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Basic Concepts
Published in Seyed Kamaleddin Yadavar Nikravesh, Nonlinear Systems Stability Analysis, 2018
Seyed Kamaleddin Yadavar Nikravesh
where l is the length of the pendulum,m is the mass of the ball, and θ is the angle suspended by the rod and the vertical axis through the pivot point. Choose appropriate state variables and write down the state equation.Find all equilibrium states of the system.Linearize the system around the equilibrium states, and determine whether the system equilibrium states are stable or not.Rewrite the pendulum model into the feedback connection form.Make a simulation model of the system in Simulink®. Simulate the system from various initial states. Is the equilibrium state of the system stable? Are the equilibrium states unique? Explain the physical intuition behind your findings.Use the function Linmod in MATLAB® to find the linearized models for the equilibrium states. Compare with the linearization that you derived.
Geometry of Local Instability in Hamiltonian Dynamics
Published in Christos H. Skiadas, Charilaos Skiadas, Handbook of Applications of Chaos Theory, 2017
M. Lewkowicz, J. Levitan, Y. Ben Zion, L. Horwitz
Equation 15.15 has the form of a geodesic equation, with a truncated connection form. (Note that performing parallel transport on the local flat tangent space of the Gutzwiller manifold [for which Γlmn and gij are compatible], the resulting connection, after raising the tensor index [as in Equation 15.8] to reach the Hamilton manifold, is exactly the“truncated” connection (15.16)). Substituting Equations 15.5 and 15.6 into Equations 15.15 and 15.16, the Kronecker deltas identify the indices of x˙m and x˙n;theresultingsquare of the velocity cancels a factor of (E — V)−1, leaving the Hamilton-Newton law as in Equation 15.11. Equation 15.15 is, therefore, a geometrically covariant form of the Hamilton-Newton law, exhibiting what can be considered an underlying geometry for the standard Hamiltonian motion.
Differential Geometry in Chemical Reaction Dynamics
Published in Takayuki Fueno, The Transition State, 2019
showing Fija being the curvature tensor for the connection form ω, the origin of holonomy. The Fija can be interpreted as a gauge field on MCM and the βia the gauge potential.6)
Unitary weaving: a rapid design-build strategy for temporary buildings
Published in Journal of Asian Architecture and Building Engineering, 2023
Yiyang Huang, Xue Zhang, Muwang Wei, Tianrui Yang
Although such an approach can achieve a discrete distribution of the weave as a whole without breaking the connection logic, it gives rise to an infinite number of permutation patterns because each unit can be connected to random points of other units, and thus, additional rules and constraints need to be introduced. This phase of the iteration focuses more on the geometry of the units and the combinatorial laws. To make the connection form more operational, further attempts to expand the unit body are made based on the unit morphology of the previous stage. B2’/D1’/D2’ is obtained by stretching the B2/D1/D2 base unit cell in the Z-axis direction. To make the two types of unitary bodies morphologically distinct, B2/D1/D2 was used as the unitary transformation structure of the woven whole and B2’/D1’/D2’ was used as the main structure, which means that we individualized a central spindle bar in each unit and the point connections were made only through these rods (Figure 8). With this constraint, the possible connections are greatly reduced, which making it easier for the designer to control the aggregation process.
A numerical method for analysing the responses of cargo containment system of an LNGC under iceberg collision
Published in Ships and Offshore Structures, 2023
Muzhi Li, Zhong Wan, Yuchao Yuan, Wenyong Tang
In this paper, a numerical method for analysing the responses of CCS under iceberg collision is proposed. The new mechanical connection form between each component is used to obtain the accurate load transfer path from the hull to CCS. The research route is shown in Figure 1. To improve computational efficiency, the numerical method is divided into the iceberg-ship collision model and the refined CCS model. Firstly, the midship model of an LNGC is coupled with the simplified CCS model. An elastic-plastic ice material model combined with compressive and tensile failure criteria is used to simulate the iceberg-ship collision. The failure modes of iceberg, the responses of structures and the ice load are obtained under different collision scenarios. Subsequently, the refined CCS model including insulation boxes, mastic ropes and couplers is coupled with the inner hull structure. The refined CCS model is essential to obtain the response of each CCS component, and the loading approach based on the results of the collision model saves calculation efficiency. Finally, the ice load transfer path and the responses of CCS are studied under different collision scenarios.
Influence of component damage on the mechanical performance of bracket set joints in ancient timber structures
Published in European Journal of Environmental and Civil Engineering, 2022
Lu Dai, Jiuzhang Chen, Xueyao Chen, Haobo Ren
In a traditional timber structure, the mechanical performance of the joint is very important for overall structural safety (Feio et al., 2014). As the most characteristic connection form of ancient Chinese timber structures, the bracket set is composed of multiple components and is the most complicated part of the structure. The bracket set can form a ductile joint with the beam and column that can transform loads and dissipate energy. The importance of the role of the bracket set within the entire structural system of ancient wooden structures cannot be ignored. Due to the construction age, the bracket sets in ancient timber structures have experienced varying degrees of damage from natural forces, such as earthquakes, rain, and snow, or man-made damage, affecting the mechanical performance of the joint and threatening the overall structural stability. If targeted research and repair cannot be carried out in time, the ancient structure will face certain potential risks. Therefore, studying the mechanical behavior of damaged bracket set joints and analyzing their influence on the mechanical properties of the structural system has vital significance for the protection of ancient wooden structures.