Narrow Results

We analyze the localization in three-layered symmetric structure consisting of linear layer between focusing nonlinear media separated by nonlinear interfaces. The mathematical formulation of the model is a one-dimensional boundary value problem for the nonlinear Schrödinger equation. We find nonlinear localized states of two types of symmetry. We derive the energies of obtained stationary states in explicit form. We obtain the localization energies as exact solutions of dispersion equations choosing the amplitude of the interface oscillations as a free parameter. We analyze the conditions of their existence depending on the combination of signs of interface parameters.

The nonlinear surface waves propagating along the ultra-thin-film layers with nonlinear properties separating three nonlinear media layers are considered. The model based on a stationary nonlinear Schrödinger equation with a nonlinear potential modeling the interaction of a wave with the interface in a short-range approximation is proposed. We concentrated on effects induced by the difference of characteristics of the layers and their two interfaces. The surface waves of three types exist in the system considered. The dispersion relations determining the dependence of surface waves energy on interface intensities and medium layer characteristics are obtained and analyzed. The localization energy is calculated in explicit form for many difference cases. The conditions of the wave localization on dependence of the layer and interface characteristics are derived. The surface waves with definite energies in specific cases existing only in the presence of the interface nonlinear response are found. All results are obtained in an explicit analytical form.

In this parametric study, the effects of soil-structure interaction on the earthquake response of structures is demonstrated by including various types of supporting media and seismic environments in the analysis of a very simple structure representing residential buildings. The effect of the type of control point selected is also addressed. The analyses are performed in frequency space by employing the substructure method and non-dimensional variables. The transformation from the frequency to time space is performed by FFT algorithm. The results are presented in the form of plots of maximum lateral (or torsional) acceleration against a reference period for various parameters appearing in the analyses.

Tunnel–medium interaction problems are one of the important problems in engineering. Because it has a high risk in terms of reliability, tunnel structures should be modeled in detail. The modeling of tunnel structures under static and dynamical loads is a difficult problem in engineering because of consists of a lot of conditions and effects, such as heterogeneous medium, soil layers, porosity, soil–structure interaction, groundwater, earthquake, etc. In this paper, aims to investigate the tunnel–medium interaction problems for nonlinear static and dynamic analyses. This study includes nonlinear static and dynamic analyses for layered porous semi-infinite viscoelastic medium with twin tunnels. The constitutive property of each layer of medium is considered in bilinear stress–strain relation with uniform porosity and Kelvin–Voigt viscoelastic property. The considered study is solved via the finite element method within the two-dimensional (2D) model. Layered medium is modeled as finite and infinite elements. In the solution process, the incremental force method is implemented and, for each load step, finite element equations are solved according to the bilinear stress–strain relation. In nonlinear dynamic analysis, the dynamic loads are divided by a certain finite number and applied incrementally depending on the time-dependent load function. At each load step, the final displacement, velocity and acceleration of that load step, obtained as a result of applying the Newmark $\beta$ method procedure, are assigned as the starting value of the next load step according to the bilinear stress–strain relation. Influences of porosity and position of tunnels on the nonlinear static and dynamic deflections of the system are investigated. Also, differences between linear and nonlinear responses are compared and discussed.