验算示例

Plastic Material Oscillations

This verification example is based on Verification Example 0122. A single-mass system without damping is subjected to an axial loading force. An ideal elastic-plastic material with characteristics is assumed. Determine the time course of the end-point deflection, velocity and acceleration.

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.

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.

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.

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.

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.

Natural Vibrations of Rectangular Membrane

A rectangular membrane is tensioned by a line force. Determine the natural frequencies of the given membrane.

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