Shear deformable beams on nonlinear viscoelastic foundation under moving loading

In this paper, a boundary element method is developed for the nonlinear response of shear deformable beams of simply or multiply connected constant cross section, traversed by moving loads, resting on tensionless nonlinear viscoelastic foundation, undergoing moderate large deflections under general boundary conditions. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse moving loading as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Three boundary value problems are formulated with respect to the transverse displacement, to the axial displacement and to a stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a system of nonlinear differential – algebraic equations (DAE), which is solved using an efficient time discretization scheme, from which the transverse and axial displacements are computed. The evaluation of the shear deformation coefficient is accomplished from the aforementioned stress function using only boundary integration. Analyses are performed to investigate the effects of various parameters, such as the load velocity, load frequency, shear rigidity, foundation nonlinearity, damping, on the beam displacements and stress resultants and to examine how the consideration of shear and axial compression affect the response of the system

NONLINEAR DYNAMIC ANALYSIS OF PLATES STIFFENED BY PARALLEL BEAMS WITH DEFORMABLE CONNECTION

In this paper a general solution to the geometrically nonlinear dynamic analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross-section, subjected to dynamic loading, is presented. The plate-beam structure is assumed to undergo moderate large deflections and the nonlinear analysis is carried out by retaining nonlinear terms in the kinematical relations. According to the proposed model, the arbitrarily placed parallel stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, making the hypothesis that the plate and the beams can slip in all directions of the connection without separation and taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting in two interface lines, along which the loading of the beams and the additional loading of the plate are defined. Six boundary value problems are formulated and solved using the analog equation method (AEM), a BEM-based method. Both free and forced transverse vibrations are considered and numerical examples with great practical interest are presented demonstrating the effectiveness, wherever possible, the accuracy, and the range of applications of the proposed method

Vibration and buckling of thin-walled composite I-beams with arbitrary lay-ups under axial loads and end moments

A finite element model with seven degrees of freedom per node is developed to study vibration and buckling of thin-walled composite I-beams with arbitrary lay-ups under constant axial loads and equal end moments. This model is based on the classical lamination theory, and accounts for all the structural coupling coming from material anisotropy. The governing differential equations are derived from the Hamilton’s principle. Numerical results are obtained for thin-walled composite I-beams to investigate the effects of axial force, bending moment and fiber orientation on the buckling moments, natural frequencies, and corresponding vibration mode shapes as well as axial-moment-frequency interaction curves

Vibration Mitigation of Wind Turbine Towers Using Negative Stiffness Absorbers

The application of dynamic vibration absorbers (DVA) to Wind Turbine (WT) towers has the potential to significantly improve the damping of the tower and the nacelle dynamic responses, increasing thus the reliability of WTs. The Tuned Mass Damper (TMD) is limited by the requirement of large masses, in association to its installation location. In this study, two alternative concepts are considered. First, the nacelle is released from the WT tower, using a low stiffness connection. This option is based on the seismic isolation concept. Additionally, a novel passive vibration absorption configuration is implemented, based on the KDamper concept. The KDamper is essentially an extension of the TMD, introducing negative stiffness (NS) elements. Instead of increasing the additional mass, the vibration absorption capability of the KDamper can be increased by increasing the value of the NS element. Therefore, the KDamper always indicates better isolation properties than a TMD with the same additional mass.  For the nonlinear dynamic response of the WT a build-in house software is developed. The dynamic performance of the proposed vibration mitigation concepts is numerically examined. All methods present superior dynamic behaviour as compared to the uncontrolled structure, however only the KDamper-based designs significantly increase the effective damping of the WT tower, retaining the additional masses in reasonable ranges