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Verification Examples
Dynamic Force Distribution
A single-mass system with dashpot is subjected to a constant loading force. Determine the spring force, the damping force and the inertial force at given test time. In this verification example, the Kelvin--Voigt dashpot, namely, a spring and a damper element in serial connection, is decomposed into its purely viscous and purely elastic parts, in order to better evaluate the reaction forces.
Single-Mass Oscillation with Dashpot
A single mass system with dashpot is subjected to the constant loading force. Determine the deflection and the velocity of the dashpot endpoint in given test time.
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.
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