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We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high accuracy which is valid for a wide range of vibration amplitudes as indicated in the presented examples.

Creep functions are often represented by "rheological models" consisting of springs and dashpots, while the actual microscopic origins of creep, such as micro-sliding along interfaces, has only recently been explicitly considered in a continuum mechanics framework. The question arises whether formal analogies between the former and the latter can be derived: This question is answered here for the rheological models of the Kelvin-Voigt and Maxwell type. Thereby, it appears a full analogy between shear stresses and strains acting on the rheological models, and those acting on a micromechanical representative volume element consisting of an elastic solid matrix with embedded viscous interfaces, whereby the respective viscosity arises from layered polar fluids absorbed at these interfaces. The corresponding Kelvin-Voigt parameters are much simpler and more intuitively related to the micromechanical quantities, when compared to the Maxwell parameters. More specifically, rheological spring parameters are always related to the shear stiffness of the elastic solid matrix, while they may additionally depend on the Poisson's ratio of the elastic solid matrix, and on the interface density. On the other hand, dashpot viscosities are always related to interface viscosities, interface radii, and interface densities; and they may even depend on the Poisson's ratio of the elastic solid matrix.

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