Academic literature on the topic 'Mechanical dynamic systems'

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 357-365).<br>In this thesis, an open-loop numerical dynamic optimization method for a class of dynamic systems is developed. The structure of the governing equations of the systems under consideration change depending on the values of the states, parameters and the controls. Therefore, these systems are called systems with varying structure. Such systems occur frequently in the models of electric and hydraulic circuits, chemical processes, biological networks and machinery. As a result, the determination of parameters and controls resulting in the optimal performance of these systems has been an important research topic. Unlike dynamic optimization problems where the structure of the underlying system is constant, the dynamic optimization of systems with varying structure requires the determination of the optimal evolution of the system structure in time in addition to optimal parameters and controls. The underlying varying structure results in nonsmooth and discontinuous optimization problems. The nonsmooth single shooting method introduced in this thesis uses concepts from nonsmooth analysis and nonsmooth optimization to solve dynamic optimization problems involving systems with varying structure whose dynamics can be described by locally Lipschitz continuous ordinary or differential-algebraic equations. The method converts the infinitedimensional dynamic optimization problem into an nonlinear program by parameterizing the controls. Unlike the state of the art, the method does not enumerate possible structures explicitly in the optimization and it does not depend on the discretization of the dynamics. Instead, it uses a special integration algorithm to compute state trajectories and derivative information. As a result, the method produces more accurate solutions to problems where the underlying dynamics is highly nonlinear and/or stiff for less effort than the state of the art. The thesis develops substitutes for the gradient and the Jacobian of a function in case these quantities do not exist. These substitutes are set-valued maps and an elements of these maps need to be computed for optimization purposes. Differential equations are derived whose solutions furnish the necessary elements. These differential equations have discontinuities in time. A numerical method for their solution is proposed based on state event location algorithms that detects these discontinuities. Necessary conditions of optimality for nonlinear programs are derived using these substitutes and it is shown that nonsmooth optimization methods called bundle methods can be used to obtain solutions satisfying these necessary conditions. Case studies compare the method to the state of the art and investigate its complexity empirically.<br>by Mehmet Yunt.<br>Ph.D.

Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays a crucial role in modeling performance on demand Micro Electro Mechanical Systems (MEMS). We start with the stability analysis of a linear delay model. We also show that in certain cases the delay model can be efficiently approximated with a much simpler model without delay. We proceed with the analysis of a non-linear Duffing equation. This model is a significantly more complex mathematical model. For instance, the existence of a periodic solution for this equation is a highly nontrivial question, which was established by Struwe. The main result of this work is to establish the existence of a periodic solution to delay Duffing equation. The paper claimed to establish the existence of such solutions, however their argument is wrong. In this work we establish the existence of a periodic solution under the assumption that the delay is sufficiently small.

<p> In order to obtain credit for an eco-roof in building energy load calculations the steady state and time-varying thermal properties (thermal mass with evapotranspiration) must be fully understood. The following study presents results of experimentation and modeling in an effort to develop dynamic thermal mass performance metrics for eco-roof systems. The work is focused on understanding the thermal parameters (foliage &amp; soil) of an eco-roof, further validation of the EnergyPlus Green Roof Module and development of a standardized metric for assessing the time-varying thermal benefits of eco-roof systems that can be applied across building types and climate zones. </p><p> Eco-roof foliage, soil and weather parameters were continuously collected at the Green Roof Integrated PhotoVoltaic (GRIPV) project from 01/20/2011 to 08/28/2011. The parameters were used to develop an EnergyPlus eco-roof validation model. The validated eco-roof model was then used to estimate the Dynamic Benefit for Massive System (DBMS) in 4 climate-locations: Portland Oregon, Chicago Illinois, Atlanta Georgia and Houston Texas. </p><p> GRIPV30 (GRIPV soil with 30% soil organic matter) was compared to 12 previously tested eco-roof soils. GRIPV30 reduced dry soil conductivity by 50%, increased field capacity by 21% and reduced dry soil mass per unit volume by 60%. GRIPV30 soil had low conductivity at all moisture contents and high heat capacity at moderate and high moisture content. The characteristics of the GRIPV30 soil make it a good choice for moisture retention and reduction of heat flux, improved thermal mass (heat storage) when integrating an eco-roof with a building. </p><p> Eco-roof model validation was performed with constant seasonal moisture driven soil properties and resulted in acceptable measured - modeled eco-roof temperature validation. LAI has a large impact on how the Green Roof Module calculates the eco-roof energy balance with a higher impact on daytime (measured - modeled) soil temperature differential and most significant during summer. </p><p> DBMS modeling found the mild climates of Atlanta Georgia and Houston Texas with eco-roof annual DBMS of 1.03, 3% performance improvement above the standard building, based on cooling, heating and fan energy consumption. The Chicago Illinois climate with severe winter and mild spring/summer/fall has an annual DBMS of 1.01. The moderate Portland Oregon climate has a below standard DBMS of 0.97.</p>

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 249-256).<br>Manufacturing systems are often composed of machines that can produce a variety of items but that most undergo time-consuming (and possibly costly) setups when switching between product types. Scheduling these setups efficiently can have important economic effects on the performance of the plant and involves a tradeoff between throughput, inventory, and operating costs. In addition, the schedule must be robust to random disruptions such as failures or raw material shortages, which are common in production environments. In this thesis, we study policies that address the setup scheduling problem dynamically, in response to current conditions in the system. A new heuristic, called the Hedging Zone Policy (HZP), is introduced and developed. It is a dynamic-sequence policy that always produces the current part type at its maximum production rate until a fixed base stock level is reached. Then, before switching setups, the policy might produce the current part type at its demand rate for some additional time. When selecting changeovers, the HZP implements two types of decision rules. If the difference between base stock and surplus level is small for all part types, the item with the largest weighted difference is selected. Otherwise, the policy uses a fixed priority ranking to select between items that are far from their base stock value. In order to demonstrate the benefits of our policy, we also adapt and implement several other heuristics that have been proposed in the literature for related models. The policies are first analyzed in a purely deterministic setting. The stability of the HZP is addressed and it is shown that a poor selection of its parameters leads to a condition in which some low-priority parts are ignored, resulting in an unstable system. Using Lyapunov's direct method, we obtain an easy-to-evaluate and not-too-conservative condition that ensures production of all part types with bounded surplus. We then compare, through a series of extensive numerical experiments with three-part-type systems, the deterministic performance of the policies in both make-to-order and make-to-stock settings. We show that the HZP outperforms other policies within its class in both cases, a fact that is mainly attributed to its priority-based decisions. When compared to the approximate optimal cost of the problem, our policy performs very well in the make-to-order case, while the simplicity of its base stock structure makes it less competitive in the deterministic make-to-stock problem. The results are then leveraged for the study of a stochastic model, where we consider the effect of random disruptions in the form of machine failures. We prove that our model converges to a fluid limit under an appropriate scaling. This fact allows us to employ our deterministic stability conditions to verify the stochastic (rate) stability of the failure-prone system. We also extend our previous numerical experiments by characterizing the performance of the policies in the stochastic setting. The results show that the HZP still outperforms other policies in the same class. Furthermore, we find that except for cases where failures occur much less or much more frequently than changeovers, the HZP outperforms a fixed-sequence policy that is designed to track a pre-determined, near-optimal deterministic schedule.<br>by Fernando Tubilla.<br>Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.<br>Includes bibliographical references (leaves 83-84).<br>The importance of alternative energy development has been dramatically increased by the dwindling supplies of oil and gas, and our growing efforts to protect our environment. A variety of meaningful steps have been taken in order to come up with cleaner, healthier and more affordable energy alternatives. Wind energy is one of the most reliable energy alternatives for countries that have sufficiently large wind sources. Due to the presence of steady and strong winds, and the distance from coastline residential, the offshore wind farm has become highly attractive as an ideal energy crisis solution. Floating wind turbine systems are being considered as a key solution to make the offshore wind farm feasible from an economic viewpoint, and viable as an energy resource. This paper presents the design of a synthetic mooring system for spar buoy floating wind turbines functioning in shallow water depths. Nacelle acceleration, static and dynamic tensions on catenaries, the maximum tension acting on the anchors are considered as design performances, and a stochastic analysis method has been used to evaluate those quantities based on sea state spectral density functions. The performance at a 100-year hurricane condition is being defined as a limiting case, and a linear wave theory has been the most fundamental theory applied for the present analysis.<br>by Sungho Lee.<br>S.M.