• Earthquakes and Structures
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• v.22 no.1
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• pp.1-13
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• 2022

When a building suffers damages under moderate to severe loading condition, its physical properties such as damping and stiffness parameters will change. There are different practical methods besides various numerical procedures that have successfully detected a range of these changes. Almost all the previous proposed methods used to work with translational components of mode shapes, probably because extracting these components is more common in vibrational tests. This study set out to investigate the influence of using both rotational and translational components of mode shapes, in detecting damages in 3-D steel structures elements. Three different sets of measured components of mode shapes are examined: translational, rotational, and also rotational/translational components in all joints. In order to validate our assumptions two different steel frames with three damage scenarios are considered. An iterative model updating program is developed in the MATLAB software that uses the OpenSees as its finite element analysis engine. Extensive analysis shows that employing rotational components results in more precise prediction of damage location and its intensity. Since measuring rotational components of mode shapes still is not very convenient, modal dynamic expansion technique is applied to generate rotational components from measured translational ones. The findings indicated that the developed model updating program is really efficient in damage detection even with generated data and considering noise effects. Moreover, methods which use rotational components of mode shapes can predict damage's location and its intensity more precisely than the ones which only work with translational data.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.711-723
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• 2015

This study investigates the identification of added mass and its location in the glass fiber reinforced polymer (GFRP) beam structures. The main emphasis of this paper is to ascertain the importance of inclusion of rotational degrees of freedom (dofs) in the introduction of added mass or damage identification. Two identification indices that include the rotational dofs have been introduced in this paper: the modal force index (MFI) and the modal rotational curvature index (MRCI). The MFI amplifies damage signature using undamaged numerical stiffness matrix which is related to changes in the altered mode shapes from the original mode shapes. The MRCI is obtained by using a higher derivative of rotational mode shapes. Experimental and numerical results are compared with the existing methods leading to a conclusion that the contributions of the rotational modes play a key role in the identification of added mass. The authors believe that the similar results are likely in the case of damage identification also.

• Structural Monitoring and Maintenance
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• v.7 no.2
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• pp.125-147
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• 2020

Damage detection of structures is one of the most important topics in structural health monitoring. In practice, the response is not available at all structural degrees of freedom, and due to the installation of sensors at some degrees of freedom, responses exist only in limited number of degrees of freedom. This paper is investigated the damage detection of structures by applying two approaches, AllDOF and Dynamic Condensation Method (DCM), based on the Modified Modal Strain Energy Method (MMSEBI). In the AllDOF method, mode shapes in all degrees of freedom is available, but in the DCM the mode shapes only in some degrees of freedom are available. Therefore by methods like the DCM, mode shapes are obtained in slave degrees of freedom. So, in the first step, the responses at slave degrees of freedom extracted using the responses at master degrees of freedom. Then, using the reconstructed mode shape and obtaining the modified modal strain energy, the damages are detected. Two standard examples are used in different damage cases to evaluate the accuracy of the mentioned method. The results showed the capability of the DCM is acceptable for low mode shapes to detect the damage in structures. By increasing the number of modes, the AllDOF method identifies the locations of the damage more accurately.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.3
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• pp.383-391
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• 1986

Mode shapes and natural frequencies of the bell type shell are analyzed numerically by the finite element method. The impulse hammer method and the Fast Fourier Transform analyzer are used for the experimental test. All types of mode shapes are expressed by the computer graphics. Numerical solutions are good agreement with the experimental results. The sustaining sound of the typical bell-type shell depend upon the first flexural mode (0-2 mode) and the second flexural mode (0-3 mode), and their mode shapes are independent upon thickness Dangjwas, holes, and added mass effects. Asymmetric effects by Dangjwas, holes and added mass give rise to beat frequencies, and the added mass is found to be most effective.

• Wind and Structures
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• v.18 no.4
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• pp.391-422
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• 2014

The high frequency force balance (HFFB) technique provides convenient measurements of integrated forces on rigid building models in terms of base bending moments and torque and/or base shear forces. These base moments or forces are then used to approximately estimate the generalized forces of building fundamental modes with mode shape corrections. This paper presents an analysis framework for coupled dynamic response of tall buildings with HFFB technique. The empirical mode shape corrections for generalized forces with coupled mode shapes are validated using measurements of synchronous pressures on a square building surface from a wind tunnel. An alternative approach for estimating the mean and background response components directly using HFFB measurements without mode shape corrections is introduced with a discussion on higher mode contributions. The uncertainty in the mode shape corrections and its influence on predicted responses of buildings with both uncoupled and coupled modal shapes are examined. Furthermore, this paper presents a comparison of aerodynamic base moment spectra with available data sets for various tall building configurations. Finally, e-technology aspects in conjunction with HFFB technique such as web-based on-line analysis framework for buildings with uncoupled mode shapes used in NALD (NatHaz Aerodynamic Loads Database) is discussed, which facilitates the use of HFFB data for preliminary design stages of tall buildings subject to wind loads.

• Coupled systems mechanics
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• v.9 no.4
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• pp.311-323
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• 2020

This paper deals with the effect of the mode shapes on the dynamic response of a multi-storey frame subjected to moving train loads which are modelled as loads of constant intervals with constant velocity using the finite element method. The multi-storey frame is modelled as a number of Bernoulli-Euler beam elements. First, the first few modes of the multi-storey frame are determined. Then, the effects of force span length to beam length ratio and velocity on dynamic magnification factor (DMF) are evaluated via 3D velocity-force span length to beam length ratio-DMF graphics and its 2D projections. By using 3D and 2D graphics, the directions of critical speeds that force the structure under resonance conditions are determined. Last, the mode shapes related to these directions are determined by the time history and frequency response graphs. This study has been limited by the vibration of the frame in the vertical direction.

• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.177-190
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• 2008

In this paper, both experimental measurement and theoretical analysis are used to investigate the out-of-plane resonant characteristics of a cantilevered piezoceramic plate in air and three different kinds of fluid. The experimental method, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), is the major technique used in this study to measure the resonant characteristics of the cantilivered piezoceramic plate. Both resonant frequencies and full-field mode shapes are obtained from this experimental technique. Numerical computations based on the finite element analysis are presented for comparison with the experimental results. Good quality of mode shapes for the cantilevered piezoceramic plate in air is obtained from the AF-ESPI technique. However, the quality decreases as the viscosity of fluids increases. From the results provided from experimental measurements and numerical computations, it is indicated that the resonant frequencies of the cantilevered piezoceramic plate in fluid decrease with the increase of the viscosity of fluids. Good agreements between the experimental measured data and the numerical calculated results are found for both resonant frequencies and mode shapes of the cantilevered piezoceramic plate in fluid.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.10a
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• pp.138-146
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• 1996

The presence of a damage, such as a crack, in a structure increases the flexibility and damping in the structure. Most of methods to detect damage or damage location uses stiffness matrix of the structural system. The modification of stiffness matrix, however, has complicated procedures to identify structural. system in the basis of finite element model and has too many degree of freedom to calculate. Identification of changes of flexibility of structure can offer damage information immediately and simple procedure can employ real time continuous monitoring system. To identify changes of the flexibility, vibration mode shapes and natural frequencies are usually used. In this paper, a procedure for damage location in continuous girder bridges using vibration data is described. The effectiveness and sensitivity of the presented method to measurement errors in mode shapes and natural frequencies are investigated using analytical results from finite element models. It is shown that the errors in the first mode shape and first natural frequency demonstrate much larger influence than those in the higher mode shapes and modal frequencies.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.213-218
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• 2006

Hot spot phenomenon is caused by non-uniform contact area between brake pad and disk frequent braking. Brake disk deformed by locally concentrated heat increases magnitude of frictional vibration. And this deformation can highly influence the judder vibration. In this experimental study, vibration and hot spot was measured in accordance with rotation of disk and pressure of master cylinder for finding the factors that causes hot spot phenomena. For comparing hot spot aspects with mode shapes of disk, mode shapes were measured by conducting modal test, and analyzed by using finite element analysis. Relation between hot spot phenomenon, and mode shape, pressure of master cylinder and rotation speed of disk respectively, was achieved by hot spot measurement and frequency analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.341-348
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• 2000

The differential equations governing the free vibrations of stepped horizontally circular curved beams with circular cross-section are derived and solved numerically. In numerical method, the Runge-Kutta and Determinant Search methods are used for computing the natural frequencies and mode shapes. Frequencies and mode shapes are reported as the functions of non-dimensional system parameters. The numerical method developed herein for computing frequencies and mode shapes are efficient and reliable.