The objective of this study is to investigate the influence of shape changes on the natural frequencies of a channel beam. To achieve this objective, the solutions of differential equations of motion for a beam experiencing coupled bending and torsion are derived using the Ritz approach. The functional of the corresponding system frequency equation is formulated. A set of polynomial that satisfies the fixed-free boundary condition is generated. The Ritz method leads the formulation to an eigen value problem for frequency calculations. A numerical examples is presented to validate the approach and to study the influence of shape changes on the dynamics of the beam structure.
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