Mean Square Value Of Response Research Articles

Optimal design of eccentricity for seismic applications

Making either mass or stiffness eccentric mitigates the translational vibration of systems subjected to base excitation. The level of mitigation depends not only on the amount of eccentricity but also on the frequency ratio (the ration of translational frequency to rotational frequency). This paper proposes a systematic approach for finding the values of eccentricity and frequency ratio that lead to the maximum reduction in translational vibrations. First an optimization problem in frequency domain is formulated. The mean square value of response is selected as the performance index. Two types of constraints including limitations on rotations and eccentricity are imposed. Kanai–Tajimi power spectral density function is used to model the ground motion. After formulating the optimization problem two structural models are studied numerically: a single story building model and a multistory building model. It is observed that using the proposed approach the performance index can be reduced by up to 50%. The time history analyses also indicate significant reductions in displacements. Finally a case study is conducted to compare the performance of the proposed strategy with that of other established passive control methods. The results of the case study show that the proposed method can be as effective as other strategies, as far as displacement control is concerned.

Approximate calculation method for integral of mean square value of nonstationary response

The response of the structure subjected to nonstationary random vibration such as earthquake excitation is nonstationary random vibration. Calculating method for statistical characteristics of such a response is complicated. Mean square value of the response is usually used to evaluate random response. Integral of mean square value of the response corresponds to total energy of the response. In this paper, a simplified calculation method to obtain integral of mean square value of the response is proposed. As input excitation, nonstationary white noise and nonstationary filtered white noise are used. Integrals of mean square value of the response are calculated for various values of parameters. It is found that the proposed method gives exact value of integral of mean square value of the response.

Simplified Calculation Method for Integral of Mean Square Value of Nonstationary Seismic Response

The seismic response of the structure is nonstationary random vibration because earthquake excitation is nonstationary random vibration. Calculating method for the statistical characteristics of such a nonstationary response is complicated. The mean square value of the response is usually used to evaluate the statistical characteristics of random response. Integral of the mean square value of the response corresponds to total energy of the response. In this paper, a simplified calculation method to obtain integral of the mean square value of the nonsatationary response is proposed. In this method, the mean square value of the stationary response is used. As an earthquake excitation, nonstationary filtered white noise is used considering the dynamic characteristics of the ground. Integrals of the mean square value of the nonstationary random response are calculated for various values of parameters. It is found that the proposed method gives exact values of integral of the mean square value of the nonstationary random response.

212 非定常不規則振動応答の自乗平均値の積分値の近似計算法 : 種々の系および入力に対する検討

The response of the structure subjected to nonstationary random vibration such as earthquake excitation is nonstationary random process. Calculating method for statistical characteristics of such a response is complicated. Mean square value is one of the representative statistical values. Then, practical and simplified method to obtain theoretical statistical value is required. Integral of mean square value of the response corresponds to total energy of the response. In this paper, a simplified calculation method to obtain integral of mean square value of the response of the structure is proposed. Nonstationary random p input excitation is given as product of envelop function and stationary random process. Mean square value of nonstationary random response is assumed to be product of square of envelop function and mean square value of stationary random response. It is found that the proposed method gives exact value of integral of mean square value of the response

Response of nonlinear systems in probability domain using stochastic averaging

Determination of probability density function (PDF) of the response for strongly nonlinear single-degree-of-freedom system subjected to both multiplicative and additive random excitations using stochastic averaging technique is faced with few difficulties. Firstly, the size of excitations should be small such that the response of the system converges weakly to a Markov process. Secondly, the excitations should preferably be broad banded so that the analytical results are reasonably accurate and finally, the nonlinear functions should be integrable if closed-formed expressions for the result are desired. The above issues are examined in the paper with a view to show (a) limiting values of the size parameter of excitations for which stochastic averaging technique can be applied to obtain reasonable estimates of PDF and mean square value of response, (b) the effect of the nature of the frequency contents of excitation on the response and (c) the use of the stochastic averaging method employing generalized harmonic functions for nonintegrable functions representing the dynamic system. It is shown that the stochastic averaging procedure provides results which compare very well with those obtained from simulation analysis not only for wide band excitations, but also for narrow band excitations for a wide range of the size parameter of excitation. Further, the procedure can be easily implemented for highly irregular functions by employing a numerical scheme with FFT.

不確定要素を含む構造物のランダム応答解析 部分構造合成法と階層法による解析

In this paper, the method to obtain the random response of a structure with uncertain parameters is proposed. The proposed method is a combination of the substructure synthesis method and the hierarchy method. The concept of the proposed method is that the hierarchy equation of each substructure is obtained using the hierachy method, and the hierarchy equation of the overall structure is obtained using the substructure synthesis method. Using the proposed method, the reduced order hierarchy equation can be obtained without analyzing the original whole structure. After the calculation of the mean square value of response, the reliability analysis can be carried out based on the first passage problem and Poisson's excursion rate. As a numerical example of structure, a simple piping system is considered. The damping constant of the support is considered as the uncertainty parameter. Then the random response is calculated using the proposed method. As a result, the proposed method is useful to analyze the random response in terms of the accuracy, computer storage and calculation time.