Applying Simulink to solve the differential equation of rotational angle of a vibrating building resting on a viscous foundation

Abstract

Dynamic effects on structures are complicated topics, both in theoretical and experimental aspects. This article aims to study more deeply the effects of the waves on the response of a receiver footing in the vicinity. This paper establishes the governing equation for the vibrating structure resting on a viscous soil foundation. By prescribing all the rotating motions happened to the footings, including the sliding moments, and the anti-sliding moments, a differential equation is established. The viscous characteristics that based on a laboratory test-based results is considered, and the dynamic equilibrium equation of all the moments is manipulated to an ordinary diffferential equation. Beside the analytical solution, solved by the conventional approach, a Matlab Simulink diagram is created to solve the equation. The result indicates there is a value of rotational angle at which the rocking structure would attain during the process of vibration in long enough time. This solution could explain the failure mode of buildings which are constructed nearby a road, are stirred and vibrated under the dynamic effects caused by traffic mobility. These dynamic effects are of low-frequency range, or between 0 to 100 Hz. A model of the finite element method, Plaxis 2D is used to validate the vibrational response of the receiver footing, concerning the effects on the far field. The soil foundation is very compressible, subjected to a vibration at different excitation frequencies. The movement of particles on the free domain of the soil surface at a distance of 50 m apart from the source of excitation results in a differential settlement for points within a receiver footing. And the displacement responses of the structure are analysed both in time domain and frequency domain. The beneficial application of Matlab Simulink for solving specific problems in Engineering Mechanics is suggested.