Mariano Febbo

Transverse vibrations of circular annular plates with edges elastically restrained against rotation, used in acoustic underwater transducers

Abstract Simply supported or clamped boundary conditions are rather ideal situations difficult to satisfy from a physical viewpoint. This paper considers a more “moderate” restriction: the case of edges elastically restrained against rotation for which no exact solution appears in the open literature. Eigenvalues corresponding to a wide range of the intervening geometric and mechanical parameters are determined. Good agreement is obtained with frequency coefficients determined two decades ago by means of a variational method. Obviously the problem is of basic interest in many ocean engineering applications: from the design of certain underwater acoustic transducers to pump and compressor elements passing through the design of naval vehicles and ocean structures.

Influence of temperature on optimum viscoelastic absorbers in cubic nonlinear systems

Recently, viscoelastic materials have been widely used for vibration control due to their efficacy and flexibility in real engineering problems. Their use as constitutive parts of dynamic vibration absorbers requires the investigation of these materials under different operating situations. In the optimal design of the absorbers, it is essential to know how the dynamical properties of the viscoelastic materials change with temperature. In a previous work, the authors presented a methodology to optimally design a linear viscoelastic dynamic vibration absorber to be attached to a cubic nonlinear single-degree-of-freedom system, in a given temperature. In the present work, a study of how temperature variations affect the optimal design of two viscoelastic absorbers, made of distinct materials (neoprene and butyl rubber), is addressed. The mathematical formulation of the problem is based on the concept of generalized equivalent parameters and the harmonic balance method is employed in the solution stage. A cubic nonlinearity in the primary system is considered and the four parameter fractional derivative model of viscoelastic materials is used. Numerical simulations are performed using a recursive equation, in order to find the new characteristics of the absorbers at different working temperatures. The results show that the answer depends not only on the temperature and the material, but also on the magnitude of the excitation load imposed to the system. For a low magnitude of the excitation load, it is verified that the neoprene absorber is less affected by a temperature variation, in terms of its vibration control capabilities. On the other hand, a large magnitude of the load can significantly affect the performance of both considered devices when the working temperature is different from the design temperature.

Influence of nonlinear constitutive relations in unimorphs piezoelectric harvesters

This paper presents the influence of nonlinear terms of a previously proposed constitutive piezoelectric equation on the dynamics of a cantilever aluminium beam with a piezoelectric unimorph PZT (MIDE QP16N) attached to it. The system is subjected to different levels of base acceleration with the intention to evidence the limits of the linear model. To carry out the analysis, a one-dimensional model is applied and solved employing a single-term solution of the harmonic balance method to compare with the experiments. A model identification of linear and nonlinear parameters such as dissipation, stiffness, and electromechanical coupling were then performed. From the results, it is possible to observe the departure of the linear model even for very low acceleration levels (0.1G). It can be concluded that the nonlinearity plays an unavoidable roll in predicting electric generation for the considered systems.

Optimum viscoelastic absorbers for cubic nonlinear systems

Dynamic vibration absorbers are efficient devices used in vibration and noise control of several mechanical systems. In recent years, some studies about these control devices comprising systems with nonlinear characteristics have emerged. In those cases, either the primary system or the dynamic absorber, or even both, can be nonlinear in terms of their stiffness. On the other hand, the absorber damping is generally modeled as viscous. The viscous damping model is widely used in numerical simulations but is very difficult to achieve in real situations. An alternative is the use of viscoelastic damping models, which brings flexibility for vibration control actions. In this work, a methodology to optimally design a viscoelastic dynamic vibration absorber when attached to a nonlinear single-degree-of-freedom system will be presented. The mathematical formulation of the problem is based on the generalized equivalent parameters concept along with the harmonic balance method. The cubic nonlinearity is considered in the primary system and the viscoelastic material is represented by the four-parameter fractional derivative model. Numerical simulations to find the optimal parameters of the absorber are performed for three different types of viscoelastic materials using nonlinear optimization techniques. For some conditions, the results show that the viscoelastic absorber linearizes the compound system when this device is properly designed and attached to it. This is mainly due to the reaction forces introduced by the absorber and the large dissipation of vibratory energy introduced by the viscoelastic material. A study of the stability of the compound system reveals that, for most of the time, the periodic solution remains stable for the whole frequency range of concern.

Non-resonant energy harvester with elastic constraints for low rotating frequencies

This paper presents a non-resonant piezoelectric energy harvester (PEH) which is designed to capture energy from low frequency rotational vibration. The proposed device works out of the plane of rotation where the motion of a mass-spring system is transferred to a piezoelectric layer with the intention to generate energy to power wireless structural monitoring systems or sensors. The mechanical structure is formed by two beams with rigid and elastic boundary conditions at the clamped end. On the free boundaries, heavy masses connected by a spring are placed in order to increase voltage generation and diminish the natural frequency. A mathematical framework and the equations governing the energy-harvesting system are presented. Numerical simulations and experimental verifications are performed for different rotation speeds ranging from 0.7 to 2.5 Hz. An output power of 125 μW is obtained for maximum rotating frequency demonstrating that the proposed design can collect enough energy for the suggested application.

A low frequency rotational energy harvesting system

This paper presents a rotary power scavenging unit comprised of two systems of flexible beams connected by two masses which are joined by means of a spring, considering a PZT (QP16N, Mide Corporation) piezoelectric sheet mounted on one of the beams. The energy harvesting (EH) system is mounted rigidly on a rotating hub. The gravitational force on the masses causes sustained oscillatory motion in the flexible beams as long as there is rotary motion. The intention is to use the EH system in the wireless autonomous monitoring of wind turbines under different wind conditions. Specifically, the development is oriented to monitor the dynamic state of the blades of a wind generator of 30 KW which rotates between 50 and 150 rpm. The paper shows a complete set of experimental results on three devices, modifying the amount of beams in the frame supporting the system. The results show an acceptable sustained voltage generation for the expected range, in the three proposed cases. Therefore, it is possible to use this system for generating energy in a low-frequency rotating environment. As an alternative, the system can be easily adapted to include an array of piezoelectric sheets to each of the beams, to provide more power generation.

On the critical forcing amplitude of forced nonlinear oscillators

The steady-state response of forced single degree-of-freedom weakly nonlinear oscillators under primary resonance conditions can exhibit saddle-node bifurcations, jump and hysteresis phenomena, if the amplitude of the excitation exceeds a certain value. This critical value of excitation amplitude or critical forcing amplitude plays an important role in determining the occurrence of saddle-node bifurcations in the frequency-response curve. This work develops an alternative method to determine the critical forcing amplitude for single degree-of-freedom nonlinear oscillators. Based on Lagrange multipliers approach, the proposed method considers the calculation of the critical forcing amplitude as an optimization problem with constraints that are imposed by the existence of locations of vertical tangency. In comparison with the Gröbner basis method, the proposed approach is more straightforward and thus easy to apply for finding the critical forcing amplitude both analytically and numerically. Three examples are given to confirm the validity of the theoretical predictions. The first two present the analytical form for the critical forcing amplitude and the third one is an example of a numerically computed solution.