An eccentric mass shaker installed on the top floor of the three-story shear frame building shown in Figure P8.15 produces a harmonic force [latex]p_0 \sin \Omega t[/latex], where [latex]p_0=45 \mathrm{kN}[/latex] and [latex]\Omega=5 \pi / 3 \mathrm{rad} / \mathrm{s}[/latex]. The frame is modeled as a single-degree-of-freedom system by assuming that the vibration shape is [latex]\boldsymbol{\psi}^T=\left[\begin{array}{lll}1 & 1.75 & 2.5\end{array}\right][/latex]. Find the history of the top-floor displacement for the first [latex]0.6 \mathrm{~s}[/latex] using a piece-wise linear representation of the forcing function and a time step of [latex]0.1 \mathrm{~s}[/latex]. Find the maximum base shear produced during this time. Neglect damping.

Maximum base shear at 0.5 s = 103.8 kN.

Question 8.P.15: An eccentric mass shaker installed on the top floor of the t...

An eccentric mass shaker installed on the top floor of the three-story shear frame building shown in Figure P8.15 produces a harmonic force $p_0 \sin \Omega t$ , where $p_0=45 \mathrm{kN}$ and $\Omega=5 \pi / 3 \mathrm{rad} / \mathrm{s}$ . The frame is modeled as a single-degree-of-freedom system by assuming that the vibration shape is $\boldsymbol{\psi}^T=\left[\begin{array}{lll}1 & 1.75 & 2.5\end{array}\right]$ . Find the history of the top-floor displacement for the first $0.6 \mathrm{~s}$ using a piece-wise linear representation of the forcing function and a time step of $0.1 \mathrm{~s}$ . Find the maximum base shear produced during this time. Neglect damping.

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