Principal parametric resonances of elastic plates actuated by periodic in-plane stresses effected by embedded piezoelectric wires are investigated to describe the morphing scenarios of flexible, ultra-lightweight panels. A mechanical model of elastic plate including geometric nonlinearities and the parametric actuation provided by the piezoelectric wires, is adopted to formulate the nonlinear equation of motion. A bifurcation analysis is carried out by means of an asymptotic approach based on the method of multiple scales leading to a comprehensive parametric study on the effect of the wires width on the morphing regions (i.e., parametric instability regions) associated with the principal parametric resonances. The threshold voltages triggering the onset of the principal parametric resonances of the lowest three symmetric modes are also calculated as a function of the wires size so as to determine the voltage requirements for the morphing activation.

A passive vibration control strategy to mitigate the accelerations of roller batteries in cableways caused by the vehicle transit is investigated. The vibration control strategy makes use of a group of Tuned Mass Dampers (TMDs) placed in different positions along the roller battery. When the frequencies of the TMDs are properly tuned to the modes to control, the energy provided by the dynamic forcing to the roller battery is transferred as kinetic energy to the TMDs. This work investigates the effectiveness of an array of linear TMDs in comparison with the performance of hysteretic TMDs that exploit the restoring forces provided by an assembly of wire ropes. First a dynamical characterization of the roller battery (modal analysis) is carried out. Then an optimization of the assembly of linear TMDs against skew-symmetric harmonic excitations is achieved by means of the Differential Evolution algorithm (DE). Subsequently, the performance of the linear TMDs assembly against the vehicle transit across the tower is assessed. Finally the performance of a network of hysteretic TMDs is studied together with practical feasibility considerations.

The nonlinear dynamic response of short cables with a tip mass subject to base excitations and undergoing primary resonance is investigated via experimental tests and by employing an ad hoc nonlinear mechanical model. The considered cables are made of several strands of steel wires twisted into a helix forming composite ropes in a pattern known as ‘laid ropes’. Such short span ropes exhibit a hysteretic behavior due to the inter-wire frictional sliding. A nonlinear one-dimensional (1D) continuum model based on the geometrically exact Euler-Bernoulli beam theory is conveniently adapted to describe the cable dynamic response. The Bouc-Wen law of hysteresis is incorporated in the moment-curvature constitutive relationship to reproduce the hysteretic behavior of short steel wire ropes subject to flexural cycles. The frequency response curves show a pronounced softening nonlinearity induced by hysteresis and inertia nonlinearity as confirmed by the experimental data acquired on a wire rope with a tip mass excited at its base by a shaker. The experimental nonlinear resonance response will be exploited to identify the constitutive parameters of the wire rope that best fit the frequency response curves at various forcing amplitudes.

Towers, roller batteries, propelling cables and vehicles are the substructures of ropeway transportation systems. High-fidelity modeling of their dynamical interactions together with a reliable identification is a key step towards the prediction of the system response under various transit conditions as well as to investigate design optimization strategies. In this work, a nonlinear mechanical model for the dynamical description of cablecar ski lift systems is discussed. The investigation is focused on the modal features and the forced dynamic response caused by the vehicles transit across the so-called compression towers. The model is validated according to experimental data acquired via a custom-design sensor network. The Enhanced Frequency Domain Decomposition (EFDD) method is employed to identify the frequencies and damping ratios.

The free undamped vibrations of cables undergoing stretching, bending and twisting are investigated. To this end, a geometrically exact model of elastic cables accounting for bending and torsional stiffness is employed. The cable kinematics retain the full geometric nonlinearities. Starting from a prestressed catenary configuration, the nonlinear equations of motion are linearized about the initial equilibrium. In particular, two initial equilibrium states (shallow and taut) are considered while varying the cable elastic axial stiffness. The influence of the bending flexibility on the cable frequencies is assessed by direct comparisons with the frequencies predicted by classical cable theories of purely extensible cables.

Circular micromembranes, subject to in-plane tension and transverse pressure and actuated by a piezoelectric film, are modeled via a geometrically exact approach that accounts for finite motions. The free vibration properties (i.e., frequencies and mode shapes) about the nonlinear equilibrium due to the in-plane prestress and the pressure field are investigated in a wide range of pressures to purposefully explore the nonlinear range. Given the pronounced hardening membrane nonlinearity, there is a high sensitivity of the fundamental frequency with respect to the applied pressure. This is due to the nonlinear increase of the membrane tension caused by the pressure. Analytical laws can be obtained by curve fitting to describe the variation of the membrane lowest frequencies with the prestress tension and the applied pressure. Such laws are useful in feasibility studies on the design of micromembranes as pressure sensors.

A linearized parametric continuum model of a long-span suspension bridge is coupled with a nonlinear quasi-steady aerodynamic model giving the aeroelastic partial differential equations of motion reduced to the state-space ordinary differential form by adopting the Galerkin method. Numerical time-domain simulations are performed to investigate the limit cycle oscillations occurring in the range of post-flutter wind speeds. Continuation tools are thus employed to path follow the limit cycles past the flutter speed where the Hopf bifurcation occurs. The stable post-flutter behavior, which can significantly affect the bridge by fatigue, terminate at a fold bifurcation. This result represents an important assessment of the conducted aeroelastic investigations. The stability range of the limit cycle oscillations is evaluated by carrying out sensitivity analyses with respect to the main design parameters, such as the structural damping and the initial wind angle of attack.

This work deals with three-dimensional (3D) modeling of container cranes including the hoisting cable length commands. The proposed models allow to effectively study the 3D motion caused by the eccentricity of initial conditions or loading conditions such as those induced by wind. The container is modeled as a 3D rigid body while the hoisting cables are treated either as inextensible trusses or as linearly elastic straight, taut cables. The 3D model with inextensible cables is shown to coalesce into existing two-dimensional models under the relevant planarity constraints. Details about the treatment of the internal inextensibility constraints are discussed. Time-marching simulations are carried out to show representative 2D and 3D responses to initial conditions and commanded motion of the trolley. The main differences between the constrained model and that with the elasticity of the cables are highlighted in the framework of a few significant design scenarios.

Refined theories are employed to study nonlinear vibrations of elastic rings in the mth flexural mode away from autoparametric resonances involving other flexural modes. A top-down modeling approach is followed to describe the rings undergoing all deformation modes in space by the Special Cosserat theory of curved rods. The specialization to extensional-flexural-shearing, then to extensional-flexural, and finally to purely flexural planar motions is illustrated. Free undamped extensional-flexural nonlinear motions involving the mth mode and its companion mode are investigated via a direct asymptotic approach based on the method of multiple scales applied to the geometrically exact equations of motion and it is shown that these motions are softening for linearly elastic rings while there are thresholds in the constitutive laws separating softening from hardening behaviors.

A parametric one-dimensional model of suspension bridges is employed to investigate their static and dynamic aeroelastic behavior in response to a gust load and at the onset of flutter. The equilibrium equations are obtained via a direct total Lagrangian formulation where the kinematics for the deck, assumed to be linear, feature the vertical and the chord-wise displacements of the deck mean axis and the torsional rotations of the deck cross sections, while preserving their shape during rotation. The cables elasto-geometric stiffness contribution is obtained by condensing the equilibrium in the longitudinal direction assuming small horizontal displacements and neglecting the cable kinematics along the bridge chord-wise direction. The equations of motion are linearized about the prestressed static aeroelastic configuration and are obtained via an updated Lagrangian formulation. The equations of motion governing the structural dynamics of the bridge are coupled with the incompressible unsteady aero-dynamic model obtained by a set of reduced-order indicial functions developed for the cross section of a suspension bridge, here represented by a rectangular cross-section. The space dependence of the governing equations is treated using the Galerkin approach borrowing as set of trial functions, the eigenbasis of the modal space. The time integration is subsequently performed by using a numerical scheme that includes the modal reduced dynamic aeroelastic Ordinary Differential Equations (ODEs) and the added aerodynamic states also represented in ODE form, the latter being associated with the lag-state formulation pertinent to the unsteady wind-induced loads. The model is suitable to analyze the effect of a time and space non uniform gust load distributed on the bridge span. The obtained aeroelastic system is also suitable to study the onset of flutter and to investigate the sensitivity of the flutter condition on geometrical and aerodynamic parameters. The flutter instability is evaluated using appropriate frequency and time domain characteristics. The parametric continuum model is exploited to perform dynamic aeroelastic flutter analysis and gust response of the Runyang Suspension Bridge over the Yangtze river in China.

A computational framework is proposed to path follow the periodic solutions of nonlinear spatially continuous systems and more general coupled multiphysics problems represented by systems of partial differential equations with time-dependent excitations. The set of PDEs is cast in first order differential form (in time) u˙ = f ( u , s , t ; c ) where u ( s,t ) is the vector collecting all state variables including the velocities/time rates, s is a space coordinate (here, one-dimensional systems are considered without lack of generality for the space dependence) and t denotes time. The vector field f depends, in general, not only on the classical state variables (such as positions and velocities) but also on the space gradients of the leading unknowns. The space gradients are introduced as part of the state variables. This is justified by the mathematical and computational requirements on the continuity in space up to the proper differential order of the space gradients associated with the unknown position vector field. The path following procedure employs, for the computation of the periodic solutions, only the evaluation of the vector field f . This part of the path following procedure within the proposed combined scheme was formerly implemented by Dankowicz and coworkers in a MATLAB software package called COCO. The here proposed procedure seeks to discretize the space dependence of the variables using finite elements based on Lagrangian polynomials which leads to a discrete form of the vector field f . A concurrent bifurcation analysis is carried out by calculating the eigenvalues of the monodromy matrix. A hinged-hinged nonlinear beam subject to a primary-resonance harmonic transverse load or to a parametric-resonance horizontal end displacement is considered as a case study. Some primary-resonance frequency-response curves are calculated along with their stability to assess the convergence of the discretization scheme. The frequency-response curves are shown to be in close agreement with those calculated by direct integration of the PDEs through the FE software called COMSOL Multiphysics. Besides primary-resonance direct forcing conditions, also parametric forcing causing the principal parametric resonance of the lowest two bending modes is considered through construction of the associated transition curves. The proposed approach integrates algorithms from the finite element and bifurcation domains thus enabling an accurate and effective unfolding of the bifurcation and post-bifurcation scenarios of nonautonomous PDEs with the underlying structures.