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Vibration CivilEngineer Example Calculation

Calculation Example – Undamped free Vibration (Part A).

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Calculate the Mass and the Stiffness matrix for the shear frame below. The mass is lumped at each level. The supports at end A,B are fixed . The columns are considered to have no mass. (Modulus of elasticity E, Storey masses m1,m2, Column moment of inertia I1,I2. )

Solution

The shear frame has two degrees of freedom, the sideways horizontal displacements u1, u2.

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   In order to find the first column of the Stiffness Matrix we apply unit displacement u1=1 and u2=0.

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In order to find the second column of the stiffness matrix we apply unit displacement u2=1 and u1=0.

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