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Dynamics of imperfect inhomogeneous nanoplate with exponentially-varying properties resting on viscoelastic foundation. (English) Zbl 1491.74068

Summary: This article tries to investigate the dynamic deflection response of exponentially functionally graded material (E-FGM) nanoplate considering the role of porosities when embedded in a visco-elastic foundation and subjected to moving load, for the first time. The effective material properties are found using an exponential model of the rule of mixture. Next, the governing equations for the nanoplates while resting on a visco-Winkler foundation are found based on the third-order shear deformation theory in conjunction with Eringen nonlocal elasticity by developing Hamilton’s principle. To solve the time-dependent governing motion equations, a state-space method is developed to find the response of the structure including simply-supported edges under moving load. Through some examples, the validation of the approach is provided before investigating the roles of nonlocality, volume fraction index (exponential parameter), porosity index, visco-elastic foundation coefficients, and velocity and time span of moving load on the forced vibration of embedded E-FGM nano-size plate under moving load.

MSC:

74K20 Plates
74M25 Micromechanics of solids
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
74D05 Linear constitutive equations for materials with memory
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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