Paulo Sergio Varoto

On the force drop off phenomenon in shaker testing in experimental modal analysis

The Electrodynamic Vibration Exciter (shakers) has been one of the most employed excitation sources in modal tests. The shaker is an electromechanical device that provides a mechanical motion due to the input signal sent to its coil. Despite being widely used, it is well known that the shaker interacts with the structure under test. In particular, when the structure passes through a given resonance, the force delivered by the shaker abruptly decreases, causing the so called drop off phenomenon. This paper aims to study this force drop off phenomenon in the single shaker modal testing. Analytical models are developed to help in understanding the physical principles involved in the interaction between the shaker and the structure under test. Experimental analyses are performed using different shakers as well as excitation signals, in order to evaluate the effects of the input signal, as well as the power amplifier operational modes, on the structure dynamics. Preliminary tests revealed that significant distortions might occur during vibration tests using shakers and these distortions significantly affect the determination of the structure response.

A state-space modeling approach for active structural acoustic control

The demands for improvement in sound quality and reduction of noise generated by vehicles are constantly increasing, as well as the penalties for space and weight of the control solutions. A promising approach to cope with this challenge is the use of active structural-acoustic control. Usually, the low frequency noise is transmitted into the vehicles cabin through structural paths, which raises the necessity of dealing with vibro-acoustic models. This kind of models should allow the inclusion of sensors and actuators models, if accurate performance indexes are to be accessed. The challenge thus resides in deriving reasonable sized models that integrate structural, acoustic, electrical components and the controller algorithm. The advantages of adequate active control simulation strategies relies on the cost and time reduction in the development phase. Therefore, the aim of this paper is to present a methodology for simulating vibro-acoustic systems including this coupled model in a closed loop control simulation framework that also takes into account the interaction between the system and the control sensors/actuators. It is shown that neglecting the sensor/actuator dynamics can lead to inaccurate performance predictions.

Experimental Study of the Nonlinear Hybrid Energy Harvesting System

This paper focuses on experimental nonlinear vibration analysis of the proposed hybrid energy harvester. A nonlinear energy harvesting structure is proposed to convert ambient vibrations to the electrical energy using the piezoelectric and electromagnetic mechanisms. A repelling magnetic force is introduced to the system to both reduce the resonant frequency of the system and increase the frequency bandwidth by making the vibrations nonlinear. The paper is the continuation of a previous work by the authors in which the vibrations of the harvester was analytically characterized. Both mono-stable and bi-stable situations are studied. Depending on the level of excitations the bi-stable system can exhibit oscillations about each of its equilibriums, chaotic vibrations or the limit cycle oscillations (LCO) over both of the equilibriums. The proper design of the harvester allows the system to perform Limit Cycle Oscillations in response to moderate base excitations. The paper discusses the experimental results on electro-mechanical vibrations and the energy generation of the nonlinear hybrid harvester at different magnetic force levels, excitation frequencies and excitation levels.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structures dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the systems analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the systems response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the systems dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation.

Numerically Simulated Results for a Deterministic Excitation with no External Loads

This paper presents a numerical example of the theory presented in Part I [1] where a model is developed to describe the requirements for laboratory simulations of field vibration environments. This example illustrates the application of such a model to simulated data in order to evaluate its accuracy in predicting field interface forces and motions, and in using field data to define appropriate test item inputs in laboratory simulations. It is assumed that no external forces act on the test item in either the field or laboratory environments. All Frequency response functions (FRFs) are calculated for all test structures from a multi degree of freedom (MDOF) discrete linear system. The equations developed in Ref. [1] are employed to estimate field interface forces and test item motions as well as to define test item inputs in the laboratory simulation. The test item motions obtained in all laboratory simulations are compared with the corresponding field motions.

Nonlinear dynamic behavior of a flexible structure to combined external acoustic and parametric excitation

Flexible structures are frequently subjected to multiple inputs when in the field environment. The accurate determination of the system dynamic response to multiple inputs depends on how much information is available from the excitation sources that act on the system under study. Detailed information include, but are not restricted to appropriate characterization of the excitation sources in terms of their variation in time and in space for the case of distributed loads. Another important aspect related to the excitation sources is how inputs of different nature contribute to the measured dynamic response. A particular and important driving mechanism that can occur in practical situations is the parametric resonance. Another important input that occurs frequently in practice is related to acoustic pressure distributions that is a distributed type of loading. In this paper, detailed theoretical and experimental investigations on the dynamic response of a flexible cantilever beam carrying a tip mass to simultaneously applied external acoustic and parametric excitation signals have been performed. A mathematical model for transverse nonlinear vibration is obtained by employing Lagrange’s equations where important nonlinear effects such as the beam’s curvature and quadratic viscous damping are accounted for in the equation of motion. The beam is driven by two excitation sources, a sinusoidal motion applied to the beam’s fixed end and parallel to its longitudinal axis and a distributed sinusoidal acoustic load applied orthogonally to the beam’s longitudinal axis. The major goal here is to investigate theoretically as well as experimentally the dynamic behavior of the beam-lumped mass system under the action of these two excitation sources. Results from an extensive experimental work show how these two excitation sources interacts for various testing conditions. These experimental results are validated through numerically simulated results obtained from the solution of the system’s nonlinear equation of motion.

Dynamic Behavior and Performance Analysis of Piezoelastic Energy Harvesters Under Model and Parameter Uncertainties

The main goal of this article is to perform a comprehensive analysis of the effects of parameter and model uncertainties on the dynamic behavior of piezoelastic energy harvesters. Piezoelectric energy harvesters demand for optimized mechanical and electric models such that optimum performance can be achieved in the mechanical-to-electrical energy conversion process. The presence of uncertainties can significantly alter the dynamic response of the harvester and therefore affecting its overall performance in terms of the amount of electrical energy available in the conversion process. Euler-Bernoulli beam theory is employed in the formulation of the energy harvesting electromechanical models that account for uncertain parameters in terms of the piezoelectric, electrical, geometric and mechanical boundary condition properties. Extensive numerical analysis are performed in frequency ranges where the device under study present multiple natural frequencies. Numerically simulated results are compared to experimental data reinforcing the importance of accounting for uncertainties in the design process of piezoelectric energy harvesters.

Experimental Analysis of a Piezoelectric Energy Harvester with Internal Resonances

A crucial issue in the design process of a piezoelectric harvester is to properly tune the device to the imposed disturbance such that the mechanical to electrical energy conversion can be enhanced. Inclusion of intentional nonlinear restoring effects has been widely exploited to meet optimal performance of the device under study. The main goal of this article is to address the issue of modal interaction on a two degrees of freedom piezoelectric energy harvester presenting commensurate natural frequencies. An experimental analysis is performed on an L-shaped metallic prototype containing lumped masses attached in specific positions such that commensurate natural frequencies in the 2:1 ratio are obtained. Preliminary experimental results indicated that under appropriate excitation condition energy could flow between the corresponding modes of vibration thus enabling additional energy generation on both commensurate frequencies.

Nonlinear Dynamics of Piezoelectric Cantilever Energy Converters Through Perturbation Theory and Experimental Analysis

It is known that the best performance of a given piezoelectric energy harvester is usually limited to excitation at its fundamental resonance frequency. If the ambient vibration frequency deviates slightly from this resonance condition then the electrical power delivered is drastically reduced. One possible way to increase the frequency range of operation of the harvester is to design vibration harvesters that operate in the nonlinear regime. The main goal of this article is to discuss the potential advantages of introducing nonlinearities in the dynamics of a beam type piezoelectric vibration energy harvester. The device is a cantilever beam partially covered by piezoelectric material with a magnet tip mass at the beam’s free end. Governing equations of motion are derived for the harvester considering the excitation applied at its fixed boundary. Also, we consider the nonlinear constitutive piezoelectric equations in the formulation of the harvester’s electromechanical model. This model is then used in numerical simulations and the results are compared to experimental data from tests on a prototype. Numerical as well as experimental results obtained support the general trend that structural nonlinearities can improve the harvester’s performance.Copyright

Influence of nonlinear effects on a piezoelectric energy harvesting device

In this paper we present an analytical investigation of a nonlinear energy harvester device. The device is composed of a cantilever beam partially covered by piezoelectric ceramics in a bimorph configuration with a magnetic lumped mass attached to the beam’s free end. The model accounts for the nonlinearity coming from the piezoelectric constitutive equations in addition to the nonlinear effect arising from the magnetic field generated by the magnetic properties of the tip mass and additional magnetic sources in the vicinity of the beam. The electromechanical coupled equations are solved numerically through the initial value problems for ordinary differential equations. The electrical power output is calculated by varying the amplitude of the base acceleration, the distance between the magnets and the load resistor. The stability of the system is also investigated. From the numerical results it is found that the influence of the parameters investigated in the frequency range of operation of the device and the nonlinear effects present on the device energy harvester extend the useful frequency range of these.Copyright