Przykłady obliczeniowe

Mathematical Pendulum

The mathematical pendulum consists of a zero‑weight rope and a mass point at its end. The pendulum is initially deflected. Determine the angle of the rope at given test time

Double Mass Oscillator

A double-mass oscillator consists of two linear springs and masses, which are concentrated at the nodes. The self-weight of the springs is neglected. Determine the natural frequencies of the system.

Vibrations with Coulomb Friction

A simple oscillator consists of mass m (considered only in x-direction) and linear spring of stiffness k. The mass is embedded on a surface with Coulomb friction and is loaded by constant-in-time axial and transversal forces.

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.

Free Vibrations of String

A thin string is tensioned by the initial strain and initially deflected. Determine the deflection of the test point at given test times.

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.

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