A Computationally Efficient Numerical Algorithm for the Transient Response of High-Speed Elastic Linkages

1979 ◽  
Vol 101 (1) ◽  
pp. 138-148 ◽  
Author(s):  
A. Midha ◽  
A. G. Erdman ◽  
D. A. Frohrib
Keyword(s):  
Transient Response ◽  
Numerical Algorithm ◽  
High Speed ◽  
Relative Size ◽  
Degree Of Freedom ◽  
Time Dependent ◽  
Computationally Efficient ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Forcing Function

A new numerical algorithm, easily adaptable for computer simulation, is developed to approximate the transient response of a single degree-of-freedom vibrating system; governing differential equation is linear and second order with time-dependent and periodic coefficients. This is accomplished by first solving the classical linear single degree-of-freedom problem with constant coefficients. The system is excited by a periodic forcing function possessing a certain degree of smoothness. The integration terms in the solution are systematically expanded into two groups of terms: one consists of non-integral terms while the other contains only integral terms. The final integral terms are bounded. For certain combinations of frequency and damping, within the sub-resonant frequency range, the relative size of the integral terms are demonstrated to be small. The algebraic expansion (non-integral) terms then approximate the solution. The solution to a single degree-of-freedom system with time-dependent and periodic parameters is made possible by discretizing the forcing period into a number of intervals and assuming the system parameters as constant over each interval. The numerical algorithm is then employed to solve an elastic linkage problem via modal superposition. Convergence of the solution is verified by refining the number of intervals of discretization.

scholarly journals Miura-ori, Basics for Designing its Folding Machines

2019 ◽  
Vol 2 ◽  
pp. 1-5
Author(s):  
Koryo Miura
Keyword(s):  
Basic Concept ◽  
High Speed ◽  
Geometric Property ◽  
Unique Property ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Geometric Properties ◽  
Single Degree Of Freedom ◽  
Single Degree

<p><strong>Abstract.</strong> The unique property of the Miura-ori map is due to the geometric property of “the single degree of freedom”. With this, one can open a map with a single pull motion. However, due to this property, the high-speed folding machine is difficult to realized. In this presentation, author investigates the natural geometric properties of Miura-ori in detail and proposes a basic concept for designing its folding machine. Though, the result does not provide a draft of a folding machine, the basics for the design parameters is beneficial for future works.</p>

Forced Vibrations of a Single-Degree-of-Freedom System With Coulomb Bearing Friction

1969 ◽  
Vol 36 (4) ◽  
pp. 871-873 ◽  
Author(s):  
E. V. Wilms
Keyword(s):  
Coulomb Friction ◽  
Degree Of Freedom ◽  
Half Cycle ◽  
Piecewise Linearization ◽  
Single Degree Of Freedom ◽  
State Response ◽  
Single Degree ◽  
Forcing Function ◽  
Bearing Friction

The equation of motion of a single-degree-of-freedom mechanical system with Coulomb friction acting at two bearings is derived. The equation is nonlinear, but may be solved by piecewise linearization. For the case of transient oscillations, the amplitude decreases by a constant ratio every half cycle and, in this respect, the behavior resembles that of viscous damping rather than the type of Coulomb damping which has previously been investigated. The steady-state response with a forcing function is determined for the case of small damping. In addition to the amplitude and phase angle of the motion, a solution requires the determination of a second angle which defines the linearized regions.

The Study of a Single Degree of Freedom System with Time Dependent Parameters

1967 ◽  
Vol 71 (678) ◽  
pp. 439-440 ◽  
Author(s):  
B. V. Dasarathy ◽  
P. Srinivasan
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Differential Equations ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Time Dependent ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stochastic Nature ◽  
Restoring Forces

The equations of motion of many mechanical systems reduce to ordinary differential equations with time dependent parameters. A single degree of freedom system, with the damping and restoring forces varying with time according to the law … m (t+k)nhas been studied using the WKBJ approximation. The general solution of the differential equation can be used to arrive at the response of such time dependent systems, subjected to excitations which are specified to be of either deterministic or stochastic nature.

An Experimental Investigation of Complicated Responses of a Two-Degree-of-Freedom Structure

1989 ◽  
Vol 56 (4) ◽  
pp. 960-967 ◽  
Author(s):  
A. H. Nayfeh ◽  
B. Balachandran ◽  
M. A. Colbert ◽  
M. A. Nayfeh
Keyword(s):  
Internal Resonance ◽  
Degree Of Freedom ◽  
Time Dependent ◽  
Theoretical Studies ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Second Mode ◽  
Quadratic Nonlinearities ◽  
Two Degree Of Freedom

Recent theoretical studies indicate that whereas large excitation amplitudes are needed to produce chaotic motions in single-degree-of-freedom systems, extremely small excitation levels can produce chaotic motions in multi-degree-of-freedom systems if they possess autoparametric resonances. To verify these results, we conducted an experimental study of the response of a two-degree-of-freedom structure with quadratic nonlinearities and a two-to-one internal resonance to a primary resonant excitation of the second mode. The responses were analyzed using hardware and software developed for performing time-dependent modal decomposition. We observed periodic, quasi-periodic, and chaotic responses, as predicted by theory. Conditions were found under which extremely small excitation levels produced chaotic motions.

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