• Earthquakes and Structures
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• v.3 no.1
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• pp.17-35
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• 2012

Simplified equations for fundamental period of vibration of skeletal structures provided by most seismic design provisions suffer from the absence of any associated confidence levels and of any reference to their empirical basis. Therefore, such equations may typically give a sector of designers the false impression of yielding a fairly accurate value of the period of vibration. This paper, although not addressing simplified codes equations, introduces a set of mathematical equations utilizing the theory of error propagation and First-Order Second-Moment (FOSM) techniques to determine bounds on the relative error in theoretically calculated fundamental period of vibration of skeletal structures. In a complementary step, and for verification purposes, Monte Carlo simulation technique has been also applied. The latter, despite involving larger computational effort, is expected to provide more precise estimates than FOSM methods. Studies of parametric uncertainties applied to reinforced concrete frame bents - potentially idealized as SDOF systems - are conducted demonstrating the effect of randomness and uncertainty of various relevant properties, shaping both mass and stiffness, on the variance (i.e. relative error) in the estimated period of vibration. Correlation between mass and stiffness parameters - regarded as random variables - is also thoroughly discussed. According to achieved results, a relative error in the period of vibration in the order of 19% for new designs/constructions and of about 25% for existing structures for assessment purposes - and even climbing up to about 36% in some special applications and/or circumstances - is acknowledged when adopting estimates gathered from the literature for relative errors in the relevant random input variables.

• Earthquakes and Structures
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• v.6 no.2
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• pp.201-216
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• 2014

Many building codes use the empirical equation to determine fundamental period of vibration where in effect of length, width and the stiffness of the building is not explicitly accounted for. Also the equation, estimates the fundamental period of vibration with large safety margin beyond certain height of the building. An attempt is made to arrive at the simple empirical equations for fundamental period of vibration with adequate safety margin, using soft computing technique of Genetic Programming (GP). In the present study, GP models are developed in four categories, varying the number of input parameters in each category. Input parameters are chosen to represent mass, stiffness and geometry of the buildings directly or indirectly. Total numbers of 206 buildings are analyzed out of which, data set of 142 buildings is used to develop these models. It is observed that GP models developed under B and C category yield the same equation for fundamental period of vibration along X direction as well as along Y direction whereas the equation of fundamental period of vibration along X direction and along Y direction is of the same form for category D. The equations obtained as an output of GP models clearly indicate the influence of mass, geometry and stiffness of the building over fundamental period of vibration. These equations are then compared with the equation recommended by other researcher.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.43-51
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• 2004

As the slenderness ratio of a high-rise building increases, the lateral load resisting system for the building is more often determined by serviceability design criteria. In serviceability design, the maximum drift and the level of vibration are controlled not to exceed the design criteria. Even though many drift method have been developed in various forms, no practical design method for wind induced vibration has been developed so far. Structural engineers rely upon heuristic or experience in designing wind induced vibration. Development of practical design method for wind induced vibration is required. Generally, wind induced acceleration responses are depending on several variables such as the weight density of a building, damping ratio, the natural period, and etc.. All parameters except the natural period or frequency are usually out of reach for structural engineers, then the wind acceleration response may be proportioned to the natural period. Therefore, in this paper, a wind induced vibration design method based on frequency control technique for high-rise is proposed. The method is applied to vibration design of a 25-story office building for performance evaluation.

• Earthquakes and Structures
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• v.4 no.4
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• pp.397-428
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• 2013

This paper examines whether the "effective period" of bilinear isolation systems, as defined invariably in most current design codes, expresses in reality the period of vibration that appears in the horizontal axis of the design response spectrum. Starting with the free vibration response, the study proceeds with a comprehensive parametric analysis of the forced vibration response of a wide collection of bilinear isolation systems subjected to pulse and seismic excitations. The study employs Fourier and Wavelet analysis together with a powerful time domain identification method for linear systems known as the Prediction Error Method. When the response history of the bilinear system exhibits a coherent oscillatory trace with a narrow frequency band as in the case of free vibration or forced vibration response from most pulselike excitations, the paper shows that the "effective period" = $T_{eff}$ of the bilinear isolation system is a dependable estimate of its vibration period; nevertheless, the period associated with the second slope of the bilinear system = $T_2$ is an even better approximation regardless the value of the dimensionless strength,$Q/(K_2u_y)=1/{\alpha}-1$, of the system. As the frequency content of the excitation widens and the intensity of the acceleration response history fluctuates more randomly, the paper reveals that the computed vibration period of the systems exhibits appreciably scattering from the computed mean value. This suggests that for several earthquake excitations the mild nonlinearities of the bilinear isolation system dominate the response and the expectation of the design codes to identify a "linear" vibration period has a marginal engineering merit.

• Journal of Korean Association for Spatial Structures
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• v.6 no.3 s.21
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• pp.43-50
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• 2006

This paper is concerned with the natural periods of ambient vibration and eigenvalue analysis. Ambient vibration tests were conducted to four bearing-wall reinforced concrete buildings ranging from twelve to nineteen stories. The performance of modeling in eigenvalue analysis was investigated using consideration of rigidity out of the plane in the slab and the non-structural bearing wall. Measured natural period was also compared with the value by the KBC2005. Natural period of the short direction in eigenvalue analysis is well fitted with the measured one. In the other hand, Natural period of the long direction in eigenvalue analysis is slightly more overestimated than the measured one. Natural period of the long direction in eigenvalue analysis was found to be enhanced by considering the effect of the stiffness out of the plane of the slab and non-structural wall in the structural modeling.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.355-360
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• 2005

This paper describes how to measure the running safety using vibration accelerometers theoretically, and considers the effect of vibration parameters, such as amplitude and period, on the running safety by numerical analysis, which shows that the running safety are decreased as those parameters are increased.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.5C
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• pp.185-192
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• 2012

The objective of this study is to present and verify a method for evaluating the fundamental period of a rockfill dam using artificially generated vibration from a blasting event. In this study, the artificial blasting vibration tests were carried out at the site adjacent to the existing Seongdeok Dam for the first time in Korea. The artificial vibrations were induced by 4 different types of blasting with the various depths of blasting boreholes and the various explosive charge weight. During the tests, the accelerations time histories were recorded at the crest of the dam. In this acceleration history, only free vibration decay part following the main vibration event was extracted and it was analyzed by frequency domain analysis using Fast Fourier Transform (FFT). From the results of FFT, the fundamental period of the target dam was evaluated. It is found that the effect of different blasting types on the fundamental period of the target dam is negligible and the fundamental period of the target dam can be consistently obtained by blasting vibration tests. Furthermore, it is found that the period of the target dam calculated by the method using blasting vibration test is similar to that obtained by the method of previous researchers using the real earthquake records. Therefore, in case that the earthquake record is not available, the fundamental period of a rockfill dam can be reasonably evaluated if blasting vibration test is allowed at the site adjacent to the dam.

• Structural Monitoring and Maintenance
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• v.4 no.4
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• pp.351-364
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• 2017

In this study effects of various parameters like a number of bays, the stiffness of the structure along with the height of the structure was examined. The fundamental period of vibration T of the building is an important parameter for evaluation of seismic base shear. Empirical equations which are given in the Indian seismic code for the calculation of the fundamental period of a framed structure, primarily as a function of height, and do not consider the effect of number of bays and stiffness of the structure. Building periods predicted by these expressions are widely used in practice, although it has been observed that there is scope for further improvement in these equations since the height alone is inadequate to explain the period variability. The aim of this study is to find the effects of a number of bays in both the directions, the stiffness of the structure and propose a new period equation which incorporates a number of bays, plan area, stiffness along with the height of the structure.

• Journal of KSNVE
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• v.9 no.5
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• pp.906-913
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• 1999

Time-dependent period and energy of free vibration of a string, whose length varies with time at a constant rate, are investigated by a traveling wave method. When the string length is increased, the vibration period increase, but the free vibration energy decrease with time. However, when the string undergoes retraction, the vibration energy increases with time. String tension together with non-zero instantaneous velocity at the moving boundary results in energy variation. Analytical solutions by the traveling wave method are compared with previous results using the perturbation method and Kotera's approach.

• Journal of Korean Physical Therapy Science
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• v.30 no.1
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• pp.72-84
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• 2023

Background: The purpose of this study was to investigate the effect of whole-body vibration stimulation training on the thickness of the transversus abdominis muscle and the balance of sitting posture in children with spastic cerebral palsy. Design: Single-subject design(A-B-A-B). Methods: The subjects of this study were 9 children with spastic cerebral palsy. The study period was 12 weeks in total, and the baseline period and the intervention period were each assigned 3 weeks. Intervention was conducted twice a week for 30 minutes. During the baseline period, trunk stabilization exercise was performed, and during the intervention period, trunk stabilization exercise and whole-body vibration stimulation training were performed. Measurements were carried out at before the experiment, baseline 1, intervention 1, baseline 2, intervention 2 and the total number of measurements was 5 times. Repeated ANOVA was performed to compare the effects of exercise according to the intervention method. Results: The thickness of the transversus abdominis muscle and the balance of the sitting posture were statistically significantly increased compared to the baseline during whole-body vibration stimulation training (p<.05). Conclusion: Therefore, it was confirmed that whole-body vibration stimulation training improved the thickness of the transversus abdominis muscle in children with spastic cerebral palsy and was an effective intervention method for improving sitting posture balance.