Model Order Reduction (MOR) denotes the theory by which one tries to catch a model of order lower than that of the real model. This is conveniently pursued in view of the design of an efficient structural control scheme, just passive within this paper. When the nonlinear response of the reference structural system affects the nature of the reduced model, making it dependent on the visited subset of the input-output space, standard MOR techniques do not apply. The mathematical theory offers some specific alternatives, which however involve a degree of sophistication unjustified in the presence of a few localized nonlinearities. This paper suggests applying standard MOR to the linear parts of the structural system, the interface remaining the original unreduced nonlinear components. A case study focused on the effects of a helicopter land crash is used to exemplify the proposal.

In this paper, the possibility of using human induced loading (HIL) to detect a decrease of tension in the cable-stays of an existing footbridge is investigated. First, a reliable finite elements model of an existing footbridge is developed by calibration with experimental data. Next, estimates of the tension in the cables are derived and their dependency on the modal features of the deck is investigated. The modelling of the HIL is briefly discussed and used to perform the nonlinear, large strain, dynamic finite elements analyses. The results of these analyses are assessed with focus on characterizing the time histories of the tension in the cables under pedestrian crossing and their effects on the deck response for different initial conditions. Finally, the control perspective is introduced in view of further research.

The paper first reviews the theory of active tendon control with decentralized Integral Force Feedback (IFF) and collocated displacement actuator and force sensor; a formal proof of the formula giving the maximum achievable damping is provided for the first time. Next, the potential of the control strategy for the control of suspension bridges with active stay cables is evaluated on a numerical model of an existing footbridge; several configurations are investigated where the active cables connect the pylon to the deck or the deck to the catenary. The analysis confirms that it is possible to provide a set of targeted modes with a considerable amount of damping, reaching ${\xi}=15%$. Finally, the control strategy is demonstrated experimentally on a laboratory mock-up equipped with four control stay cables equipped with piezoelectric actuators. The experimental results confirm the excellent performance and robustness of the control system and the very good agreement with the predictions.

This paper presents an experimental study on constructing a tunable secondary suspension for high-speed trains using magneto-rheological fluid dampers (referred to as MR dampers hereafter), in the interest of improving lateral ride comfort. Two types of MR dampers (type-A and type-B) with different control ranges are designed and fabricated. The developed dampers are incorporated into a secondary suspension of a full-scale high-speed train carriage for rolling-vibration tests. The integrated rail vehicle runs at a series of speeds from 40 to 380 km/h and with different current inputs to the MR dampers. The dynamic performance of the two suspension systems and the ride comfort rating of the rail vehicle are evaluated using the accelerations measured during the tests. In this way, the effectiveness of the developed MR dampers for attenuating vibration is assessed. The type-A MR dampers function like a stiffness component, rather than an energy dissipative device, during the tests with different running speeds. While, the type-B MR dampers exhibit significant damping and high current input to the dampers may adversely affect the ride comfort. As part of an ongoing investigation on devising an effective MR secondary suspension for lateral vibration suppression, this preliminary study provides an insight into dynamic behavior of high-speed train secondary suspensions and unique full-scale experimental data for optimal design of MR dampers suitable for high-speed rail applications.

The design of a semi-active (SA) control system addressed to mitigate wind induced structural demand to high wind turbine towers is discussed herein. Actually, the remarkable growth in height of wind turbines in the last decades, for a higher production of electricity, makes this issue pressing than ever. The main objective is limiting bending moment demand by relaxing the base restraint, without increasing the top displacement, so reducing the incidence of harmful "p-delta" effects. A variable restraint at the base, able to modify in real time its mechanical properties according to the instantaneous response of the tower, is proposed. It is made of a smooth hinge with additional elastic stiffness and variable damping respectively given by springs and SA magnetorheological (MR) dampers installed in parallel. The idea has been physically realized at the Denmark Technical University where a 1/20 scale model of a real, one hundred meters tall wind turbine has been assumed as case study for shaking table tests. A special control algorithm has been purposely designed to drive MR dampers. Starting from the results of preliminary laboratory tests, a finite element model of such structure has been calibrated so as to develop several numerical simulations addressed to calibrate the controller, i.e., to achieve as much as possible different, even conflicting, structural goals. The results are definitely encouraging, since the best configuration of the controller leaded to about 80% of reduction of base stress, as well as to about 30% of reduction of top displacement in respect to the fixed base case.

A particle tuned mass damper (PTMD) system is the combination of a traditional tuned mass damper (TMD) and a particle damper (PD). This paper presents the results of an experimental and analytical study of the damping performance of a PTMD attached to the top of a benchmark model under wind load excitation. The length ratio of the test model is 1:200. The vibration reduction laws of the system were explored by changing some system parameters (including the particle material, total auxiliary mass ratio, the mass ratio between container and particles, the suspending length, and wind velocity). An appropriate analytical solution based on the concept of an equivalent single-unit impact damper is presented. Comparison between the experimental and analytical results shows that, with the proper use of the equivalent method, reasonably accurate estimates of the dynamic response of a primary system under wind load excitation can be obtained. The experimental and simulation results show the robustness of the new damper and indicate that the damping performance can be improved by controlling the particle density, increasing the amount of particles, and aggravating the impact of particles etc.

In this paper a different formulation for the response of structural systems controlled by Tuned Liquid Column Damper (TLCD) devices is developed, based on the mathematical tool of fractional calculus. Although the increasing use of these devices for structural vibration control, it has been demonstrated that existing model may lead to inaccurate prediction of liquid motion, thus reflecting in a possible imprecise description of the structural response. For this reason the recently proposed fractional formulation introduced to model liquid displacements in TLCD devices, is here extended to deal with TLCD controlled structures under base excitations. As demonstrated through an extensive experimental analysis, the proposed model can accurately capture structural responses both in time and in frequency domain. Further, the proposed fractional formulation is linear, hence making identification of the involved parameters extremely easier.

This paper is concerned with the dynamics of hyperelastic solids and structures. We seek for a smart control actuation that produces a desired (prescribed) displacement field in the presence of transient imposed forces. In the literature, this problem is denoted as displacement tracking, or also as shape morphing problem. One talks about shape control, when the displacements to be tracked do vanish. In the present paper, it is assumed that the control actuation is provided by imposed eigenstrains, e.g., by the electric field in piezoelectric actuators, or by thermal actuators, or via analogous physical effects, such as magneto-striction or pre-stress. Structures with a controlled eigenstrain-type actuation belong to the class of smart structures. The action of the eigenstrains can be conveniently characterized by actuation stresses. Our theoretical derivations are performed in the framework of the theory of small incremental dynamic deformations superimposed upon a statically pre-deformed configuration of a hyperelastic solid or structure. We particularly ask for a distribution of incremental actuation stresses, such that the incremental displacements follow exactly a prescribed trajectory field, despite the imposed incremental forces are present. An exact solution of this problem is presented under the assumption that the actuation stresses can be tailored freely and applied everywhere within the body. Extending a Neumann-type solution strategy, it is shown that the actuation stresses due to the distributed control eigenstrains must satisfy certain quasi-static equilibrium conditions, where auxiliary body-forces and auxiliary surface tractions are to be taken into account. The latter auxiliary loading can be directly computed from the imposed forces and from the desired displacement field to be tracked. Hence, despite the problem is a dynamic one, a straightforward computation of proper actuator distributions can be obtained in the framework of quasi-static equilibrium conditions. Necessary conditions for the functioning of this concept are presented. Particularly, it must be required that the intermediate configuration is infinitesimally superstable. Previous results of our group for the case of shape control and displacement tracking in linear elastic structures are included as special cases. The high potential of the solution is demonstrated via Finite Element computations for an irregularly shaped four-corner plate in a state of plain strain.

In the present paper we discuss the stability and the post-buckling behaviour of thin piezoelastic plates. The first part of the paper is concerned with the modelling of such plates. We discuss the constitutive modelling, starting with the three-dimensional constitutive relations within Voigt's linearized theory of piezoelasticity. Assuming a plane state of stress and a linear distribution of the strains with respect to the thickness of the thin plate, two-dimensional constitutive relations are obtained. The specific form of the linear thickness distribution of the strain is first derived within a fully geometrically nonlinear formulation, for which a Finite Element implementation is introduced. Then, a simplified theory based on the von Karman and Tsien kinematic assumption and the Berger approximation is introduced for simply supported plates with polygonal planform. The governing equations of this theory are solved using a Galerkin procedure and cast into a non-dimensional formulation. In the second part of the paper we discuss the stability and the post-buckling behaviour for single term and multi term solutions of the non-dimensional equations. Finally, numerical results are presented using the Finite Element implementation for the fully geometrically nonlinear theory. The results from the simplified von Karman and Tsien theory are then verified by a comparison with the numerical solutions.

In this paper a nonlinear, bistable, single degree of freedom system is considered. It consists of a Duffing oscillator externally excited by a non-resonant, harmonic force. A customized perturbation scheme is proposed to achieve an approximate expression for periodic solutions. It is based on the evaluation of the quasi-steady (slow) solution, and then on a variable change followed by two perturbation steps which aim to capture the fast, decaying contribution of the response. The reconstructed solution, given by the sum of the slow and fast contributions, is in a good agreement with the one obtained by numerical integration.