Base Moment for a Class of Linear Systems

by Jacobo Bielak,

Serial Information: Journal of the Engineering Mechanics Division, 1969, Vol. 95, Issue 5, Pg. 1053-1062

Document Type: Journal Paper

Abstract: Contributions of the second and higher modes to the overturning moment at the base of any classical linear system whose fundamental mode is given by a straight line are shown to vanish identically. A necessary and sufficient condition for a nonuniform shear beam to exhibit a linear first mode is obtained. In particular, it is shown that a shear beam with uniform cross section and mass density will have a linear fundamental mode shape if and only if the shearing stiffness is distributed parabolically. For such a beam, the higher mode shapes are given by odd degree Legendre polynomials.

Subject Headings: Linear functions | Beams | Stiffening | Paraboloid | Polynomials |

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