Przykłady obliczeniowe
Bending Vibrations with Axial Force
A cantilever of rectangular cross‑section has a mass at its end. Furthermore, it is loaded by an axial force. Calculate the natural frequency of the structure. Neglect the self‑weight of the cantilever and consider the influence of axial force for the stiffness modification.
Impulse Applied to Simply Supported Beam
A concentrated force is applied for a short period of time at the mid‑span of a simply supported beam. Considering only small deformation theory and assuming that the mass of the beam is concentrated at its mid‑span, determine its maximum deflection.
Suddenly Applied Load to Simply Supported Beam
A concentrated force is suddenly applied at the mid‑span of a simply supported beam at given time. Considering only small deformation theory, determine the maximum deflection of the beam.
Torsional Vibrations
A double‑mass system consists of two shafts and two masses represented by the corresponding moments of inertia, concentrated in given distance as nodal masses. The left shaft is fixed, and the right mass is free. Neglecting the self‑weight of the shafts, determine the torsional natural frequencies of the system.
Natural Vibrations of Rectangular Plate
A rectangular steel plate of dimensions is simply supported at its edges. Determine the natural frequencies of the rectangular plate.
Natural Vibrations of Circular Plate
A circular steel plate is clamped around its circumference. Determine the natural frequencies of the circular plate.
Natural Vibrations of Circular Membrane
A circular membrane is tensioned by a line force. Determine the natural frequencies of the circular membrane.
Natural Vibrations of Rectangular Membrane
A rectangular membrane is tensioned by a line force. Determine the natural frequencies of the given membrane.
Natural Vibrations of String
A thin string is tensioned by the axial force. Determine the natural frequencies of the string.
Equivalent Loads
A cantilever beam with I-beam cross-section of length L is defined. The beam has five mass points with masses m acting in X-direction. The self-weight is neglected. The frequencies, the mode shapes and the equivalent loads of this 5-DOF system are analytically calculated and compared with results from RSTAB and RFEM.
