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This paper analyzes the thermoelastic dynamic behavior of simply supported viscoelastic nanobeams of fractional derivative type due to a dynamic strength load. The viscoelastic Kelvin–Voigt model with fractional derivative with Bernoulli–Euler beam theory is introduced. The generalized thermoelastic heat conduction model with a two-phase lag is also used. It is assumed that the beam is rotating at a uniform angular velocity and that the thermal conductivity varies linearly depending on the temperature. Due to a variable harmonic heat and retreating time-dependent load, the nanobeam is excited. The Laplace integral transformation technique is used as the solution method. The thermodynamic temperature, deflection function, bending moment, and displacement are numerically calculated. Results of fractional and integer viscoelastic material models are compared. In the studied system, the effect of the nonlocal parameter, viscosity and varying load on the solutions is shown, and the temperature-dependence of the thermal conductivity is analyzed.

With the development of high-speed railways, the double-line mode of ballastless tracks is being adopted increasingly worldwide. In some sections where subgrades need to be laid, this type of line mode is also applied above the subgrade, thus forming double-line track-subgrade structure. In this structure, the subgrade on one side of the double-line is subjected to the eccentric pressure of the load when the unidirectional train is running (the most common operating condition in actual operation). When the subgrade contains embankment layer, the complexity of the problem is increased. Therefore, a 1:4 scale test model of the double-line ballastless track-subgrade system was constructed in this paper in order to study the dynamic responses of the double-line track-subgrade structure with embankment layer under the unidirectional high-speed train loads. By considering the similarity of shear wave velocities, a new uniform dynamic similarity method was adopted to design the track, subgrade and foundation models. The effects of a series of sine waves with 1–30Hz excitation frequency and three kinds of loading modes on the speed, soil stress and acceleration response of the track and subgrade were systematically investigated. The relationship between the effective composite values of velocity beneath the track and the depth was finally obtained. The results show that the dynamic stress attenuation of the subgrade bottom layer under larger axle loads are relatively faster. It is found that the dynamic stress attenuation of the subgrade bottom layer is relatively fast under the high-frequency uniform excitation of large axial heavy load.

This presents a mathematical model proposed by the author for description of deformation process of a shell structure under the action of a load that depends linearly on time. Material orthotropy, geometric nonlinearity, transverse shifts are taken into account. A distinctive feature of the model is the use of a refined discrete method for taking into account stiffeners, proposed by the author earlier. Prior to this, the method was used only in static or isotropic dynamic problems. It is proposed to add correction normalizing factors, which makes it possible to obtain the most accurate values of critical loads. The methodology of the calculation algorithm under dynamic loading is based on the Kantorovich method and the Rosenbrock method, which allows solving rigid ordinary differential equation (ODE) systems. New numerical results for cylindrical panels are obtained. The influence of the number of stiffening elements on the values of the critical load is shown. A comparison with the classical discrete method of taking into account stiffeners is carried out. For the problems considered in this paper, the phase portraits of the system are shown.