Abstract
This paper derives an analytical model of a straight beam with a T-shaped cross section for use in the high-frequency range, defined here as approximately 1 to 35 kHz. The web, the right part of the flange, and the left part of the flange of the T-beam are modeled independently with two-dimensional elasticity equations for the in-plane motion and Mindlin flexural plate equation for the out-of-plane motion. The differential equations are solved with unknown wave propagation coefficients multiplied by circular spatial domain functions. These algebraic equations are then solved to yield the wave propagation coefficients and thus produce a solution to the displacement field in all three directions. An example problem is formulated and compared with solutions from fully elastic finite element modeling, a previously derived analytical model, and Timoshenko beam theory. It is shown that the accurate frequency range of this new model is significantly higher than that of the analytical model and the Timoshenko beam model, and, in the frequency range up to 35 kHz, the results compare very favorably to those from finite element analysis.
Highlights
This paper is a direct extension of a previous effort [1,2] that modeled the dynamics of a straight T-beam
In the new model derived here, the Love-Kirchhoff plate equations are replaced by Mindlin plate equations [4], whose theoretical basis includes shear deformation and rotary inertia terms, resulting in a higher-frequency range of analysis
This paper develops an analytical model of a T-shaped beam for high-frequency range analysis
Summary
This paper is a direct extension of a previous effort [1,2] that modeled the dynamics of a straight T-beam. The assumptions of the Love-Kirchhoff plate equations typically produce model results that are too stiff, especially as the frequency increases.
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