To simulate the effects of an earthquake on a rigid building

To simulate the effects of an earthquake on a rigid building, the base of the building is assumed to be connected to ground through a translational resilient element K and a torsional resilient element K_T. If the ground is assumed to have a translational motion of x_1(t), determine the equations of motion of the building using in terms of y and theta Alembert\'s principle.

Solution

solution:

whenever building given initial force unit step input building will start translating in x direction as well rotation

1)hence equation of motion for translation is

mx\'\'+kx=f(t)

for rotation s degree as

ms\'\'+kts=f(t)

on equatingwe get

mx\'\'+kx=ms\'\'+kts

angle is given by

s=y/x

hence on changing x\'\' and x by y and s we get

ms\'\'+kts-m[((s^2)(ys\'\'-sy\'\')-(ys\'-sy\')2s\')s^3]-k(y/s)=0

this equation will give vibration induced in building