The determination that the resonant frequency be sufficiently large for certain structures may permit the use of more economical static rather than dynamic structural analysis methods for seismic qualification. An extended configuration such as a valve yoke with massive actuator is frequently modeled as a cantilever beam with a single lumped mass at its end; the natural frequency being a well known function of the bending stiffness of the beam, length and mass. For actuators with a mass distribution, not readily represented by concentrated mass, this could lead to gross errors in frequency calculation. To demonstrate this, a mathematical model was formulated of a rigid "dumbell" supported at the end of a cantilever beam. Closed-form solutions were obtained for natural frequencies of simple cantilever, combined bending-rotation, torsional, and axial modes of vibration. The ratios of these frequencies were presented in terms of the stiffness and geometric parameters. For many realistic combinations of parameters, it was demonstrated that the torsional and combined bending mode frequencies are much smaller than the simple bending frequency; thus invalidating the employment of static seismic analysis. More sophisticated, but still economical, computerized procedures are suggested that will avoid this error and may predict unforeseen resonances.
展开▼
