A nonlinear piezoelectric shunt absorber with 2:1 internal resonance: experimental proof of concept

An experimental proof of concept of a new semi-passive nonlinear piezoelectric shunt absorber, introduced theoretically in a companion article, is presented in this work. This absorber is obtained by connecting, through a piezoelectric transducer, an elastic structure to a resonant circuit that includes a quadratic nonlinearity. This nonlinearity is obtained by including in the circuit a voltage source proportional to the square of the voltage across the piezoelectric transducer, thanks to an analog multiplier circuit. Then, by tuning the electric resonance of the circuit to half the value of one of the resonances of the elastic structure, a two-to-one internal resonance is at hand. As a result, a strong energy transfer occurs from the mechanical mode to be attenuated to the electrical mode of the shunt, leading to two essential features: a nonlinear antiresonance in place of the mechanical resonance and an amplitude saturation. Namely, the amplitude of the elastic structure oscillations at the antiresonance becomes, above a given threshold, independent of the forcing level, contrary to a classical linear resonant shunt. This paper presents the experimental setup, the designed nonlinear shunt circuit and the main experimental results.

Regularity of a weak solution to a linear fluid-composite structure interaction problem

In this manuscript, we deal with the regularity of a weak solution to the fluid-composite structure interaction problem introduced in [12]. The problem describes a linear fluid-structure interaction between an incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh-like elastic structure. The fluid and the mesh-supported structure are coupled via the kinematic and dynamic boundary coupling conditions describing continuity of velocity and balance of contact forces at the fluid-structure interface. In [12], it is shown that there exists a weak solution to the described problem. By using the standard techniques from the analysis of partial differential equations we prove that such a weak solution possesses an additional regularity in both time and space variables for initial and boundary data satisfying the appropriate regularity and compatibility conditions imposed on the interface.

Anti-sway method for reducing vibrations on a tower crane structure

We develop a solution to the problem of the behavior of a tower crane considered as a deformable system, and therefore subject to vibrations, whereas the controlled movement of a payload is implemented. The motion of the payload is calculated taking into account the normal vibration modes of the tower crane and the swaying of the payload. A “command smoothing” method relative to an open-loop system is used for reducing the sway of the payload, through smoothing the original command by the crane operator. This leads, as a consequence, to a reduction in the vibrations of the crane structure. An iterative calculation of the sway angle and the corresponding applied velocity profiles as input to the crane motors is applied. The tower crane is considered as a high nonlinear underactuated system; it is modeled considering the possible deformation of the structure. The results relating to the normal deformations of the crane are obtained, highlighting how these vibrations are strongly attenuated when an anti-sway system for the payload is implemented. Therefore, it is shown how this control leads to the best results in terms of performance for both the payload movement (shortest possible profile for the rotation movement and damping of the load oscillation) and the structure of the tower crane. Applying the method described in this paper, the structure of the tower crane does not undergo the strong horizontal and vertical oscillations that occur when the elastic structure is not considered in the crane model.

On the kinematics of a concave sidecut line deformed on a flat surface

The present paper investigates the static equilibrium of a thin elastic structure with concave sidecut pressed against a flat rigid surface, as an idealization of a ski or snowboard undergoing the conditions of a carved turn. An analytical model is derived to represent the contact behaviour and provide an explanation for concentrated loads occurring at the sidecut extremities. The deformations are prescribed assuming tied contact along the sidecut line and neglecting torsional deformations. The loading conditions leading to this ideal deformed state are then sought, in order to better understand the mechanics of the turn. The results are illustrated with different sidecut geometries and compared with finite element computations for validation purposes. Depending on the function describing the sidecut line, concentrated force and moment are found to take place at the sidecut extremities.

PARAMETRIC BENDING VIBRATIONS OF ELASTIC STRUCTURES WITH VARIABLE SECTIONS ON VIBRATION MOUNTINGS

The article is devoted to the study of the oscillatory motion of an elastic structure with variable sections on rolling bearings with straightened surfaces, which simulates a number of technical solutions, which has received its practical embodiment in the problem of ensuring the seismic resistance of building structures and vibration isolation of massive bodies. Equations of motion of an elastic structure with variable sections on rolling bearings bounded by high-order surfaces of revolution are obtained. The resonant modes of parametric vibrational motion of an elastic structure with variable sections are investigated using the Ritz variational method. In the resonant zone of the oscillatory movements of the base, the movement of the elastic structure will be small, and when the natural frequencies of the elastic structure coincide with the frequency of the disturbance, the phenomenon of resonance will appear. The amplitude of the parametric disturbance of the resonant zones of bending vibrations of elastic structures expands with increasing The amplitude-frequency characteristics of parametric oscillations depend on the parameters of the structure. An increase in the parameters of the base of wedge-shaped elastic structures leads to a shift of the resonance curves towards an increase in the disturbance frequencies

Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach

A cost function involving the eigenvalues of an elastic structure is optimized using a phase-field approach, which allows for topology changes and multiple materials.We show continuity and differentiability of simple eigenvalues in the phase-field context. Existence of global minimizers can be shown, for which first order necessary optimality conditions can be obtained in generic situations. Furthermore, a combined eigenvalue and compliance optimization is discussed.