Modes of the homogeneous chain dynamics

Abstract

This paper presents a study of modes of homogeneous mechanical chain dynamics for different kinds of homogenous connection between material mass particles in the chain, and by different chain boundary conditions. The application of these results for describing of mechanical properties of real materials is very useful. Also, by using phenomenological maps and mathematical analogy, and the previous study of modes of the homogeneous mechanical chain dynamics, it is possible to present a study of modes of the homogeneous mechanical multiplate or multibeam complex sandwich system dynamics. The finite number of coupled fractional-order differential equations of creep vibrations of a creeping connected multimaterial particle homogeneous chain system have been derived. The material particles are constrained by standard creep light elements. The constitutive relations of a stress-strain state of the standard creep light elements are expressed through members of the fractional-order derivatives. By using Laplace transform method, the Laplace transform of the analytical solution of system coupled fractional-differential equations of corresponding dynamical free creep dynamical processes are obtained. Also, by using trigonometric method system determinants are obtained in the suitable form for application to the inverse Laplace transforms. By using inverse Laplace transform, time series functions are obtained as a particular mode component. By using visualization of these separated components, an analysis of the dynamical creep component processes in material particle displacements has been achieved. Also, an analysis and comparison between signals in the corresponding homogeneous chains with ideal elastic or viscoelastic standard light elements between material particles are pointed out.