Mathematical Modeling of Bernoulli-Euler Beam on Elastic Foundation With Viscous Damping, Forcing Term and Thermal Effects

Student: CLEMENT OJO FALADE (Project, 2025)
Department of Applied Mathematics With Statistics
Ekiti State University, Ado-Ekiti, Ekiti State

Abstract

This project studied the dynamic response of a Bernoulli-Euler beam resting onan elastic foundation and subjected to spatially distributed forcing, viscous damping, and thermal effects. A governing equation incorporating axial tension andtemperature variations is derived, allowing simulation of beam deflection undervarying conditions. Non-dimensionalization and numerical simulations reveal howcombined thermal expansion and damping influence deflection. This model provides more understanding for structural designs in environments exposed to bothmechanical loads and thermal variations, which enhances resilience and stabilityunder dynamic forces.

Keywords
Elastic foundation Bernoulli-Euler beam Non-dimensionalization Dynamic response
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