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Journal articles on the topic 'Complex mdof structural systems'

Author: Grafiati

Published: 10 March 2023

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1

F. Masri, S., F. Tasbihgoo, J. P. Caffrey, A. W. Smyth, and A. G. Chassiakos. "Data-based model-free representation of complex hysteretic MDOF systems." Structural Control and Health Monitoring 13, no. 1 (January 2006): 365–87. http://dx.doi.org/10.1002/stc.147.

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2

Reyes-Salazar, Alfredo, Federico Valenzuela-Beltran, David de Leon-Escobedo, Eden Bojorquez-Mora, and Arturo Lopez Barraza. "Combination rules and critical seismic response of steel buildings modeled as complex MDOF systems." Earthquakes and Structures 10, no. 1 (January 25, 2016): 211–38. http://dx.doi.org/10.12989/eas.2016.10.1.211.

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3

Chen, Menghui, Xiaoshu Gao, Cheng Chen, Tong Guo, and Weijie Xu. "A Comparative Study of Meta-Modeling for Response Estimation of Stochastic Nonlinear MDOF Systems Using MIMO-NARX Models." Applied Sciences 12, no. 22 (November 14, 2022): 11553. http://dx.doi.org/10.3390/app122211553.

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Complex dynamic behavior of nonlinear structures makes it challenging for uncertainty analysis through Monte Carlo simulations (MCS). Surrogate modeling presents an efficient and accurate computational alternative for a large number of MCS. The previous study has demonstrated that the multi-input multi-output nonlinear autoregressive with exogenous input (MIMO-NARX) model provides good discrete-time representations of deterministic nonlinear multi-degree-of-freedom (MDOF) structural dynamic systems. Model order reduction (MOR) is executed to eliminate insignificant modes to reduce the computational burden due to too many degrees of freedom. In this study, the MIMO-NARX strategy is integrated with different meta-modeling techniques for uncertainty analysis. Different meta-models including Kriging, polynomial chaos expansion (PCE), and arbitrary polynomial chaos (APC) are used to surrogate the NARX coefficients for system uncertainties. A nine-DOF structure is used as an MDOF dynamic system to evaluate different meta-models for the MIMO-NARX. Good fitness of statistical responses is observed between the MCS results of the original system and all surrogated MIMO-NARX predictions. It is demonstrated that the APC-NARX model with the advantage of being data-driven is the most efficient and accurate tool for uncertainty quantification of nonlinear structural dynamics.

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4

McElhaney, J. M., A. Palazzolo, and A. Kascak. "Modeling and Simulation Methods for MDOF Structures and Rotating Machinery With Impact Dampers." Journal of Engineering for Gas Turbines and Power 119, no. 2 (April 1, 1997): 436–46. http://dx.doi.org/10.1115/1.2815594.

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Previously published work on applied impact damping typically relates to SDOF models or simple MDOF models such as the classical cantilever beam. Structural models often require an extremely large number of DOF with mode shapes that are generally very complex. Dynamics simulation of these typically becomes both complicated and time consuming. The nonlinear behavior of impact dampers further complicates such simulation in that standard linear solutions are not possible. The primary objective in this research extends previous work by applying impact dampers to MDOF structures that are modeled with general three-dimensional “beam” finite elements. Modal-based models of the MDOF systems and efficient impact damper tracking algorithms were also developed that significantly reduced CPU time for simulation. Significant among the objectives was obtaining an impact damper design for the MDOF casing structure of the Space Shuttle Main Engine (SSME), High-Pressure Oxygen Turbo-Pump (HPOTP), subject to pump rotor shaft unbalance. Impact damper performance is based on suppression of vibration at casing critical frequencies for rotor speed ranges, at rotor full speed, and very high unbalance to simulate a defect such as losing an impeller blade fragment or a cracked bearing [6]. Simulations show significant reductions in vibration at the casing critical frequencies and very high unbalance levels while little or no improvement was observed off resonance. Additionally, the previous work with an experimental rotor bearing system (RBS) and impact damper was modeled using the developed modal-based methods. Simulation of the resulting model response shows remarkable agreement with the experimental. Finally, both the RBS and the HPOTP were modeled and simulated as unstable systems with attached impact dampers. The simulations predict that the impact damper is an excellent stabilizing mechanism for a range of instability driver values. Simulation of the models in this research with the developed modal based algorithms were accomplished with excellent efficiency, and accurate results.

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5

Reyes-Salazar, Alfredo, Achintya Haldar, Ramon Eduardo Rodelo-López, and Eden Bojórquez. "Effect of Damping and Yielding on the Seismic Response of 3D Steel Buildings with PMRF." Scientific World Journal 2014 (2014): 1–21. http://dx.doi.org/10.1155/2014/915494.

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The effect of viscous damping and yielding, on the reduction of the seismic responses of steel buildings modeled as three-dimensional (3D) complex multidegree of freedom (MDOF) systems, is studied. The reduction produced by damping may be larger or smaller than that of yielding. This reduction can significantly vary from one structural idealization to another and is smaller for global than for local response parameters, which in turn depends on the particular local response parameter. The uncertainty in the estimation is significantly larger for local response parameter and decreases as damping increases. The results show the limitations of the commonly used static equivalent lateral force procedure where local and global response parameters are reduced in the same proportion. It is concluded that estimating the effect of damping and yielding on the seismic response of steel buildings by using simplified models may be a very crude approximation. Moreover, the effect of yielding should be explicitly calculated by using complex 3D MDOF models instead of estimating it in terms of equivalent viscous damping. The findings of this paper are for the particular models used in the study. Much more research is needed to reach more general conclusions.

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6

Reyes-Salazar, Alfredo, Eden Bojorquez, Achintya Haldar, Arturo Lopez-Barraza, and J. Luz Rivera-Salas. "Ductility Reduction Factors for Steel Buildings Modeled as 2D and 3D Structures." Applied Mechanics and Materials 595 (July 2014): 166–72. http://dx.doi.org/10.4028/www.scientific.net/amm.595.166.

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The global ductility parameter (μG), commonly used to represent the capacity of a structure to dissipate energy, and the associated ductility reduction factor (Rμ), are estimated for steel buildings with perimeter moment resisting frames (PMRF), which are modeled as 2D and 3D complex MDOF systems. Results indicate that the μG value of 4, commonly assumed for moment resisting steel frames, cannot be justified. A value of 3 is more reasonable. The values of μG and Rμ may be quite different for 2D and 3D structural representations or for local and global response parameters, showing the limitation of the commonly used Equivalent Lateral Force Procedure (ELFP). Thus, the ductility and ductility reduction factors obtained from simplified structural representation must be taken with caution.

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7

Valenzuela-Beltrán, Federico, Mario D. Llanes-Tizoc, Edén Bojórquez, Juan Bojórquez, Robespierre Chávez, Jesus Martin Leal-Graciano, Juan A. Serrano, and Alfredo Reyes-Salazar. "Effect of the Distribution of Mass and Structural Member Discretization on the Seismic Response of Steel Buildings." Applied Sciences 12, no. 1 (January 3, 2022): 433. http://dx.doi.org/10.3390/app12010433.

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The response of steel moment frames is estimated by first considering that the mass matrix is the concentrated type (ML) and then consistent type (MC). The effect of considering more than one element per beam is also evaluated. Low-, mid- and high-rise frames, modeled as complex-2D-MDOF systems, are used in the numerical study. Results indicate that if ML is used, depending upon the response parameter under consideration, the structural model, the seismic intensity and the structural location, the response can be significantly overestimated, precisely calculated, or significantly underestimated. Axial loads at columns, on an average basis, are significantly overestimated (up to 60%), while lateral drifts and flexural moments at beams are precisely calculated. Inter-story shears and flexural moments at columns, on average, are underestimated by up to 15% and 35%, respectively; however, underestimations of up to 60% can be seen for some individual strong motions. Similarly, if just one element per beam is used in the structural modeling, inter-story shears and axial loads on columns are overestimated, on average, by up to 21% and 95%, respectively, while the lateral drifts are precisely calculated. Flexural moments at columns and beams can be considerably underestimated (on average up to 14% and 35%, respectively), but underestimations larger than 50% can be seen for some individual cases. Hence, there is no error in terms of lateral drifts if ML or one element per beam is used, but significant errors can be introduced in the design due to the overestimation and underestimation of the design forces. It is strongly suggested to use MC and at least two elements per beam in the structural modeling.

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8

Qiang, Pei, Er Liang Chen, and Xiao Dong Zhao. "Dynamic Calculation of MDOF Systems Based on GIS." Advanced Materials Research 446-449 (January 2012): 3019–22. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.3019.

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The paper presents an integration of a Geographic Information System (GIS) and Multiple Degree of Freedom (MDOF) model for structural dynamic calculations. The input data of MDOF is stored in the format of spatial data model in GIS with 2D and 3D with the help of Google SketchUp. The output data of MDOF can be viewed in both 2D graph and 3D visualization after simulation calculation in GIS. A case study of dynamic response of campus buildings is presented to illustrate how the GIS-coupled system has been developed. Results show that the proposed GIS-model integrated system can perform a large number of dynamic responses of MDOF affected by earthquakes, promote better earthquake resistant behavior of building structure in urban regions, and thus optimize hazard assessment, vulnerability estimation and seismic risk reduction.

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9

Wang, Xiaohan, Weihang Ren, Baocheng Liu, and Dong Hu. "Structural Dynamics and Vibration Analysis of the MDOF Systems." Journal of Physics: Conference Series 2381, no. 1 (December 1, 2022): 012004. http://dx.doi.org/10.1088/1742-6596/2381/1/012004.

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Abstract Because the vibration of buildings plays an important role in resisting an earthquake, we need some methods to analyze the vibration of the MDOF systems. This paper proposes a method to analyze the structural dynamics and vibration of the MDOF systems by using the “modal superposition method” and the “Duhamel integral”. We set the system consisting of mass, stiffness, and damping to correspond to actual situations. The results obtained in this research include the E.O.M: natural frequency and mode shape of the building model, which can show the resonance of the building. Based on our analysis, designers can make a more appropriate design of buildings that can reduce the mortality in the earthquake.

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Tang, Yu, Chao Luo, and Bo Fu. "Choices of the Critical Frequency for φ in TL-φ Algorithms When Applied to Multi-Degree of Freedom Systems." Buildings 12, no. 6 (June 20, 2022): 863. http://dx.doi.org/10.3390/buildings12060863.

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TL-φ algorithms are newly developed explicit structure-dependent integration algorithms utilized for solving the temporally discretized equations of motion. In contrast to the existing algorithms, the most significant improvement of TL-φ algorithms is in diminishing the amount of period errors by introducing a precorrection coefficient φ into the integration parameters of TL-φ algorithms, which is related to the critical frequency of a system. In the previous work, the fundamental frequency of the system is deemed to be the critical frequency, so that φ is a constant scaling corresponding to the fundamental frequency for both single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems. However, for a MDOF system, the first mode may not contribute to the total response more than other ones under a given external excitation, calculating φ only by the fundamental frequency will underestimate the contribution of the higher-frequency modes to structural dynamics. In this paper, choices of the critical frequency for φ when applying TL-φ algorithms to MDOF systems are investigated thoroughly. By considering the initial structural properties of the system and the frequency characteristics of the external excitation simultaneously, a calculation criterion of φ for MDOF systems under specific external excitations is proposed. Four numerical examples with different initial structure properties and loading conditions are designed, and the results demonstrate that the proposed criterion can be potentially used to solve structural dynamic problems of MDOF systems with a more desirable numerical dispersion performance.

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11

Najafgholipour, Mohammadamir, and Navid Soodbakhsh. "Modified Differential Transform Method for Solving Vibration Equations of MDOF Systems." Civil Engineering Journal 2, no. 4 (May 7, 2016): 123–39. http://dx.doi.org/10.28991/cej-2016-00000019.

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Vibration equations of discrete multi-degrees-of-freedom (MDOF) structural systems is system of differential equations. In linear systems, the differential equations are also linear. Various analytical and numerical methods are available for solving the vibration equations in structural dynamics. In this paper modified differential transform method (MDTM) as a semi-analytical approach is generalized for the system of differential equations and is utilized for solving the vibration equations of MDOF systems. The MDTM is a recursive method which is a hybrid of Differential Transform Method (DTM), Pade' approximant and Laplace Transformation. A series of examples including forced and free vibration of MDOF systems with classical and non-classical damping are also solved by this method. Comparison of the results obtained by MDTM with exact solutions shows good accuracy of the proposed method; so that in some cases the solutions of the vibration equation that found by MDTM are the exact solutions. Also, MDTM is less expensive in computational cost and simpler with compare to the other available approaches.

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12

Sun, Wei-Joe, and Ahsan Kareem. "Response of MDOF systems to nonstationary random excitation." Engineering Structures 11, no. 2 (April 1989): 83–91. http://dx.doi.org/10.1016/0141-0296(89)90017-5.

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13

Bontempi, F., and F. Casciati. "Non-linear dynamics versus chaotic motion for MDOF structural systems." Chaos, Solitons & Fractals 7, no. 10 (October 1996): 1659–82. http://dx.doi.org/10.1016/s0960-0779(96)00061-6.

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14

Chen, T. Y. "Structural modification with frequency response constraints for undamped mdof systems." Computers & Structures 36, no. 6 (1990): 1013–18. http://dx.doi.org/10.1016/0045-7949(90)90208-j.

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15

Di Paola, M., and G. Falsone. "Stochastic dynamics of MDOF structural systems under non-normal filtered inputs." Probabilistic Engineering Mechanics 9, no. 4 (January 1994): 265–72. http://dx.doi.org/10.1016/0266-8920(94)90018-3.

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16

Ali, Sk Faruque, and Ananth Ramaswamy. "Optimal fuzzy logic control for MDOF structural systems using evolutionary algorithms." Engineering Applications of Artificial Intelligence 22, no. 3 (April 2009): 407–19. http://dx.doi.org/10.1016/j.engappai.2008.09.004.

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17

Nazri, Fadzli Mohamed, and Nicholas A. Alexander. "Exploring the relationship between earthquake intensity and building damage using single and multi-degree of freedom models." Canadian Journal of Civil Engineering 41, no. 4 (April 2014): 343–56. http://dx.doi.org/10.1139/cjce-2012-0477.

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The correlation between intensity and damage measure for generic moment-resisting steel frames (MRSF) that are subjected to earthquake shaking was analysed using optimised nonlinear single degree of freedom (SDOF) models. The parameters for these SDOF models are based on nonlinear quasi-static pushover analyses of the multi-degree of freedom (MDOF) building systems. This intensity–damage relationship was then compared with those obtained from incremental dynamic analysis (IDA), that is a MDOF approach. Results show that the general trend line of intensity–damage measures for nonlinear SDOF model was qualitatively similar to the MDOF model that in this case represents a full nonlinear finite element analysis of the MRSF. While the SDOF model is not a precise match to the MDOF model, results suggests that it can be used in the vital role of ground motion record selection because of its computational efficiency. Furthermore, it is shown that the accuracy of intensity–damage estimates from the SDOF models can be improved if optimal damping, pseudo-yield, and ultimate loads are chosen. The efficacy of various intensity measures on damage are compared and contrasted.

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18

Xiao, Mei Ling, Liao Yuan Ye, and Chun Tao Gao. "Seismic Reliability Analysis of MDOF Systems Based on Odd Exponent Wavelet." Advanced Materials Research 194-196 (February 2011): 1711–15. http://dx.doi.org/10.4028/www.scientific.net/amr.194-196.1711.

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This study proposed non-failure or non-disabled probability of structure suffering random dynamic load within given time. A wavelet method based on its conception was proposed for seismic dynamic reliability analysis of MDOF system：From the Duhamel integral of the dynamic structural response, the structure stochastic response was expressed as earthquake ground motion’s wavelet transform. The ground motion and structure responses were modeled as non-stationary random process using odd exponent wavelets. The first-passage failure criterion and maximum probability were employed to estimate the structural dynamic reliability. The primary advantage of the proposed method is that it does not need to calculate spectral moments from the power density function integral, which are usually difficult to obtain the analytical expressions.

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19

Aggumus, Huseyin, and Rahmi Guclu. "Robust H∞ Control of STMDs Used in Structural Systems by Hardware in the Loop Simulation Method." Actuators 9, no. 3 (July 20, 2020): 55. http://dx.doi.org/10.3390/act9030055.

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This paper investigated the performance of a semi-active tuned mass damper (STMD) on a multi-degree of freedom (MDOF) building model. A magnetorheological (MR) damper was used as a control element that provided semi-activity in the STMD. The Hardware in the Loop Simulation (HILS) method was applied to mitigate the difficulty and expense of experimental studies, as well as to obtain more realistic results from numerical simulations. In the implementation of this method for the STMD, the MR damper was set up experimentally, other parts of the system were modeled as computer simulations, and studies were carried out by operating these two parts simultaneously. System performance was investigated by excitation with two different acceleration inputs produced from the natural frequencies of the MDOF building. Additionally, a robust H ∞ controller was designed to determine the voltage transmitted to the MR damper. The results showed that the HILS method could be applied successfully to STMDs used in structural systems, and robust H ∞ controls improve system responses with semi-active control applications. Moreover, the control performance of the MR damper develops with an increase in the mass of the STMD.

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20

Han, Xiaojing, and Emmanuel Pagnacco. "Response EPSD of chain-like MDOF nonlinear structural systems via wavelet-Galerkin method." Applied Mathematical Modelling 103 (March 2022): 475–92. http://dx.doi.org/10.1016/j.apm.2021.10.036.

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Muscolino, Giuseppe, and Giuseppe Ricciardi. "Probability density function of MDOF structural systems under non-normal delta-correlated inputs." Computer Methods in Applied Mechanics and Engineering 168, no. 1-4 (January 1999): 121–33. http://dx.doi.org/10.1016/s0045-7825(98)00137-6.

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22

Sun, Yu, Jinsong Zhou, Dao Gong, and Yuanjin Ji. "Study on multi-degree of freedom dynamic vibration absorber of the car body of high-speed trains." Mechanical Sciences 13, no. 1 (March 17, 2022): 239–56. http://dx.doi.org/10.5194/ms-13-239-2022.

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Abstract. To absorb the vibration of the car body of the high-speed train in multiple degrees of freedom, a multi-degree of freedom dynamic vibration absorber (MDOF DVA) is proposed. Installed under the car body, the natural frequency of the MDOF DVA from each DOF can be designed as a DVA for every single degree of freedom of the car body. Hence, a 12-DOF model including the main vibration system and an MDOF DVA is established, and the principle of Multi-DOF dynamic vibration absorption is analyzed by combining the design method of a single DVA and genetic algorithm. Based on a high-speed train dynamics model including an under-car-body MDOF DVA, the vibration control effect on each DOF of the MDOF DVA is analyzed by the virtual excitation method. Moreover, a high static and low dynamic stiffness (HSLDS) mount is proposed based on a cam–roller–spring mechanism for the installation of the MDOF DVA due to the requirement of the low vertical dynamic stiffness. From the dynamic simulation of a non-linear model in the time domain, the vibration control performance of the MDOF DVA installed with a nonlinear HSLDS mount on the car body is analyzed. The results show that the MDOF DVA can absorb the vibration of the car body in multiple degrees of freedom effectively and improve the running ride quality of the vehicle.

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23

Vazquez Feijoo, J. A., K. Worden, P. Montes Garcia, L. Lagunez Rivera, N. Juarez Rodriguez, and A. Pech Pérez. "Analysis of MDOF nonlinear systems using associated linear equations." Mechanical Systems and Signal Processing 24, no. 8 (November 2010): 2824–43. http://dx.doi.org/10.1016/j.ymssp.2010.04.008.

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24

Jia, Ying-Qi, Chao Wang, Rui-Fu Zhang, Ling-Zhi Li, and Zhou-Dao Lu. "A Double Shape Memory Alloy Damper for Structural Vibration Control." International Journal of Structural Stability and Dynamics 21, no. 07 (April 21, 2021): 2150098. http://dx.doi.org/10.1142/s021945542150098x.

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Shape memory alloy (SMA) dampers are widely investigated passive control systems for structural vibration mitigation. However, the damping robustness of conventional austenite SMA dampers may be affected by environmental temperature. In this study, an innovative double SMA damper (DSD) system is presented to improve the temperature robustness of the SMA dampers. In the proposed system, double SMA hysteretic elements with different phase transition temperatures are arranged in parallel, where the SMA element with lower transition temperature behaves as austenite under room temperature, and the other with higher transition temperature behaves as martensite. To study the vibration control effect, both single-degree-of-freedom (SDOF) and multiple-degree-of-freedom (MDOF) structures with DSD systems are employed. The thermal and mechanical behaviors of the SMA elements and the working principle of DSD are also introduced. Thereon, the equivalent linearization method for SMA’s output force and the motion-governing equations for SDOF structure with DSD are derived. Moreover, parametric studies are conducted to investigate the performance of the proposed DSD system in both frequency and time domains. Also, numerical analysis for the MDOF structure with DSD systems is carried out to illustrate the trend in response reduction with an increasing number of degrees of freedom. The analytical results show that the DSD can mitigate the structural seismic response more effectively than the conventional one with acceptable residual deformation, and is capable of delaying the degradation of SMA’s energy dissipation capacity. Less SMA material is required for the proposed DSD to fulfill the same mitigation requirement, and it is suitable for general applications for temperature robustness.

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25

Badla, Oualid, T. Bouzid, and P. Martinez Vazquez. "Inelastic Analysis of Mdof Systems Damaged by Earthquakes, Posteriorly Subjected to Wind Load." Civil Engineering Journal 7, no. 3 (March 1, 2021): 575–93. http://dx.doi.org/10.28991/cej-2021-03091675.

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This paper deals with the analysis of the inelastic response of buildings originally damaged by earthquakes and subjected to earthquake aftershock and wind loading. The overall aim is to establish the effect of wind actions on structural stability. To that end, one four-story bare frame benchmarked by the European Laboratory for Structural Assessment, is subject to various levels of winds and earthquake joint load while monitoring changes on the ductility demand. In this paper is shown that the combined action of strong winds and earthquakes, however its low probability of occurrence, would cause a decrease of strength reduction factors and considerably increase the ductility demand of damaged infrastructure hence inducing additional risks that would otherwise remain unquantified. The paper examines the non-linear performance of Multi-degree of freedom systems subject to various levels of winds and earthquake load and deals with the estimation of strength reduction factors. This is a relatively unexplored area of research which builds on past developments whereby inelastic performance of buildings has been discussed. It also links to various other paths of development such as structural reliability, forensic and control systems engineering. Doi: 10.28991/cej-2021-03091675 Full Text: PDF

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Guenfaf, Lakhdar, and Mohamed Azira. "Generalized Minimum Variance Control for MDOF Structures under Earthquake Excitation." Journal of Control Science and Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/7458654.

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Control of a multi-degree-of-freedom structural system under earthquake excitation is investigated in this paper. The control approach based on the Generalized Minimum Variance (GMV) algorithm is developed and presented. Our approach is a generalization to multivariable systems of the GMV strategy designed initially for single-input-single-output (SISO) systems. Kanai-Tajimi and Clough-Penzien models are used to generate the seismic excitations. Those models are calculated using the specific soil parameters. Simulation tests using a 3DOF structure are performed and show the effectiveness of the control method.

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Pradlwarter, H. J., and G. I. Schuëller. "Equivalent linearization—a suitable tool for analyzing MDOF-systems." Probabilistic Engineering Mechanics 8, no. 2 (January 1993): 115–26. http://dx.doi.org/10.1016/0266-8920(93)90005-g.

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28

Carlos, Iturregui Arranz, Soria Herrera Jose Manuel, Muñoz Díaz Ivan, and García Palacios Jaime Higinio. "Energy balance analysis in non linear dynamic equivalent systems." MATEC Web of Conferences 148 (2018): 03002. http://dx.doi.org/10.1051/matecconf/201814803002.

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The aim of the paper is to present a critical analysis for nonlinear dynamic vibrations. It is applicable to single degree of freedom –SDOF- of reinforced concrete –RC- structures, revealing its multi degree of freedom –MDOF- performance, showing contrast using the balance of energy, using six accelerograms based on type I and II spectrum, according with Eurocode-8. The degradation curve was obtained applying a new formulation, based on the system work and complementary work, into the pushover analysis. A new method incorporating the Bouc-Wen-Baben-Noori theory and global damage was used for the analysis, adding relevance to the: energy balance in its dissipative part, analysis of the structure’s fundamental parameters, relation’s effective period, equivalent damping and global ductility. The powers, energies and works developed are analyzed, creating a precise balance since energy enters selectively. Hence, an equivalent damping containing a viscous and hysteretic part is predictable, accordingly to the variation of the building’s nonlinear properties. Evaluation of the adequateness and safety level are also obtainable. The controlled parameters contrasted with the balance predicts the structure’s MDOF situation, at any moment related with seismic events. This methodology can be used to stablish a systematic control of nonlinearities for other structural schemes.

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Mitseas, Ioannis P., and Michael Beer. "Fragility analysis of nonproportionally damped inelastic MDOF structural systems exposed to stochastic seismic excitation." Computers & Structures 226 (January 2020): 106129. http://dx.doi.org/10.1016/j.compstruc.2019.106129.

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30

Falsone, Giovanni, and Fabio Neri. "The non-stationary cross-correlation coefficients in the seismic analysis of MDOF structural systems." Earthquake Engineering & Structural Dynamics 32, no. 14 (2003): 2289–99. http://dx.doi.org/10.1002/eqe.319.

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Hozhabrossadati, Seyed Mojtaba, and Ahmad Aftabi Sani. "Free Vibration of MDOF Systems with Nonperiodically Time-Varying Mass." International Journal of Structural Stability and Dynamics 18, no. 06 (June 2018): 1850077. http://dx.doi.org/10.1142/s0219455418500773.

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This paper deals with the free vibration response of MDOF mass-spring systems with time-variable mass and constant stiffness. To show the necessity of this study, a review on the related published articles is presented. After formulating the governing initial value problem which is a coupled system of differential equations with variable coefficients, the differential transform method (DTM) is employed to obtain an analytical solution. The proposed solutions are verified against exact results available in the literature. It is demonstrated that the effect of time-variable mass is equivalent to viscous damping. This viscous damping can be positive or negative depending on the sign of the mass change rate. This role is thoroughly investigated via numerical examples.

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32

Zhang, Zongfen, and Suhuan Chen. "The standard deviations of the eigensolutions for random MDOF systems." Computers & Structures 39, no. 6 (January 1991): 603–7. http://dx.doi.org/10.1016/0045-7949(91)90201-v.

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Wu, Qiaoyun, Hai Feng, Shiye Xiao, Hongping Zhu, and Xixuan Bai. "Passive Control Analysis and Design of Twin-Tower Structure with Chassis." International Journal of Structural Stability and Dynamics 20, no. 06 (June 2020): 2040010. http://dx.doi.org/10.1142/s0219455420400106.

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In this paper, a symmetrical twin-tower structure with chassis connected with passive dampers is coupled as 2-DOF (degree of freedom) model. Using the stationary white noise as seismic excitation, the frequency–response function and the vibration energy expression of the symmetrical twin-tower structure are established based on the simplified 2-DOF model. Furthermore, based on the principle of minimum energy, the analytical expressions of the optimization parameters of two kinds of passive dampers are deduced, and the effectiveness of the dampers with optimized coefficients on structural control is verified by numerical examples of 2-DOF and MDOF (multi-degree-of-freedom) systems, respectively. Finally, the control effects of the two kinds of dampers under different control strategies on the responses of displacement of the top, base shear, structural vibration energy, and maximum inter-story drift of the symmetrical twin-tower structure are discussed through three-dimensional finite element numerical examples. It is verified that the analytical expressions of optimum parameters of the two kinds of dampers proposed based on the 2-DOF model are also beneficial to reduce the responses of the MDOF systems and actual engineering.

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BARATTA, ALESSANDRO, and OTTAVIA CORBI. "AN ENHANCED TECHNIQUE FOR ANALYZING STRUCTURAL VIBRATION PROBLEMS UNDER SHOT NOISE LOADING." International Journal of Structural Stability and Dynamics 05, no. 04 (December 2005): 597–614. http://dx.doi.org/10.1142/s021945540500174x.

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The present paper deals with dynamic nonlinear systems loaded by badly defined forcing actions. As an improvement on the first approximate procedure developed by the authors, a more feasible and reliable alternative entropic closure approach is presented herein. Such a procedure allows one to deal with high order nonlinearities, and it can be suitably generalized to treating multi-degree of freedom (MDOF) systems. In fact, the effectiveness of the proposed approach is intricately linked to the exact calculation of some multiple integrals related to the approximate expression of the chosen response probability function. To this end, a procedure that can guarantee high accuracy in the computation of integrals is also studied, which helps in validating the whole approach.

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Wang, Mengfu, and Xiyuan Zhou. "On precise time integration method for non-classically damped MDOF systems." Earthquake Engineering and Engineering Vibration 5, no. 1 (June 2006): 79–85. http://dx.doi.org/10.1007/s11803-006-0613-2.

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Rezaee, Milad, and Aly Mousaad Aly. "Proposed Theory of Semiactive Gains for Smart Dampers in MDOF Systems." Journal of Structural Engineering 145, no. 12 (December 2019): 04019155. http://dx.doi.org/10.1061/(asce)st.1943-541x.0002453.

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TINGATINGA, ERIC AUGUSTUS, HIDEJI KAWAKAMI, and HIDENORI MOGI. "GRAVITY EFFECTS ON EARTHQUAKE RESPONSE OF A FLEXURE BUILDING: A SHEAR BUILDING COMPARISON." International Journal of Structural Stability and Dynamics 10, no. 02 (June 2010): 187–203. http://dx.doi.org/10.1142/s0219455410003488.

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An analytical building model including the nonlinear effects caused by gravity is presented in this paper. Governing equations are derived for both single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) models with large displacements taken into account, and solutions are obtained by direct integration and modal analysis. The response of typical structures subjected to harmonic ground excitation was expressed in exact and approximate forms, compared with the response of an equivalent shear building. Numerical examples show that while gravity generally decreases the natural frequency of elastic SDOF systems with small displacement approximations, actual natural frequency increases with ground motion. The difference in the natural frequency and response of MDOF systems to the equivalent shear building is not only due to gravity, but also caused by the geometry of the structure. Exact solution shows that the frequency varies with ground motion amplitude.

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Yaghmaei-Sabegh, Saman, Shabnam Neekmanesh, and Jorge Ruiz-García. "Evaluation of approximate methods for estimating maximum displacement response of MDOF systems." Soil Dynamics and Earthquake Engineering 101 (October 2017): 125–36. http://dx.doi.org/10.1016/j.soildyn.2017.07.020.

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39

De Bortoli, Marta, and Farzin Zareian. "Performance Prediction Equations for Linear Planar Structural Systems: Concept, Formulation, and Validation." Earthquake Spectra 34, no. 2 (May 2018): 697–718. http://dx.doi.org/10.1193/110716eqs194m.

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This paper presents and validates an analytical formulation, denoted as Performance Prediction Equations (PPEs), that relates the seismic response engineering demand parameter (EDP) of buildings to earthquake parameters such as magnitude, epicentral distance, and type of faulting. PPEs are conceptually novel and can be readily included in any hazard calculation program to directly estimate EDP hazard curves. The PPEs presented herein are based on the linearization of response spectrum analysis (RSA) formulation for estimation of the seismic response of multi-degree-of-freedom (MDOF) models for planar structural systems. Equations for mean and variance are provided for floor displacement, interstory drift ratio, and normalized base shear. The input parameters needed to apply the proposed PPEs are the modal properties of the structural system and the selection of an existing ground motion model (GMM). The proposed PPEs are validated against simulated results using a set of planar building models and the Campbell-Bozorgnia 2014 GMM. The comparison confirms that the proposed PPEs provide an accurate estimate of the statistics of the said EDPs.

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Ahmadi, Ehsan, Mahdi Kiani, Farzaneh Paytam, and Faramarz Khoshnoudian. "Equivalent linearization parameters of soil-MDOF structure systems subjected to pulse-like earthquakes." Soils and Foundations 58, no. 6 (December 2018): 1371–82. http://dx.doi.org/10.1016/j.sandf.2018.08.006.

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Reyes-Salazar, Alfredo, Eden Bojorquez, Federico Valenzuela-Beltran, and Juan I. Velazquez-Dimas. "Combination Rules and Maximum Response for Steel Buildings with PMRF Represented by Complex 3D MDOF Systems." Applied Mechanics and Materials 595 (July 2014): 159–65. http://dx.doi.org/10.4028/www.scientific.net/amm.595.159.

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The seismic responses of 3D steel buildings with perimeter moment resisting frames (PMRF), modeled as complex MDOF systems, are estimated and the accuracy of the commonly used rules to combine the individual effects of the seismic components, as well as the influence of the correlation of the components and the correlation of the individual effects on the accuracy of the rules, are studied. The responses are also estimated for several incidence angles of the horizontal components and the critical one is identified. It is observed that the rules underestimate the axial load but they reasonably overestimate the interstory and base shear. The effect of individual components may be highly correlated, not only for normal components, but also for totally uncorrelated components. Moreover, the rules are not always inaccurate in the estimation of the combined response for correlated components. On the other hand, totally uncorrelated components are not always related to an accurate estimation of the combined response. The critical response does not occur for principal components and the corresponding incidence angle of the seismic components varies from one earthquake to another. In the general case, the critical response can be estimated as 1.30 times that of the principal components.

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Kong, Fan, Pol D. Spanos, Jie Li, and Ioannis A. Kougioumtzoglou. "Response evolutionary power spectrum determination of chain-like MDOF non-linear structural systems via harmonic wavelets." International Journal of Non-Linear Mechanics 66 (November 2014): 3–17. http://dx.doi.org/10.1016/j.ijnonlinmec.2014.06.002.

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Wang, Yumei. "Displacement-based determination of BRBs in retrofitting an RC frame building." Advances in Structural Engineering 24, no. 8 (January 6, 2021): 1755–66. http://dx.doi.org/10.1177/1369433220981665.

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An RC frame school building was designed with lower fortification requirements than required. It collapsed in the 2008 Ms8.0 Wenchuan earthquake. This study evaluated the building’s deficiency and practiced a retrofit design based on traditional demand-capacity method but with a displacement-based (DB) procedure, in which target capacities were obtained from the equivalent single-degree-of-freedom (ESDOF) systems defined by target mode shapes of the MDOF system, and shear demands were assessed using an R- μ- T relationship to match different capacity levels. To make the DB procedure code-conforming, the retrofitting elements (BRBs) were simplified as bi-linear elements, with the two-phase parameters corresponding to the code’s two-stage requirements. Shear distribution to the MDOF building was also determined by displacement shapes. BRBs’ stiffness demands and sizes were from the difference of the required and available shear resistances. The effectiveness of the method was validated by time history analyses. Different earthquake level simulations showed that, the method realized the design goals but did not lead to over-retrofitting; the BRBs took most of the shear demand but would not induce other unexpected failures. So the method was suitable for retrofitting similar structures.

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Shevtsova, Olga. "Structural features of complex hydrochemical systems." E3S Web of Conferences 127 (2019): 02029. http://dx.doi.org/10.1051/e3sconf/201912702029.

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The set of non-conservative hydrochemical parameters is considered as a complex system, which displays collective behavior. It is found that the collective behavior is described by the power relation between the time variability (the standard deviations) and the average concentrations of different hydrochemical parameters in the scale range 100 – 0:0001 mg/kg. The exponent can be 0:7 – 0:9. Power law scaling is the mathematical expression of self similarity and fractality. The complex systems of nonconservative chemical parameters have a structure that can be characterized by exponent, normalization coefficient, standard error, correlation coefficient, and by sharp deviations of the individual parameters from the regression line and from the most probable average and standard deviation values, if any. It is shown with specific examples that changes in the hydrochemical systems structure are the result of the manifestation of biogeochemical processes and the dynamics of water. Regression analysis of collective behavior of complex hydrochemical systems is one of the examples of the use of modern information technologies based on the methods of system analysis.

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Liaw, C. Y., C. G. Koh, and P. K. Fong. "Complex dynamics of simple structural systems." Journal of the Chinese Institute of Engineers 12, no. 4 (June 1989): 409–14. http://dx.doi.org/10.1080/02533839.1989.9677178.

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SchuÃ«ller, G. I., and H. J. Pradlwarter. "Uncertainty analysis of complex structural systems." International Journal for Numerical Methods in Engineering 80, no. 6â7 (November 5, 2009): 881–913. http://dx.doi.org/10.1002/nme.2549.

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GARRIDO, RUBEN, and FRANCISCO J. RIVERO-ANGELES. "HYSTERESIS AND PARAMETER ESTIMATION OF MDOF SYSTEMS BY A CONTINUOUS-TIME LEAST SQUARES METHOD." Journal of Earthquake Engineering 10, no. 2 (March 2006): 237–64. http://dx.doi.org/10.1080/13632460609350595.

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Dziedziech, K., W. J. Staszewski, and T. Uhl. "Wavelet-Based Frequency Response Function: Comparative Study of Input Excitation." Shock and Vibration 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/502762.

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Time-variant systems can be found in many areas of engineering. It is widely accepted that the classical Fourier-based methods are not suitable for the analysis and identification of such systems. The time-variant frequency response function—based on the continuous wavelet transform—is used in this paper for the analysis of time-variant systems. The focus is on the comparative study of various broadband input excitations. The performance of the method is tested using simulated data from a simple MDOF system and experimental data from a frame-like structure.

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YEH, KEN, WEILING CHIANG, and DERSHIN JUANG. "APPLICATION OF FUZZY CONTROL THEORY IN ACTIVE CONTROL OF STRUCTURES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 04, no. 03 (June 1996): 255–74. http://dx.doi.org/10.1142/s0218488596000160.

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The purpose of this paper is to apply fuzzy control theory in active structural control. A single-degree-of-freedom (SDOF) structure is used to develop the basic approach. The approach is then extended to multi-degree-of-freedom (MDOF) structures with the usage of weighted displacement and weighted velocity. A band-pass white noise or large amount of earthquake records are used as excitations to the structures to calculate the normalized displacements and velocities for obtaining the range of weighted displacements and velocities. Several examples are utilized to demonstrate the feasibility of fuzzy control methodology. It is shown that the fuzzy controller can achieve satisfactory results in the application of active control of structures and the feasibility is verified.

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Zhao, Xueyan Y., Zi-Qiang Lang, Gyuhae Park, Charles R. Farrar, Michael D. Todd, Zhu Mao, and Keith Worden. "A New Transmissibility Analysis Method for Detection and Location of Damage via Nonlinear Features in MDOF Structural Systems." IEEE/ASME Transactions on Mechatronics 20, no. 4 (August 2015): 1933–47. http://dx.doi.org/10.1109/tmech.2014.2359419.

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