Determine the first sixteen natural frequencies of a double cross with a square cross-section. Each of the eight arms is modeled by means of four beam elements and has a pin support at the end (the x- and y-deflections are restricted). The vibrations are considered only in plane xy. The problem is defined according to The Standard NAFEMS Benchmarks.
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.
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.
A single-mass system with dashpot is subjected to a constant loading force. Determine the spring force, damping force, and inertial force at the 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.
A single-mass system with dashpot is subjected to constant loading force. Determine the deflection and velocity of the dashpot endpoint in the given test time.
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 the given test time.
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.
A simple oscillator consists of mass m (considered only in the 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 transverse forces.