Lumped Parameter Beams Based on Impedance Methods

by Vernon H. Neubert, (M.ASCE), Prof. of Engrg. Mech.; Pennsylvania State Univ., University Park, PA,
Hong T. Hahn, Grad. Student; Dept. of Engrg. Mech., Pennsylvania State Univ., University Park, PA,
Hae Lee, Sr. Res. Engr.; Westinghouse Res. Labs., Beulah Road, Pittsburgh, PA,

Serial Information: Journal of the Engineering Mechanics Division, 1970, Vol. 96, Issue 1, Pg. 69-82

Document Type: Journal Paper


In predicting the response of structures to dynamic loading, the analyst must often replace the physical system having an infinite number of degrees-of-freedom with a lumped parameter model having a finite number. To represent a system adequately in a particular frequency range using only a few degrees of freedom, it is important to make the impedance or dynamic stiffness accurate in that frequency range. Two lumped parameter models for a clamped-clamped Bernoulli-Euler are derived by making the impedance accurate at the boundaries in the low-frequency range. It is shown that the six separate impedance functions in the four-by-four impedance matrix can be matched using a three-parameter, symmetrical element. The impedance models are compared with others, some of which predict natural frequencies with less error. The impedance models represent more accurately the shear forces and bending moments due to steady-state or transient excitations.

Subject Headings: Model accuracy | Dynamic structural analysis | Parameters (statistics) | Beams | Errors (statistics) | Dynamic models | Physical models | Structural models

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