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Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform

Qureshi Sania

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 1

83--89

Closed form solutions for mathematical systems are not easy to find in many cases. In particular, linear systems such as the population growth/decay model, RLC circuit, mixing problems in chemistry, first-order kinetic reactions, and mass spring damper system in mechanical and mechatronic engineering can be handled with tools available in theoretical study of linear systems. One such linear system has been investigated in the present research study. The second order linear ordinary differential equation called the mass spring damper system is explored under the Caputo type differential operator while using the Sumudu integral transform. The closed form solution has been found in terms of the Fox H-function wherein different aspects of the solution can be obtained with variation in α ∈ 2 (1;2] and β ∈ 2 (0;1]: The classical mass spring damper model is retrieved for α = β = 1:

Determination of the internal resistance of a hammer drill chisel

Nikolov N., Sinapov P.

Journal of Theoretical and Applied Mechanics

2018

Vol. 56 nr 1

169--178

The present work examines damped oscillations of a chisel, represented as a distributed parameters system. The system is discretized with the finite element method. Rayleigh’s law is used for the modelling of the resistance. The internal resistance of the mechanical system has been determined by an experiment, then enshrined in the numerical model. Comparison and analysis of the results have been made.