Modeling of three-dimensional beam nonlinear vibrations generalizing Hencky’s ideas

In this contribution, a novel nonlinear micropolar beam model suitable for metamaterials design in a dynamics framework is presented and discussed. The beam model is formulated following a completely discrete approach and it is fully defined by its Lagrangian, i.e., by the kinetic energy and by the potential of conservative forces. Differently from Hencky’s seminal work, which considers only flexibility to compute the buckling load for rectilinear and planar Euler–Bernoulli beams, the proposed model is fully three-dimensional and considers both the extensional and shear deformability contributions to the strain energy and translational and rotational kinetic energy terms. After having introduced the model formulation, some simulations obtained with a numerical integration scheme are presented to show the capabilities of the proposed beam model.

The Evolution of Lateral Dose Distributions of Helium Ion Beams in Air: From Measurement and Modeling to Their Impact on Treatment Planning

To start clinical trials with the first clinical treatment planning system supporting raster-scanned helium ion therapy, a comprehensive database of beam characteristics and parameters was required for treatment room-specific beam physics modeling at the Heidelberg Ion-Beam Therapy Center (HIT). At six different positions in the air gap along the beam axis, lateral beam profiles were systematically measured for 14 initial beam energies covering the full range of available energies at HIT. The 2D-array of liquid-filled ionization chambers OCTAVIUS from PTW was irradiated by a pencil beam focused at the central axis. With a full geometric representation of HIT’s monitoring chambers and beamline elements in FLUKA, our Monte Carlo beam model matches the measured lateral beam profiles. A second set of measurements with the detector placed in a water tank was used to validate the adjustments of the initial beam parameters assumed in the FLUKA simulation. With a deviation between simulated and measured profiles below ±0.8 mm for all investigated beam energies, the simulated profiles build part of the database for the first clinical treatment planning system for helium ions. The evolution of beamwidth was also compared to similar simulations of the clinically available proton and carbon beam. This allows a choice of treatment modality based on quantitative estimates of the physical beam properties. Finally, we investigated the influence of beamwidth variation on patient treatment plans in order to estimate the relevance and necessary precision limits for lateral beam width models.

High-fidelity aeroelastic analyses of wind turbines in complex terrain: FSI and aerodynamic modelling

This paper shows high-fidelity Fluid Structure Interaction (FSI) studies applied on the research wind turbine of the WINSENT project. In this project, two research wind turbines are going to be erected in the South of Germany in the WindForS complex terrain test field. The FSI is obtained by coupling the CFD URANS/DES code FLOWer and the multiphysics FEM solver Kratos, in which both beam and shell structural elements can be chosen to model the turbine. The two codes are coupled in both an explicit and an implicit way. The different modelling approaches strongly differ with respect to computational resources and therefore the advantages of their higher accuracy must be correlated with the respective additional computational costs. The presented FSI coupling method has been applied firstly to a single blade model of the turbine under standard uniform inflow conditions. It could be concluded that for such a small turbine, in uniform conditions a beam model is sufficient to correctly build the blade deformations. Afterwards, the aerodynamic complexity has been increased considering the full turbine with turbulent inflow conditions generated from real field data, in both a flat and complex terrains. It is shown that in these cases a higher structural fidelity is necessary. The effects of aeroelasticity are then shown on the phase-averaged blade loads, showing that using the same inflow turbulence, a flat terrain is mostly influenced by the shear, while the complex terrain is mostly affected by low velocity structures generated by the forest. Finally, the impact of aeroelasticity and turbulence on the Damage Equivalent Loading (DEL) is discussed, showing that flexibility is reducing the DEL in case of turbulent inflow, acting as a damper breaking larger cycles into smaller ones.

Analytical Solution for Vibrations of a Modified Timoshenko Beam on Visco-Pasternak Foundation Under Arbitrary Excitations

An analytical solution is derived for dynamic response of a modified Timoshenko beam with an infinite length resting on visco-Pasternak foundation subjected to arbitrary excitations. The modified Timoshenko beam model is employed to further consider the rotary inertia caused by the shear deformation of a beam, which is usually neglected by the traditional Timoshenko beam model. By using Fourier and Laplace transforms, the governing equations of motion are transformed from partial differential forms into algebraic forms in the Laplace domain. The analytical solution is then converted into the time domain by applying inverse transforms and convolution theorem. Some widely used loading cases, including moving line loads for nondestructive testing, travelling loads for seismic wave passage, and impulsive load for impact vibration, are also discussed in this paper. The proposed generic solutions are verified by comparing their degraded results to the known solutions in other literature. Several examples are performed to further investigate the differences of the beam responses obtained from the modified and the traditional Timoshenko beam models. Results show that the modified Timoshenko beam simulates the beam responses more accurately than the traditional model, especially under the dynamic loads with a high frequency. The analytical solutions proposed in this paper can be conveniently used for design and applied as an effective tool for practitioners.

Coriolis Force Sliding Mode Control Method for the Rotary Motion of the Central Rigid Body-Flexible Cantilever Beam System in TBM

Beam slab structure is often encountered in a complex tunnel boring machine. Beam slab structure is subject to dynamic load, which is easy to cause fatigue damage and affect its service life. Therefore, it is necessary to control the vibration of this kind of beam slab structure. In this study, the central rigid body-flexible beam model is established for the rotating beam and plate rotating around the y-axis. Based on the Hamilton variational principle, the dynamic equation of the central rigid body-flexible beam system is established, and the dynamic model of the central rigid body-flexible beam system considering the influence of Coriolis force and centrifugal force is given. The vibration control of the central rigid body-flexible beam system is studied. The vibration mode of the rotating Euler Bernoulli beam is determined by using the elastic wave and vibration mode theory. The influence of the rotating motion on the beam vibration is analyzed, and the variable structure control law is designed to suppress the beam vibration. Numerical simulation results show that the control method can effectively suppress the first-order and second-order vibration of the beam and verify the effectiveness of the control strategy.