Complex potential by hydrodynamic analogy for the determination of flexure-torsion induced stresses in De Saint Venant beams with boundary singularities

In this paper, a novel complex potential function for the solution of the flexure–torsion problem in De Saint Venant beams is proposed, considering the simultaneous presence of external shear and torsion excitations. By defining a fictitious vector field and taking advantage of a hydrodynamic analogy, the proposed complex potential function allows the stress vector field and the unitary twist rotation of the cross-section to be determined at once, and, therefore, returns the complete solution of the problem. The proposed approach is well-suited for domains having boundary singularities. A numerical application, implemented by using the Complex Variable Boundary Element Method (CVBEM), is reported for an elliptical cross-section to show the validity of the proposed complex potential. Finally, two singularity problems are analyzed, considering an L-shaped and an epicycloid-shaped cross-section

Simplified design of nonlinear energy sinks for MDOF structures excited by white noise base excitations

Passive control devices are often used to protect slender and flexible structures from dynamic actions, including earthquakes, wind and waves. The Nonlinear Energy Sink (NES) has recently received increasing attention from researchers because of its capability to passively and irreversibly absorb a significant amount of energy from the primary system over a wide range of frequencies. In this paper, the application of two NESs acting in orthogonal directions is considered to mitigate the response of a multi degree of freedom structure. Parameters for each NES are obtained by considering a single degree of freedom structure, whose mass and frequency are designed based on the fundamental mode of the original structure along the direction of action of the device, and applying the empirical expressions proposed in Oliva et al. (2017). Compared to standard Monte Carlo simulations, the use of these expressions requires a significant lower computational effort, making their implementation suitable for practical engineering purposes. A numerical application on a three-dimensional building is presented to demonstrate the effectiveness of the proposed method. The NESs performance is analysed varying the direction of the ground motion, showing the potential of this passive control system in civil engineering applications. Results are reported in terms of statistics of the structural response, determined by Monte Carlo simulation, and analysis of the energy dissipated by the control devices

Numerical and experimental comparison between two different blade configurations of a wind generator

This paper presents a comparison between the structural behaviour of a wind generator with straight blades and a composite prototype of a wind generator with helical blades. Numerical structural analyses are performed by means of FEM models by using ANSYS MechanicalTM software package. Furthermore, laboratory dynamic experimental tests are carried out on real scale specimens of the two wind generator configurations in order to find their modal properties in terms of natural frequencies and modal shapes. The results of the experimental campaign are then used to update the numerical models by minimizing an objective function. Total stresses and deformations of the two wind generator configurations, coming from the updated numerical models, are evaluated and compared to quantitatively point out the improvement of the structural behaviour obtained by the use of composite materials

Viscoelastic bearings with fractional constitutive law for fractional tuned mass dampers

The paper aims at studying the effects of the inherent fractional constitutive law of viscoelastic bearings used as devices for tuned mass dampers. First, the proper constitutive law of the viscoelastic supports is determined by the local constitutive law. Then, the characteristic force-displacement relationship at the top of the bearing is found. Taking advantage of the whole bearing constitutive laws, the tuning of the mass damper is proposed by defining the damped fractional frequency, which is analogous to the classical damped frequency. The effectiveness of the optimal tuning procedure is validated by a numerical application on a system subjected to a Gaussian white noise

Nonlinear energy sink and Eurocode 8: an optimal design approach based on elastic response spectra

In this paper, the authors propose novel empirical formulae for the optimal design of Nonlinear Energy Sinks (NESs) to control seismic induced vibrations in structures. While large part of the existing literature on NES for seismic applications is based on deterministic analyses of the structural response to recorded ground motions, herein the effectiveness of the device is studied in a stochastic framework. In fact, the seismic excitation has been modeled using a response spectra consistent power spectral density function, taking into account design spectra prescribed into Eurocode 8. Statistics of the structural response have been determined by Monte Carlo Simulations, performing nonlinear time-domain analyses to investigate the dependence of the optimal NES parameters on the main characteristics of the primary system and on the seismic load amplitude. The outcomes of these analyses have been translated into empirical expressions allowing for computing the optimal NES stiffness and damping. Since these are closed-form relationships depending on the main structure and the response spectra parameters, their use allows for an immediate estimate of the NES optimal design configuration, avoiding demanding numerical analyses and making their implementation suitable for practical engineering purposes. The accuracy of the design formulae has been tested by comparison with numerical optimisations for a set of possible configurations of the main structure and for varying intensity of the external excitation. Although the proposed relationships have been extrapolated from single degree of freedom system responses, applications to multi degree of freedom structures is quite straightforward, as shown through two case studies involving the analysis of a 2D multistorey structure and a 3D multi-bay frame controlled by two orthogonal NESs

Closed-form stochastic response of linear building structures to spectrum-consistent seismic excitations

Design codes typically define the seismic action in terms of pseudo-acceleration response spectra, encouraging the use of the modal superposition method for the evaluation of the structural response. For linear structural systems, provided that the ground shaking has been appropriately modelled, the full characterization of the response processes of interest can be achieved with the application of random vibration theory. An analytical model for the power spectral density (PSD) functions consistent with seismic response spectra has been recently proposed. In this paper, taking advantage of this novel PSD model, closed-form approximate expressions of the spectral moments are derived and numerically validated for the seismic response of single- and multi-degree of freedom systems. For demonstration purposes, the proposed formulation is applied to the case of base isolated multi-story buildings, aimed at overcoming the difficulties associated with the non-classical nature of their damping. The paper shows how the proposed approach can be used for a computationally efficient evaluation of the probabilistic distribution of the structural response maxima

A NOVEL ANALYTICAL MODEL OF POWER SPECTRAL DENSITY FUNCTION COHERENT WITH EARTHQUAKE RESPONSE SPECTRA

In the most advanced seismic codes earthquake loads are often defined by means of pseudo-acceleration Response Spectra (RS) and the use of modal superposition analysis method is strongly encouraged. The effectiveness of the design procedures is thus limited by the underlying hypotheses, such as the linearity of the system and the reliability of the modal correlation coefficients used to combine the modal responses for MDOF systems. On the other hand, linear systems response statistics could be easily computed by using stochastic analysis tools, once a stochastic characterization of the seismic action is provided. In this paper a few-parameters analytical model for the definition of Power Spectral Density functions (PSD) coherent with Response Spectra is proposed. Closed-form relationships between the parameters involved in the definition of the PSD and the RS defined by several international seismic codes are provided. The reliability of this tool is assessed by means of a numerical campaign by comparing stochastic analysis and Monte-Carlo simulations. By using the proposed approach, the seismic action can be defined both in terms of RS and in terms of PSD, and, therefore, the engineer can choose the most appropriate analysis tool for his purpose