Dynamical behavior of micro-structured solids with conformable time fractional strain wave equation

Abstract

The wave propagation in micro structured solids is described by conformable time fractional strain wave equation and should be able to account for several scales of micro-structure. [Formula presented]-expansion method has been used to propagate the different types of solutions like hyperbolic functions, trigonometric functions and rational functional solutions. All the solutions are listed with their existence criterion on the parameters. A sufficient condition for the convergence of [Formula presented]-expansion method is provided. Meantime, considered equation is transformed into planar dynamical system after using traveling wave transfiguration. Then quasiperiodic behavior is investigated for the discussed model for different values of the physical parameters (α,ϖ,ζ,V and β) after applying a periodic external force. Further, to strengthen the claimed results sensitive analysis is used for different initial value problems.