Nonlinear Behaviors of Torsional Elastic Support Arch under External Excitations

Nonlinear dynamics of a hinged-hinged shallow arch with torsional springs constrained at both ends in case of 1:1 internal resonance are investigated. The dynamic governing equations are achieved by introducing the basic assumptions and dimensionless variables. The effects of torsional springs are considered in frequencies and modes by the corresponding linear equation and boundary conditions. The two internal resonance types of mode crossing and mode veering are found in dynamic system with torsional constraints. The equation was performed by a full-basis Galerkin discretization and the multiple scale method was used to study the internal resonances by perturbation analysis, which leads to averaging equations, whose coefficients is concerned with the stiffness of torsional spring. The numerical analytical results of the 1:1 internal resonance between the two lowest modes show that the nonlinear interaction between the involved internal resonance modes is activated. Moreover, when the parameters are controlled in a certain range there have periodic, quasi-periodic and chaotic windows in dynamic system.