Non‐linear dynamic analysis by three‐dimensional ordinary differential equations

2005 ◽  
Vol 22 (4) ◽  
pp. 453-479
Author(s):  
E.G. Ladopoulos
1973 ◽  
Vol 40 (3) ◽  
pp. 809-811 ◽  
Author(s):  
Y. O. Bayazitoglu ◽  
M. A. Chace

The equations of motion for any discrete, lower pair mechanical system can be obtained by analyzing a branched, three-dimensional compound pendulum of indefinite length. In this paper, a set of expressions which provides the equations of motion of arbitrary mechanical dynamic systems directly as ordinary differential equations are presented. These expressions and the associated technique is applicable to linear and nonlinear unconstrained dynamic systems, kinematic systems and multidegree-of-freedom constrained systems.


2021 ◽  
Vol 11 (11) ◽  
pp. 4898
Author(s):  
Jin-Seon Kim ◽  
Ju-Seong Jung ◽  
Dong-Keun Jung ◽  
Eui-Yong Kim ◽  
Kang-Seok Lee

The present study proposes a new seismic retrofitting method using a concrete-filled tube modular frame (CFT-MF) system, a novel technique to overcome and improve the limitations of existing seismic strengthening methods. This CFT-MF seismic retrofitting method makes the most of the advantages of both concrete and steel pipes, thereby significantly improving constructability and increasing integration between the existing structure and the reinforcement joints. This method falls into the category of typical seismic retrofitting methods that focus on increasing strength, in which the required amount of seismic reinforcement can be easily estimated. Therefore, the method provides an easy solution to improving the strength of existing reinforced concrete (RC) structures with non-seismic details that are prone to shear failure. In the present study, a full-size two-story test frame modeled from existing domestic RC structures with non-seismic details was subjected to pseudo-dynamic testing. As a result, the effect of the CFT-MF system, when applied to existing RC structures, was examined and verified, especially as to its seismic retrofitting performance, i.e., restoring force characteristics, stiffness reinforcement, and seismic response control. In addition, based on the pseudo-dynamic testing results, a restoring force characteristics model was proposed to implement non-linear dynamic analysis of a structure retrofitted with the CFT-MF system (i.e., the test frame). Finally, based on the proposed restoring force characteristics, non-linear dynamic analysis was conducted, and the results were compared with those obtained by the pseudo-dynamic tests. The results showed that the RC frame (building) with no retrofitting measures applied underwent shear failure at a seismic intensity of 200 cm/s2, the threshold applied in seismic design in Korea. In contrast, in the frame (building) retrofitted with the CFT-MF system, only minor earthquake damage was observed, and even when the maximum seismic intensity (300 cm/s2) that may occur in Korean was applied, small-scale damage was observed. These results confirmed the validity of the seismic retrofitting method based on the CFT-MF system developed in the present study. The non-linear dynamic analysis and the pseudo-dynamic test showed similar results, with an average deviation of 10% or less in seismic response load and displacement.


2021 ◽  
Vol 21 (2) ◽  
pp. 569-588
Author(s):  
KINZA ARSHAD ◽  
MUHAMMAD ASHRAF

In the present work, two dimensional flow of a hyperbolic tangent fluid with chemical reaction and viscous dissipation near a stagnation point is discussed numerically. The analysis is performed in the presence of magnetic field. The governing partial differential equations are converted into non-linear ordinary differential equations by using appropriate transformation. The resulting higher order non-linear ordinary differential equations are discretized by finite difference method and then solved by SOR (Successive over Relaxation parameter) method. The impact of the relevant parameters is scrutinized by plotting graphs and discussed in details. The main conclusion is that the large value of magnetic field parameter and wiessenberg numbers decrease the streamwise and normal velocity while increase the temperature distribution. Also higher value of the Eckert number Ec results in increases in temperature profile.


2021 ◽  
Author(s):  
Muhammad Yasir ◽  
Masood Khan ◽  
Awais Ahmed ◽  
Malik Zaka Ullah

Abstract In this work, an analysis is presented for the unsteady axisymmetric flow of Oldroyd-B nanofluid generated by an impermeable stretching cylinder with heat and mass transport under the influence of heat generation/absorption, thermal radiation and first-order chemical reaction. Additionally, thermal and solutal performances of nanofluid are studied using an interpretation of the well-known Buongiorno's model, which helps us to determine the attractive characteristics of Brownian motion and thermophoretic diffusion. Firstly, the governing unsteady boundary layer equation's (PDEs) are established and then converted into highly non-linear ordinary differential equations (ODEs) by using the suitable similarity transformations. For the governing non-linear ordinary differential equations, numerical integration in domain [0, ∞) is carried out using the BVP Midrich scheme in Maple software. For the velocity, temperature and concentration distributions, reliable results are prepared for different physical flow constraints. According to the results, for increasing values of Deborah numbers, the temperature and concentration distribution are higher in terms of relaxation time while these are decline in terms of retardation time. Moreover, thermal radiation and heat generation/absorption are increased the temperature distribution and corresponding boundary layer thickness. With previously stated numerical values, the acquired solutions have an excellent accuracy.


2020 ◽  
Vol 2020 (0) ◽  
pp. 513
Author(s):  
Masato TAKEUCHI ◽  
Kensuke HARA ◽  
Hiroshi YAMAURA

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