Dynamics of the Disk-Pendulum Coupled System With Vertical Excitation

This paper investigates the static and dynamic characteristics of the semi-elliptical rocking disk on which a pendulum pinned. This coupled system’s response is also analyzed analytically and numerically when a vertical harmonic excitation is applied to the bottom of the rocking disk. Lagrange’s Equation is used to derive the motion equations of the disk-pendulum coupled system. The second derivative test for the system’s potential energy shows how the location of the pendulum’s pivotal point affects the number and stability of equilibria, and the change of location presents different bifurcation diagrams for different geometries of the rocking disk. For both vertically excited and unforced cases, the coupled system shows chaos easily, but the proper chosen parameters can still help the system reach and keep the steady state. For the steady state of the vertically excited rocking disk without a pendulum, the variation of the excitation’s amplitude and frequency result in the hysteresis for the amplitude of the response. When a pendulum is pinned on the rocking disk, three major categories of steady states are presently in the numerical way.

Energy efficiency policies: A retrospective examination

We review literature on several types of energy efficiency policies: appliance standards, financial incentive programs, information and voluntary programs, and management of government energy use. For each, we provide a brief synopsis of the relevant programs, along with available existing estimates of energy savings, costs, and cost-effectiveness at a national level. The literature examining these estimates points to potential issues in determining the energy savings and costs, but recent evidence suggests that techniques for measuring both have improved. Taken together, the literature identifies up to four quads of energy savings annually from these programs - at least half of which is attributable to appliance standards and utility-based demand-side management, with possible additional energy savings from the U.S. Department of Energy's (DOE's) ENERGY STAR, Climate Challenge, and Section 1605b voluntary programs to reduce carbon dioxide (CO 2) emissions. Related reductions in CO 2 and criteria air pollutants may contribute an additional 10% to the value of energy savings above the price of energy itself. Copyright © 2006 by Annual Reviews. All rights reserved.