Torsional vibrations of a suspended beam and plate

The paper analyzes the torsional vibrations of a suspended beam and suspended plates: square and triangular. The equations of motion for the analyzed systems were derived using the energy method. For the beam, the square plate, and the equilateral triangular plate, discrete equivalent models with lumped masses were applied. The angular frequencies and vibration periods of the beam and plates were determined.The subject of this paper is the analysis of torsional vibrations of a suspended beam and suspended plates. The energy method was used to derive the equations of motion for the analyzed systems. For the beam, the square plate, and the equilateral triangular plate, discrete equivalent models were applied.
In the case of all three systems, their vibration equations were solved, determining the angular frequencies and vibration periods of the beam and plates.
2. TORSIONAL VIBRATIONS OF A SUSPENDED BEAM AND PLATE
Let a homogeneous rigid horizontal beam AB with total mass m and length l be suspended at both ends by two identical inextensible vertical cables of a given length L. In the static equilibrium position, both cables are parallel to each other.
Our task will be to determine the angular frequency and period of small vibrations resulting from a small rotation of the beam around the vertical axis OC passing through its center of mass C, as shown in Figure 1. (…)

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