Internal resonance and bending analysis of thick visco-hyper-elastic arches

Abstract In this study, a comprehensive analysis of visco-hyper-elastic thick soft arches under an external time-independent as well time-dependent loads is presented from bending and internal resonance phenomenon perspectives. Axial, transverse rotation motions are considered for modelling the arch in framework Mooney–Rivlin Kelvin–Voigt schemes third-order shear deformable models. The assumed to be incompressible modelled using von Kármán geometric nonlinearity strain–displacement relationship. Using virtual work method, equations derived. For vibration analysis, three, coupled, highly nonlinear obtained force-moment balance method. Newton–Raphson method together with dynamic equilibrium technique used analyses. A detailed study on influence having visco-hyper-elasticity curvature frequency response system given detail, deformation due applied static load presented. thick, different slenderness ratios shown, forced discussed. Moreover, studied showing that term structure can lead three-to-one resonances, rich response. results step forward studying behaviour biological structures tissues. Graphic abstract