Verification Examples

Spring with Clearance

VE 0119

3 May 2019

A single-mass system with clearance and two springs is initially deflected. Determine the natural oscillations of the system - deflection, velocity and acceleration time course.

Plastic Material Oscillations

VE 0124

14 November 2018

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

VE 0121

10 July 2018

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

VE 0120

21 February 2018

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

VE 0118

4 December 2017

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

VE 0112

27 October 2017

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

VE 0117

27 October 2017

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

VE 0116

16 October 2017

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

VE 0111

18 July 2017

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

VE 0115

18 July 2017

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.

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