Determination of the exact mode frequencies of multi-storey structures by state-space method and a comparison with mode superposition method

2021 ◽  
Vol 7 (1) ◽  
pp. 1
Author(s):  
Ahmad Yamin Rasa ◽  
Mehmet Hamit Özyazıcıoğlu
Keyword(s):  
State Space ◽  
Superposition Method ◽  
State Space Method ◽  
Approximate Methods ◽  
Mode Superposition ◽  
Damping Matrix ◽  
Mode Superposition Method ◽  
Frame Buildings ◽  
Exact And Approximate Methods ◽  
Space Method

A comparative research has been carried out for obtaining the time-consuming exact solution (state-space) and approximate solution (mode superposition) of transient and steady-state vibrations of linearly damped linear frame buildings. In the mode superposition method, the proportional damping matrix has been constructed by different approaches such as modal combination of mass and stiffness matrixes (Rayleigh) and disregarding the off-diagonal elements of the non-classical damping matrix, while in the state-space method the non-proportional damping matrix is constructed in exact situation. These observations are individually investigated, which the most suitable parameter to render the approximate results as close as possible to the exact results. Harmonic forces are applied on the different storeys of three and five storey frame buildings, and the responses are displayed in comparative tables and figures. The maximum responses are calculated by square root of sum of the squares (SRSS) method. A MATLAB code is generated and the equations of exact and approximate methods are solved.

Complex mode superposition method of nonproportionally damped linear systems with hysteretic damping

2020 ◽  
pp. 107754632094346
Author(s):  
Panxu Sun ◽  
Hong Yang ◽  
Yunjun Deng
Keyword(s):  
Linear System ◽  
Time Domain ◽  
Superposition Method ◽  
Viscous Damping ◽  
Complex Mode ◽  
Mode Superposition ◽  
Damping Matrix ◽  
Mode Superposition Method ◽  
Hysteretic Damping ◽  
Damping Model

The vibration response of a damped linear system is always calculated based on the mode superposition method. However, the construction of the damping matrix is difficult for the conventional mode superposition methods based on the viscous damping model, and this problem is much more serious for nonproportionally damped linear systems. The damping matrix based on the hysteretic damping model is easy to construct and unique, which is determined only by the structural stiffness and material loss factor. The time-domain motion equation of a multi-degree-of-freedom nonproportionally damped linear system is easily constructed based on the hysteretic damping model. According to the characteristics of external excitation, the general solution of the corresponding homogeneous equation and special solution of the corresponding nonhomogeneous equation can be solved. By the aid of the easiness of the damping matrix, a complex mode superposition method based on the hysteretic damping model is proposed for the nonproportionally damped linear system. Based on the proposed method, a user subroutine in ANSYS and MATLAB is developed to calculate vibration responses in time-domain dynamic analyses. A shaking table test of a cantilever plate composed of host and damping layers is conducted to validate the proposed method. The method proposed in this article is unconditionally convergent, and its convergence is independent of the time step of time-domain analyses. Compared with the common complex mode superposition method based on the viscous damping model, the simulation results of the proposed method are closer to the test results, and its accuracy and efficiency are higher. In addition, the calculation results of the proposed method are unique, which is irrelevant to the choice of vibration modes.

A new state-space method for exponentially damped linear systems

2019 ◽  
Vol 212 ◽  
pp. 137-144 ◽  
Author(s):  
Xinhai Wu ◽  
Huan He ◽  
Guoping Chen
Keyword(s):  
State Space ◽  
Linear Systems ◽  
State Space Method ◽  
Space Method

Study on Small Fluctuation Stability in Air Cushion Surge Chamber Based on State Space Method

2017 ◽  
Author(s):  
Jiachun Liu ◽  
Jian Zhang ◽  
Xiaodong Yu ◽  
Hui Xie
Keyword(s):  
State Space ◽  
Great Influence ◽  
State Space Method ◽  
Actual System ◽  
Small Fluctuation ◽  
Chamber Height ◽  
Air Chamber ◽  
Water Conveyance ◽  
Air Cushion ◽  
Space Method

In this paper, on the basis of the state space method and actual system arrangement, the small fluctuation mathematical model of the water conveyance system with air cushion surge chamber (ACSC) was established. According to the basic equations of ACSC, the ideal gas state equation and the units constant output equation, the formula describing the stable cross-section area (SCSA) of ACSC was deduced, and the small fluctuation stability (SFS) of water conveyance system was analyzed. The corresponding results showed that the air chamber constant had a great influence on the SCSA of ACSC. When the air chamber constant became larger, the quality of the system small fluctuation went worse. The higher upstream water level and the lower initial air chamber height will lead to a smaller initial air chamber constant of ACSC, which is destructive for the stability of the system small fluctuation; As long as the equivalent air quality and air chamber volume are constant, good quality system small fluctuations could be obtained when the initial air chamber height is small and the area of ACSC is large.

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