Search results for " Long-range forces"

Dynamics of non-local systems handled by fractional calculus

2007

Mechanical vibrations of non-local systems with long-range, cohesive, interactions between material particles have been studied in this paper by means of fractional calculus. Long-range cohesive forces between material particles have been included in equilibrium equations assuming interaction distance decay with order α . This approach yields as limiting case a partial fractional differential equation of order α involving space-time variables. It has been shown that the proposed model may be obtained by a discrete, mass-spring model that includes non-local interactions by non-adjacent particles and the mechanical vibrations of the particles have been obtained by an approximation fractional …