• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.579-589
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• 1999

A new way to reduce the eigenvalue computation effort in structural dynamics is presented in this paper. The degrees of freedom of a structure may be classified into groups that are termed as sub-degrees of freedom. The eigenvalue analysis is performed with each of sub-degrees of freedom so that the computing time is much shortened. Since the dynamic coupling between sub-degrees of freedom is selected to be small and it may be considered as a perturbation, the perturbation algorithm is used to obtain an accuratae result. The accuracy of perturbation depends on the coupling between sub-degrees of freedom. The weaker the coupling is, the more accurate the result is. The procedure can be used to simplify a problem of three dimensions to that of two dimensions or from two dimensions to one dimension. The application to a truss and a space frame is shown in the paper.

• 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.

• Structural Engineering and Mechanics
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• v.10 no.6
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• pp.603-619
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• 2000

Analysis of a framed structure for vertical vibration requires a lot of computational efforts because large number of degrees of freedom are generally involved in the dynamic responses. This paper presents an efficient modeling technique for vertical vibration utilizing substructuring technique and super elements. To simplify the modeling procedure each floor in a structure is modeled as a substructure. Only the vertical translational degrees of freedom are selected as master degrees of freedom in the inside of each substructure. At the substructure-column interface, horizontal and rotational degrees of freedom are also included considering the compatibility condition of slabs and columns. For further simplification, the repeated parts in a substructure are modeled as super elements, which reduces computation time required for the construction of system matrices in a substructure. Finally, the Guyan reduction technique is applied to enhance the efficiency of dynamic analysis. In numerical examples, the efficiency and accuracy of the proposed method are demonstrated by comparing the response time histories and the analysis time.

• Structural Engineering and Mechanics
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• v.9 no.5
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• pp.433-448
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• 2000

In this paper we deal with the numerical solution of the Reissner-Mindlin plate problem with the use of high order finite elements. In previous papers we have solved the problem using approximation spaces of Serendipity type, in order to minimize the number of internal degrees of freedom. Since further numerical experiences have evidenced that the addition of bubble functions improved the quality of the results we have modified the previous family of hierarchic finite elements, adding internal degrees of freedom, to make a systematic analysis of their performance. Of course, more degrees of freedom are introduced. Nonetheless the numerical results indicate that the reduction of the error outnumbers the increase of degrees of freedom and therefore bubble plus elements are preferable.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.3 s.246
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• pp.310-317
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• 2006

Currently most practical vibration and structural problems in automotive suspensions require the use of the finite element method to obtain their structural responses. When the finite element model has a very large number of degrees of freedom the harmonic and dynamic analyses are computationally too expensive to repeat within a feasible design process time. To alleviate the computational difficulty, this paper presents a moment-matching based model order reduction (MOR) which reduces the number of degrees of freedom of the original finite element model and speeds up the necessary simulations with the reduced-size models. The moment-matching model reduction via the Arnoldi process is performed directly to ANSYS finite element models by software mor4ansys. Among automotive suspension components, a knuckle is taken as an example to demonstrate the advantages of this approach for vibration simulation. The frequency and transient dynamic responses by the MOR are compared with those by the mode superposition method.

• Wind and Structures
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• v.10 no.5
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• pp.421-435
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• 2007

A two-dimensional flutter analysis method (2d-3DOF method) was developed to simultaneously investigate the relationship between oscillation parameters and aerodynamic derivatives of three degrees of freedom, and to clarify the coupling effects of different degrees of freedom in flutter instability. With this method, the flutter mechanism of two typical bridge deck sections, box girder section and two-isolated-girder section, were numerically investigated, and both differences and common ground in these two typical flutter phenomena are summarized. Then the flutter stabilization effect and its mechanism for long-span bridges with box girders by using central-slotting were studied by experimental investigation of aerodynamic stability and theoretical analysis of stabilizing mechanism. Possible explanation of new findings in the evaluation trend of critical wind speed through central vent width is finally presented.

• Smart Structures and Systems
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• v.25 no.1
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• pp.1-22
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• 2020

The modal strain energy method is one of the efficient methods for detecting damage in the structures. Due to existing some limitations in real-world structures, sensors can only be located on a limited number of degrees of freedom (DOFs) of a structure. Therefore, the mode shape values in all DOFs of structures cannot be measured. In this paper, a modified modal strain energy based index (MMSEBI) is introduced to locate damaged elements of structures when a limited number of sensors are used. The proposed MMSEBI is based on the reconstruction of mode shapes using Improved Reduction System (IRS) method. Therefore, in the first step by employing IRS method, mode shapes in slave degrees of freedom are estimated by those of master degrees of freedom. In the second step, the proposed MMSEBI is used to located damage elements. In order to evaluate the efficiency of the proposed method, two numerical examples are considered under different damage patterns considering the measurement noise. Moreover, the universal threshold based on statistical hypothesis testing principles is applied to damage index values. The results show the effectiveness of the proposed MMSEBI for the structural damage localization when comparing with the available damage index named MESBI. The results demonstrate that the presented method can be used as a practical strategy for structural damage identification, especially when a limited number of sensors are installed on the structure. Finally, the combination of MMSEBI and IRS method can provide a reliable tool to identify the location of damage accurately.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.5 no.2
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• pp.29-37
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• 1996

High speed engines with high power are increasingly on demands and almost engines employ crankshafts Such problems as bending and torsional vibrations become the point at issue in crankshaft analysis and design. In this study to overcome the diffiiculty with the large amount of computation in finite element vibration analysis of a crankshaft, a reduction method based on influence coefficient and lumped parameter is presented. which reduces the computation amount effectively and can be used in vibrational analysis and design of any types of crankshafts Crank journal and pinparts are meodelled as elements with 6degrees of freedom per node. Crank web part is modelled using equivalent mass and stiffness matices . based up on lumped parameter and influence coefficient respectively to reduce total degrees of freedom considerablely. To confirm the scheme of the study the results are compared with the known data and they are coincident. Also a simple crankshaft is designed and manufactured for experiments. The calculated results using reduction method and the experimental results agree well The scheme of this study can be utilized in evaluation results agree well. The calculated result are compared with the known data and they are coincident. Also a simple crankshaft is designed and manufactured for experiments. The calculated results using reduction method and the experimental results agree well. The scheme of this study can be utilized in evaluation and development of high speed engine.

• Ocean Systems Engineering
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• v.7 no.3
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• pp.179-193
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• 2017

Dynamic response analysis of offshore triceratops with stiffened buoyant legs under impact and non-impact waves is presented. Triceratops is relatively new-generation complaint platform being explored in the recent past for its suitability in ultra-deep waters. Buoyant legs support the deck through ball joints, which partially isolate the deck by not transferring rotation from legs to the deck. Buoyant legs are interconnected using equally spaced stiffeners, inducing more integral action in dispersing the encountered wave loads. Two typical nonlinear waves under very high sea state are used to simulate impact and non-impact waves. Parameters of JONSWAP spectrum are chosen to produce waves with high vertical and horizontal asymmetries. Impact waves are simulated by steep, front asymmetric waves while non-impact waves are simulated using Stokes nonlinear irregular waves. Based on the numerical analyses presented, it is seen that the platform experiences both steady state (springing) and transient response (ringing) of high amplitudes. Response of the deck shows significant reduction in rotational degrees-of-freedom due to isolation offered by ball joints. Weak-asymmetric waves, resulting in non-impact waves cause steady state response. Beat phenomenon is noticed in almost all degrees-of-freedom but values in sway, roll and yaw are considerably low as angle of incidence is zero degrees. Impact waves cause response in higher frequencies; bursting nature of pitch response is a clear manifestation of the effect of impact waves on buoyant legs. Non-impact waves cause response similar to that of a beating phenomenon in all active degrees-of-freedom, which otherwise would not be present under normal loading. Power spectral density plots show energy content of response for a wide bandwidth of frequencies, indicating an alarming behaviour apart from being highly nonlinear. Heave, being one of the stiff degrees-of-freedom is triggered under non-impact waves, which resulted in tether tension variation under non-impact waves as well. Reduced deck response aids functional requirements of triceratops even under impact and non-impact waves. Stiffened group of buoyant legs enable a monolithic behaviour, enhancing stiffness in vertical plane.

• Journal of Ocean Engineering and Technology
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• v.13 no.1 s.31
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• pp.23-28
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• 1999

For offshore structures, dynamic analysis becomes increasingly important as water depth increases and structural configuration becomes more slender. In the case of dynamic analysis of frame structures, much computer time and high cost are required due to many degrees of freedom, In this paper, a new technique of permutating a segment of frame structure to a beam is developed, which is called here Beam Permutation Technique. The technique is based on definition of stiffness matrix of the beam which is obtained by defining the actions(or forces) required to obtain unit translation or rotation for each degree of freedom wiht al other degree of freedom restrained to zero displacement or rotation. In the technique, an assumption is made that relative positions of nodes in the ends of the segment are not variable, The technique can significantly reduce the degrees of freedom of frame structures and thus the computiong time in dynamic analysis. The natural frequencies and static displacements of the permutated beam are obtained and compared to those of ANSYS with a good agreement.