A Semi Analytical Method for Dynamic Analysis of Beam Resting on Inertial Soil

Accurate dynamic analysis of beams supported on soil is essential for the safe and economical design of vibrationresistant and earthquake-resistant structures. Earlier contributions, such as the semi-analytical framework developed by Guenfoud, Bosakov, and Laefer (2009), provided reliable predictions for beams on elastic half-spaces with inertial properties. However, these formulations are mathematically intensive and often difficult to apply directly in engineering practice. Conventional soil models, including Winkler’s subgrade reaction method and continuum-based elastic models, either oversimplify soil behaviour or involve complex derivations, further limiting their practical utility. The present study introduces a modified version of the semi-analytical method for beams resting on an elastic half-space with inertial properties, reformulated to reduce mathematical complexity without compromising accuracy. The approach incorporates soil inertia effects while enabling more straightforward evaluation of displacements under vertical loading. To illustrate its effectiveness, the dynamic response of a beam measuring 10 m in length, 1 m in width, and 0.5 m in depth is investigated. The corresponding Eigenfrequencies and natural shapes of the beam are determined, and the results show close agreement with those obtained from established analytical methods. This refinement not only simplifies computational effort but also makes the analysis more accessible for engineering applications. The method thus provides a practical and reliable tool for studying beam–soil interaction dynamics, with direct relevance for the design of safer and more cost-effective structural systems.