Mitigating mass eccentricity effects on the rotational response of setbacks structures: An analytical solution for linear systems

Structures ◽  
2020 ◽  
Vol 28 ◽  
pp. 1539-1556
Author(s):  
George K. Georgoussis ◽  
Anna Mamou
Keyword(s):  
Analytical Solution ◽  
Linear Systems ◽  
Mass Eccentricity ◽  
Rotational Response

scholarly journals Approximation Techniques for Solving Linear Systems of Volterra Integro-Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ahmad Issa ◽  
Naji Qatanani ◽  
Adnan Daraghmeh
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Differential Equations ◽  
Linear Systems ◽  
Collocation Method ◽  
Wavelet Method ◽  
Numerical Examples ◽  
Approximation Techniques ◽  
Sinc Functions ◽  
Chebyshev Wavelet

In this paper, a collocation method using sinc functions and Chebyshev wavelet method is implemented to solve linear systems of Volterra integro-differential equations. To test the validity of these methods, two numerical examples with known exact solution are presented. Numerical results indicate that the convergence and accuracy of these methods are in good a agreement with the analytical solution. However, according to comparison of these methods, we conclude that the Chebyshev wavelet method provides more accurate results.

Controller Gain Design of 2-D Linear Systems Based on the Existing 1-D Analytical Solution

2013 ◽  
Vol 681 ◽  
pp. 55-59
Author(s):  
Wen Jeng Liu
Keyword(s):  
Analytical Solution ◽  
Linear Systems ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Gain ◽  
Two Dimensional ◽  
Numerical Examples ◽  
One Dimensional ◽  
Controller Gain ◽  
Necessary And Sufficient

Abstract. A controller gain design problem of two-dimensional (2-D) linear systems is proposed in this paper. For one-dimensional (1-D) systems, the necessary and sufficient conditions have been established for the problem, and an analytical solution for the feedback gain is given by [1]. Based on the existing 1-D analytical solution, a 2-D state feedback controller gain can be designed to achieve the desired poles. Finally, two numerical examples are shown to exhibit the validity of the proposed approach.

scholarly journals Model of time-varying linear systems and Kolmogorov equations

2015 ◽  
Vol 25 (2) ◽  
pp. 201-214
Author(s):  
Assen V. Krumov
Keyword(s):  
Analytical Solution ◽  
Linear Systems ◽  
Sufficient Conditions ◽  
Original System ◽  
Approximate Model ◽  
Time Varying ◽  
Kolmogorov Equations ◽  
Varying Coefficients ◽  
Method Of Solution ◽  
Time Varying Coefficients

Abstract In the paper an approximate model of time-varying linear systems using a sequence of time-invariant systems is suggested. The conditions for validity of the approximation are proven with a theorem. Examples comparing the numerical solution of the original system and the analytical solution of the model are given. For the system under the consideration a new criterion giving sufficient conditions for robust Lagrange stability is suggested. The criterion is proven with a theorem. Examples are given showing stable and non stable solutions of a time-varying system and the results are compared with the numerical Runge-Kutta solution of the system. In the paper an important application of the described method of solution of linear systems with time-varying coefficients, namely analytical solution of the Kolmogorov equations is shown.

scholarly journals The Role of Mass Eccentricity on the Earthquake Induced Torsion in Buildings

2018 ◽  
Vol 7 (3.32) ◽  
pp. 29
Author(s):  
George K. Georgoussis ◽  
Anna Mamou
Keyword(s):  
Numerical Modeling ◽  
Analytical Solution ◽  
Numerical Modelling ◽  
Optimum Location ◽  
Reasonable Accuracy ◽  
Structural Element ◽  
Torsional Response ◽  
Mass Eccentricity

This paper investigates the effect of mass eccentricity on the earthquake induced torsion in buildings. An analytical solution is proposed, which identifies the location of a key structural element for which the torsional response of a structure is minimized for any height wise variation of the mass eccentricities. The accuracy of the analytical solution is then verified with parametric numerical modelling on 9-story buildings with height wise variations of the accidental eccentricities. The numerical modeling results show that the top rotations and base torques have an inverted peak, which indicates an optimum location of the key structural element, for which the torsional response of the structure is minimized. The location of the key element which minimizes the torsional response of the structure predicted by the analytical solution is verified with reasonable accuracy by the numerical modeling results.         

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