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.
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.
A double‑mass system consists of two shafts and two masses represented by the corresponding moments of inertia, concentrated in a 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.
A cantilever of rectangular cross‑section has a mass at the 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 the axial force for the stiffness modification.
A concentrated force is suddenly applied at the mid‑span of a simply supported beam at a given time. Considering only the small deformation theory, determine the maximum deflection of the beam.
A concentrated force is applied for a short period of time at the mid‑span of a simply supported beam. Considering only the small deformation theory and assuming that the mass of the beam is concentrated at its mid‑span, determine its maximum deflection.
A two‑story, single‑bay frame structure is subjected to earthquake loading. The modulus of elasticity and cross‑section of the frame beams are much larger than those of the columns, so the beams can be considered rigid. The elastic response spectrum is given by the standard SIA 261/1:2003. Neglecting self-weight and assuming the lumped masses are at the floor levels, determine the natural frequencies of the structure. For each frequency obtained, specify the standardized displacements of the floors as well as equivalent forces generated using the elastic response spectrum according to the standard SIA 261/1.2003.
Time history analysis of a cantilever beam (SDOF system) excited by a periodic function. Vertical deformations and accelerations calculated with direct integration and modal analysis in RF‑/DYNAM Pro - Forced Vibrations are compared with the analytical solution.