When designing a structure subject to dynamic loads (like earthquakes or wind), a significant issue is estimating its natural period(s) of vibration, which mainly depend on its mass and stiffness. An effective way to avoid damage from earthquakes is to reduce its natural period. This project was inspired by safe design taught in CIV102 at the University of Toronto.

In a two-storey structure, there are two degrees of freedom which are described by a set of coupled, 2nd-order differential equations (see below). The β€œLollipop Model” of a building lumps the stiffness and masses of each floor and connects them with springs.

(m1)(x1'') = (-k1)(x1) + (-k2)(x1 - x2)

(m2)(x2'') = (-k2)(x2 - x1)

m1: lumped mass of first storey; k1: lumped stiffness of first storey

What it does

This project models a two-storey building subject to free vibration. It defines the mass and stiffness of each storey and simulates the coupled 2nd-order differential equations to measure the displacement of each storey over time. A fast-Fourier transform is then applied onto this data to estimate the resonant frequencies.

How we built it

A MATLAB Live Script sets the building parameters and performs the FFT, whereas the Simulink model simulates the free vibration.

What's next

Next steps are to simulate multiple storeys or optimize the building's physical characteristics (mass and stiffness) under certain constraints. Also, external forces (forced vibration) and viscous damping forces can be considered.

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