Nonlinear analysis of the forced response of a beam with three mode interaction

摘要: An analysis is presented for the primary resonance of a clamped-hinged beam, which occurs when frequency excitation near one natural frequencies,ωn . Three mode interaction (ω2 ≈ 3ω1 and ω3 ω1 + 2ω2) considered its influence on response studied. The case two 3ω1) also to compare it with three interaction. straight beam experiencing mid-plane stretching governed by nonlinear partial differential equation. By using Galerkin's method governing equation reduced system nonautonomous ordinary equations. multiple scales applied solve system. Steady-state responses their stability are examined. Results numerical investigations show that there exists no significant difference between both modal interactions' influences responses.