Efficient Method for Evaluating Steady-State Response of Periodically Time-Varying Linear Systems, with Application to an Elastic Slider-Crank Mechanism
This paper presents the development of an efficient and direct method for evaluating the steady-state response of periodically time-varying linear systems. The method is general, and its efficacy is demonstrated in its application to a high-speed elastic mechanism. The dynamics of a mechanism comprised of elastic members may be described by a system of coupled, inhomogeneous, nonlinear, second-order partial differential equations with periodically time-varying coefficients. More often than not, these governing equations may be linearized and, facilitated by separation of time and space variables, reduced to a system of linear ordinary differential equations with variable coefficients. Closed-form, numerical expressions for response are derived by dividing the fundamental time period of solution into subintervals, and establishing an equal number of continuity constraints at the intermediate time nodes, and a single periodicity constraint at the end time nodes of the period. The symbolic solution of these constraint equations yields the closed-form numerical expression for the response. The method is exemplified by its application to problems involving a slider-crank mechanism with an elastic coupler link.
K. Farhang and A. Midha, "Efficient Method for Evaluating Steady-State Response of Periodically Time-Varying Linear Systems, with Application to an Elastic Slider-Crank Mechanism," American Society of Mechanical Design, Design Engineering Division, American Society of Mechanical Engineers (ASME), Jan 1994.
1994 ASME Design Technical Conferences
Mechanical and Aerospace Engineering
Keywords and Phrases
Control System Analysis; Differential Equations}}dynamic Response; Elasticity; Linearization; Mechanisms; Numerical Analysis; Time Varying Control Systems
Article - Conference proceedings
© 1994 American Society of Mechanical Engineers (ASME), All rights reserved.