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In this work, we study the effect of the thickness variation of viscoelastic layer inserted in a laminated multi-layer beam in forced vibration on the vertical displacements and on the natural frequencies. The new structure is a sandwich structure composed by two external layers (top and bottom facesheets) of aluminum and viscoelastic core of 3M ISD112 polymers. The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. The finite element method including the viscoelastic model of fractional derivatives for modeling the sandwich structure is used. The system resolution of the nonlinear equations of motion of the sandwich structure is required to use a numerical integration method as the explicit method of Newmark to obtain the transient response. Also, ANSYS finite element modeling is applied to the sandwich structure to calculate the frequency response in harmonic vibration. The increase in the thickness of the viscoelastic layer leads to a decrease in the amplitudes of vibration. The natural frequencies found by the two methods are very close to the frequencies found experimentally in the literature.

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This paper studies the presence effects of two or more adjacent structures on the tunnel responses and vice versa due to surface and underground traffic loads. The study is numerically carried out by using Finite element Plaxis2D software©. The obtained results demonstrate that the dynamical interaction between the tunnel and the structures is significantly influenced by varying the number and distance between the adjacent structures, the depth of the tunnel and the location of the traffic load. These results can be considered and used in realistic and practical cases and also to help build efficient and more comfortable construction projects.