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Nonlinear analysis of a forced geometrically nonlinear Hinged-Clamped beam involving three modes interactions with internal resonance and submitted to thermal and mechanical loadings is investigated. Based on the extended Hamilton’s principle, the PDEs governing the thermoelastic vibration of planar motion is derived. Galerkin’s orthogonalization method is used to reduce the governing PDEs of motion into a set of nonlinear non-autonomous ordinary differential equations. The system is solved for the three modes involved by the use of the multiple scales method for amplitudes and phases. For steady states responses, the Newton-Raphson shooting technique is used to solve the three systems of six parametric nonlinear algebraic equations obtained. Results are presented in terms of influences of temperature variations on the response amplitudes of different substructures when each of the modes is excited. It is observed for all substructures and independent of the mode excited a shift within the frequency axis of the temperature influenced amplitude response curves on either side of the temperature free-response curve. Moreover, it is found that thermal loads diversely influence the interacting substructures. Depending on the directly excited mode, higher oscillation amplitudes are found in some substructures under negative temperature difference, while it is observed in others under positive temperature change and in some others for temperature free-response curves.

Vibrational behavior and structural failure of a metallic beam submitted to simultaneous action of axial load and fire exposure are investigated. Analyses are made at ambient conditions and for two types of fire, ISO 834 fire and parametric fire. Vibrational equation based on heat conduction equation and field equations are constructed and numerically solved to obtain the responses in terms of time histories, bending moment in fire and time to failure against axial load ratio. The heat flux is high enough to affect material properties of the structure and their variation with temperature is taking into account in the mathematical formulation. Results show that heat flux resulting from fire action transforms the buckling problem occurring at room temperature into a bending one. Non-reversible responses and sooner arising of failure are observed for ISO 834 fire even for axial load ratio not able to cause buckling at room temperature. Unlike the case of ISO fire, parametric fire improves reversible deflections within the exposure time and later occurring of failure.