Acoustic waveguide filters made up of rigid stacked materials with elastic joints

Meccanica - The acoustic dispersion properties of monodimensional waveguide filters can be assessed by means of the simple prototypical mechanical system made of an infinite stack of periodic...     

Nonlinear wave propagation in locally dissipative metamaterials via Hamiltonian perturbation approach

Nonlinear Dynamics - The cellular microstructure of periodic architected materials can be enriched by local intracellular mechanisms providing innovative distributed functionalities. Specifically,...     

Screening of magnetic fields by charged Bose condensate

The space-space component of the photon polarization operator is calculated in zero frequency limit for a medium with Bose-Einstein condensate (BEC) of electrically charged particles. It is found that the polarization operator tends to a finite value at vanishing photon 3-momentum, as it happens in superconducting media. It means that magnetic fields are exponentially screened in such a medium analogously to the Debye screening of electric charges. At non-zero temperature the screened magnetic field oscillates and contains a contribution which drops only as a power of distance. This phenomenon is unknown for superconductors, even in BEC phase and can be potentially observable.     

A parametric multi-body section model for modal interactions of cable-supported bridges

A parametric section model is formulated to synthetically describe the geometrically nonlinear dynamics of cable-stayed and suspended bridges through a planar elastic multi-body system. The four-degrees-of-freedom model accounts for both the flexo-torsional motion of the bridge deck and for the transversal motion of a pair of hangers or stay cables. After linearization around the pre-stressed static equilibrium configuration, the coupled equations of motion governing the global deck dynamics and the local cable motion are obtained. A multi-parameter perturbation method is employed to solve the modal problem of internally resonant systems. The perturbation-based modal solution furnishes, first, explicit formulae for the parameter combinations which realize the internal resonance conditions and, second, asymptotic approximations of the resonant frequencies and modes. Attention is focused on the triple internal resonance among a global torsional mode of the deck and two local modes of the cables, due to the relevant geometric coupling which maximizes the modal interaction. The asymptotic approximation of the modal solution is found to finely describe the multiple veering phenomenon which involves the three frequency loci under small variation of the most significant mechanical parameters, including terms of structural coupling or disorder. Moreover, the veering amplitude between any two of the three frequency loci can be expressed as an explicit parametric function. Finally, the disorder is recognized as the only parameter governing a complex phenomenon of triple modal hybridization involving all the resonant modes. The entire hybridization process is successfully described by an energy-based localization factor, presented in a new perturbation-based form, valid for internally resonant system.     

Damping performance of two simple oscillators coupled by a visco-elastic connection

A simple dynamic system composed of two linear oscillators is employed to analyze the passive control performance that can be achieved through a visco-elastic damper connecting two adjacent free-standing structures. By extension, the model may also describe the energy dissipation which can be obtained by an internal coupling between two quasi-independent sub-systems composing a single complex structure. Two alternatives are evaluated for the linear coupling by considering either the serial or the parallel spring–dashpot arrangement known as the Kelvin–Voigt and the Maxwell damper model, which may synthetically reproduce the constitutive behavior of different industrial devices. The complex eigenvalues of the coupled system are parametrically analyzed to determine the potential benefits realized by different combinations of the coupling stiffness and damping coefficient. A design strategy to assess these parameters is outlined, driven by the relevant observation that a perfect tuning of the natural frequencies always corresponds, in the parameter space, to the maximum modal damping for one of the resonant modes, independent of the damper model. The effectiveness of the proposed strategy is discussed for different classes of the controlled system, depending on the mass and stiffness ratio of the component oscillators. As a major result, different design parameter charts for the two damper models are carried out and compared to each other. Performance indexes are introduced to quantitatively evaluate the passive control performance with respect to the mitigation of the system forced response under harmonic and seismic ground excitation. The analyses confirm the validity of the design strategy for a well-balanced mitigation of the displacement and acceleration response in both the oscillators.     

One-to-two global-local interaction in a cable-stayed beam observed through analytical, finite element and experimental models

The mechanism of cable end angle-variation induced oscillations in the non-linear interactions between beams and cables in stayed-systems is first explained by a proposed analytical model. It is then verified by both experimental and finite element models. The non-linear interaction maximizes its effects for cable oscillations when inherent quadratic coupling between local and global modes produces energy transfer from low to high frequency vibrations by means of a one-to-two global-local autoparametric resonance. The response of the analytical model is fully described using a continuation method applied directly to the reduced two degree of freedom discrete model showing that, for a selected one-to-two global-local resonant system, primary harmonic excitation of the global mode produces large oscillations of the local mode at twice the excitation frequency. Detailed comparisons between the responses of the analytical model, experimental results and finite element simulations show excellent agreement both in the qualitative behaviour and in the calculated/measured response amplitudes.     

Static and dynamic response of elastic suspended cables with thermal effects

Cable structures are often subjected to severe and variable environmental conditions, and their mechanical behavior is known to be particularly sensitive to different ambient factors. The paper analyzes temperature effects on the static and dynamic response of suspended inclined cables through a continuous monodimensional model including geometric nonlinearities. Uniform temperature changes are introduced through a non-homogeneous constitutive law for the material linear elasticity. Exact and approximate solutions of the equations governing the cable static equilibrium under self-weight are achieved, and the significance of the temperature-dependent variation of tension and sag are parametrically investigated. The spectral properties characterizing the free dynamics are obtained in a closed-form fashion for shallow parabolic cables within the low frequency vibration range. The sensitivity of the linear frequencies to temperature changes is discussed, outlining two thermal effects, which are distinguished by their different origins, geometric or static. For a generic temperature change, the geometric effect produces a systematic increment or reduction of all the frequencies, for both symmetric and anti-symmetric modes. The static effect stiffens or softens only the symmetric modes, and may prevail over the competing geometric effect, depending on the cable Irvine parameter. Finally, the thermal effects on the frequency veering and modal hybridization phenomena, which characterize quasi-resonant shallow cubic cables, are analyzed.