By Farzad Ebrahimi
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8. 38 Mode ANSYS Euler Timoshenk 2D Shell 3D Solid o Experiment Table 1. Natural frequencies [Hz] comparison for the stepped beam in Jaworski and Dowell (2008) Note: ω1B , ω2 B are the first and second out-of-plane bending mode frequencies, respectively. ω1c denotes the first in-plane bending mode frequency. CMA represents component modal analysis. 34 Mod e Advances in Vibration Analysis Research No crack Exp. (2002) ed Exp. (2002) d Exp. (2002) ed Exp. 003 Table 2. (2002) dc 1 = 12 mm at Mod e No crack Exp.
Dynamic Stiffness Matrix (DSM) method, on the other hand, provides an analytical solution to the free vibration problem, achieved by combining the coupled governing differential equations of motion of the system into a single higher order ordinary differential equation. Enforcing the boundary conditions then leads to the system’s DSM and the most general closed form solution is then sought. The DSM formulation results in a non-linear eigenvalue problem and the bi-section method, combined with the root counting algorithm developed by Wittrick & Williams (1971), is then used as a solution technique.
The face materials are homogeneous and elastic, while the core material is assumed to be homogeneous, orthotropic and rigid in the z-direction. • The transverse displacement w does not vary throughout the thickness of the beam. • The shear within the faces is negligible. • The bending strain within the core is negligible. • There is no slippage or delamination between the layers during deformation. Using the model and assumptions described above, Ahmed (1971) used the principle of minimum potential energy to obtain the differential equations of motion and corresponding boundary conditions.
