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We investigated theoretically and experimentally the nonlinear responseof a clamped-clamped buckled beam to a subharmonic resonance of orderone-half of its first vibration mode. We used a multi-mode Galerkindiscretization to reduce the governing nonlinear partial-differentialequation in space and time into a set of nonlinearly coupledordinary-differential equations in time only. We solved the discretizedequations...
Approximate methods for analyzing the vibrations of an Euler--Bernoulli beam resting on a nonlinear elastic foundation are discussed. The cases of primary resonance (Ω ≈ Ωn) and subharmonic resonance of order one-half (Ω ≈ 2 Ωn), where Ω is the excitation frequency and Ωn is the natural frequency of the nth mode of the beam, are investigated. Approximate solutions based on discretization via...
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