On nonlinear vibrations of an elastic plate on a fractional viscoelastic foundation in a viscoelastic medium in the presence of the one-to-one internal resonance

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

“…The vast majority of those recent contributions are devoted to the analysis of free vibrations and parametric analyses of the dependence of dynamic characteristics in systems on various details of the model, see e.g., . The second large group of papers concerns the harmonic forced vibrations, both linear [155,[214][215][216] and geometrically nonlinear [217][218][219][220][221][222][223][224][225][226][227][228][229]. The other group of contributions focuses on the vibrations forced by a moving load or a moving mass, e.g., [193,[230][231][232].…”

“…A large variety of types of structural elements is considered, including beams [187,194,195,206,213,228,232], plates [193,202,203,214,218,220,227], shells [204], composite beams [186,198,201,207,211,215,224,225], composite plates [155,185,191,199,200,210,212,222,223,226], composite shells [190,216,219,221], nanobeams [184,189,196], FG nanoplates [192,197,208,[229][230][231], and FG nanoshells/nanopanels [188,209,217].…”

“…It is known that the use of fractional derivatives significantly improves the properties of VE models. Following this knowledge, this type of mathematical description of Kelvin-Voigt material was introduced in several papers [203,227].…”

“…There are also attempts to model the foundation in the Pasternak configuration combined with standard linear solid viscoelasticity in its fractional variant [195,202,227,232].…”