Pressure control system with nonlocal friction

TL;DR

This paper investigates a pressure control system with nonlocal friction, analyzing its motion through differential equations with local and nonlocal dissipative forces, providing exact solutions and long-term behavior insights.

Contribution

It introduces a differential equation model with combined local and nonlocal friction terms, deriving exact solutions and analyzing long-term dynamics.

Findings

Exact solutions for displacement and velocity are obtained.

Nonlocal dissipative forces influence long-term behavior.

The system's stability depends on the type of nonlocal friction.

Abstract

We analyze the motion of a pressure control system described by a differential equation with nonlocal dissipative force. This system is composed by an oscillator, a membrane and a constant force. We consider the dissipative memory kernel consisting of two terms. One of them is described by the Dirac delta function which represents a local friction, whereas for the second one we consider two types: the exponential and power-law functions which represent nonlocal dissipative forces. For these cases, one can obtain exact solutions for the displacement and velocity. The long-time behaviors of these quantities are also investigated.