Abstract
In the case of conventional analysis of beams, lateral components (along the width) of the beam are neglected, but this assumption is not always suitable for the case of real beams. In this paper we propose general higher-order equations for one-dimensional static and dynamic beam theories including the effects of lateral components as well as transverse components of general anisotropic beams by expanding the displacements of double infinite-power series with respect to the transverse and lateral coordinates of the beam. Some typical examples of the general higher-order equations given by the truncation of the series are compared with the previously proposed beam theories, and the interrelations among those theories are examined. Futhermore, static and dynamic numerical examples are shown for the cases of infinite beams subjected to sinusoidal loadings and frequency spectrum of simply supported beams.
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