Analysis of Forced Vibrations in Timoshenko Beams Using the Coupled Displacement Field Concept

Abstract

Modular construction is an excellent technique for achieving the rapid and safe development of facilities in light of the COVID-19pandemic. Beams are fundamental to modular construction. However, owing to various environmental conditions, novel methods are required to collect the characteristics for conducting structural analysis of beams according to the required needs. In this study, the performance of the coupled displacement field method in beam analysis was evaluated. The expressions for the transverse displacement were derived using an allowable function of total rotation. The function was obtained using the finite-element approximation method based on undetermined coefficients. Thus, the equation of motion was derived using the principle of conservation of energy. The Newmark method and mode superposition technique were then used to solve the obtained equations in MATLAB. The resultsshowed that the method used was suitable in applications that require the analysis of high-slenderness beams in modular constructions. In this method, strong vibrations were induced in the beam owing to its greater flexibility. The recommended method is less complex than other energy methods because the computational effort is halved. Therefore, this formulation can be applied to conduct the free vibration analysis of flexible structural members under various shears using Timoshenko beam models under various boundary conditions. Thus, the coupled displacement field method can be used to derive appropriate solutions to other complex problems, such as modular construction.