Chaotic vibrations of beams on nonlinear elastic foundations subjected to reciprocating loads

• Melnikov function is extracted for chaotic motion of a beam resting on a nonlinear foundation.
• Nonlinear dynamic behavior of an Euler–Bernoulli beam under reciprocating load is analyzed.
• Results indicate the beam chaotic motion is strongly dependent on the reciprocating frequency.

Chaotic vibration of beams resting on a foundation with nonlinear stiffness is investigated in this paper. Cosine–cosine function is employed in modeling of the reciprocating load. The equation of motion is derived and solved to obtain corresponding Poincaré section in phase–space. Lyapunov exponent as a criterion for chaos indication is obtained. Dynamic behavior of the beam is examined in resonance condition. Homoclinic orbits are captured and their corresponding Melnikov's functions are established. A parametric study is then carried out and effects of linear and nonlinear parameters on the chaotic behavior of the system are studied.