Calculation of Damping constant in case of Damped free vibration.

Keyword

Damped free vibration,Underdamping,Damping constant,Damped natural frequency,Undamped natural frequency,Initial displacement,Initial velocity,Natural period.

Reference

・『耐震規定と構造動力学』（石山祐二）

Remarks

※1：If input s(2) is equal to s(1) or less, s(2) will be set to s(2)=s(1)+i2*T*1.5 automatically.
※2：・Formula 1：x(t)=e^(-h*ω*t)*(x(0)*cos(ωd*t)+(v(0)+h*ω*x(0))/ωd*sin(ωd*t)).
※2：・Formula 2：x(t)=(x(0)^2+((v(0)+h*ω*x(0))/ωd)^2)^0.5*e^(-h*ω*t).
・h=Damping constant.
・ω=Undamped natural frequency.
・ωd=Damped natural frequency.
・x(0)=Initial Displacement.
・v(0)=Initial Velocity.
・h=((ln(xi1/xi2))^2/((2*π*n)^2+(ln(xi1/xi2))^2))^0.5.

History

・2014/08/14：layout change.
・2009/03/29：Moved from www.am-consulting.co.jp to here.