, but would be inconvenient for design engineers. This paper proposes a simplified method to determine the acceleration amplitudes of long-span floor system subjected to walking or running load, which can be carried out manually. To theoretically analyze the acceleration response, the floor system is simplified as an anisotropic rectangular plate and the mode decomposition method is used. To facilitate the calculation of acceleration amplitude a_P, a coefficient α_wmn or α_Rmn is introduced, with the former depending on the geometry and support condition of floor system and the latter on the contact duration t_R and natural frequency. The proposed simplified method is easy for practical use and gives safe structural designs.