Browsing by Subject "Continuous"
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Item Direct linearization of continuous and hybrid dynamical systems(2009-05-15) Parish, Julie Marie JonesLinearized equations of motion are important in engineering applications, especially with respect to stability analysis and control design. Traditionally, the full, nonlinear equations are formed and then linearized about the desired equilibrium configuration using methods such as Taylor series expansions. However, it has been shown that the quadratic form of the Lagrangian function can be used to directly linearize the equations of motion for discrete dynamical systems. Here, this development is extended to directly generate linearized equations of motion for both continuous and hybrid dynamical systems, where a hybrid system is described with both discrete and continuous generalized coordinates. The results presented require only velocity level kinematics to form the Lagrangian and find equilibrium configuration(s) for the system. A set of partial derivatives of the Lagrangian are then computed and used to directly construct the linearized equations of motion about the equilibrium configuration of interest. This study shows that the entire nonlinear equations of motion do not have to be generated in order to construct the linearized equations of motion. Several examples are presented to illustrate application of these results to both continuous and hybrid system problems.Item Fatigue behavior of post-installed shear connectors used to strengthen continuous non-composite steel bridge girders(2016-08) Ghiami Azad, Amir Reza; Engelhardt, Michael D.; Williamson, Eric B., 1968-; Helwig, Todd A; Jirsa, James O; Taleff, Eric MMany older bridges in Texas are constructed with floor systems consisting of a concrete slab over steel girders. A potentially economical means of strengthening these floor systems is to connect the existing concrete slab and steel girders using post-installed shear connectors to change the behavior of the beam from non-composite to partially-composite. Since fatigue is one of the main concerns in designing bridges, investigating the fatigue properties of these post-installed shear connectors becomes crucial. Results from direct-shear testing show that post-installed shear connectors have a better fatigue life compared to conventional welded shear studs. However, based on currently available data from direct-shear tests, fatigue life of post-installed shear connectors is still inadequate for economical retrofit in some cases. Furthermore, it is unclear if direct-shear tests provide an appropriate means of evaluating fatigue performance. The objective of this dissertation is to develop new and more accurate approaches for evaluating the fatigue characteristics of post-installed shear connectors. This objective is addressed through large-scale beam fatigue tests and computational studies. The focus of the work is on evaluating fatigue life of shear connectors based on both slip and stress demands.