scholarly journals Exact Derivation of Global Form of All Periodic Solutions for Zero Stiffness Impact Oscillator using Initial Value Correction Periodize Method (Case of Viscous Damping Free System)

2006 ◽  
Vol 72 (715) ◽  
pp. 706-713
Author(s):  
Hitoshi IMAMURA
Keyword(s):  
Periodic Solutions ◽  
Viscous Damping ◽  
Initial Value ◽  
Impact Oscillator ◽  
Free System ◽  
Global Form ◽  
Exact Derivation

Dynamic Motion Analysis of Plane Mechanisms With Coulomb and Viscous Damping via the Joint Force Analysis

1975 ◽  
Vol 97 (2) ◽  
pp. 551-560 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Dynamic Equilibrium ◽  
Viscous Damping ◽  
Force Analysis ◽  
Initial Value ◽  
Damping Force ◽  
Joint Force ◽  
Coulomb Damping ◽  
Dynamic Motion ◽  
Joint Forces ◽  
Input Torque

Analysis of response of determinate plane mechanisms to known driving input force, or input torque, via the joint force analysis is presented. Coulomb damping and viscous damping forces in the pair bearings are included. Equations of dynamic equilibrium are solved for the components of the normal joint forces and for the motion of the mechanism as initial-value problems. The rotation of the resultant joint force, due to the fact that the pair member on a link is the inner member or the outer member of the pair, is considered by defining a generalized Coulomb damping force. Links of the mechanisms are considered rigid. The plane 4R and slider-crank switch mechanisms are investigated. Explicit solutions and numerical examples are given.

scholarly journals A case of boundedness in Littlewood's problem on oscillatory differential equations

1976 ◽  
Vol 14 (1) ◽  
pp. 71-93 ◽  
Author(s):  
G.R. Morris
Keyword(s):  
Positive Integer ◽  
Small Parameter ◽  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Initial Value ◽  
Closed Curves ◽  
Essential Step ◽  
Period 2 ◽  
All Solutions

It is shown that all solutions of ẍ + 2x3 = p(t) are bounded, the notation indicating that p is periodic. It is not necessary to have a small parameter multiplying p.The essential step is to show by appeal to Moser's theorem that, under the mapping (of the initial-value plane) which corresponds to the equation, there are invariant simple closed curves. This implies also that there is an uncountable infinity of almost-periodic solutions and, for each positive integer m, an infinity of periodic solutions of least period 2mπ (2π being taken as the least period of p ).It is suggested that for a large class of equations the same attack would show all solutions of ẍ + g(x) = p(t) bounded. However, in order to show the method clearly, no generalisation is attempted here.

scholarly journals On periodic solutions to a class of delay differential variational inequalities

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nguyen Thi Van Anh
Keyword(s):  
Variational Inequalities ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Conditional Stability ◽  
Sufficient Condition ◽  
Initial Value ◽  
Periodic Problems ◽  
Existence Of Periodic Solutions ◽  
Delay Differential ◽  
Differential Variational Inequalities

<p style='text-indent:20px;'>In this paper, we introduce and study a class of delay differential variational inequalities comprising delay differential equations and variational inequalities. We establish a sufficient condition for the existence of periodic solutions to delay differential variational inequalities. Based on some fixed point arguments, in both single-valued and multivalued cases, the solvability of initial value and periodic problems are proved. Furthermore, we study the conditional stability of periodic solutions to this systems.</p>

A MONOTONE-ITERATIVE METHOD FOR FINDING PERIODIC SOLUTION OF AN IMPULSIVE DIFFERENTIAL EQUATIONS AND APPLICATION

2008 ◽  
Vol 01 (02) ◽  
pp. 247-256
Author(s):  
JIAWEI DOU
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Upper And Lower Solutions ◽  
Impulsive Differential Equations ◽  
Iteration Process ◽  
Impulsive System ◽  
Monotone Iterative Method ◽  
Initial Value ◽  
Monotone Iterative ◽  
Monotone Iterations

In this paper, using the method of upper and lower solutions and its associated monotone iterations, we establish a new monotone-iterative scheme for finding periodic solutions of an impulsive differential equations. This method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iteration process in the same fashion as for impulsive differential equations initial value problem. This method is constructive and can be used to develop a computational algorithm for numerical solution of the periodic impulsive system. Our existence result improves a result established in [1]. The result is applied to a model of mutualism of Lotka–Volterra type which involves interactions among a mutualist-competitor, a competitor and a mutualist, the existence of positive periodic solutions of the model is obtained.

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