International Journal of Structural Stability and Dynamics

Nonlinear coupling of a piezoelectric cantilever to an external magnetic force increases the power harvested from a broadband vibration source for relatively large acceleration vibrations. A threshold exists in the minimum acceleration needed for enhancement of the cantilever response. Below this threshold the nonlinear coupling damps the cantilever motion, and the power output is reduced compared to the noncoupled cantilever. By reducing the size of the coupling magnet, the acceleration required to scavenge usable power can be greatly reduced. The smaller diameter magnet decreases the spatial extent of the magnetic force, reducing the acceleration required to surmount the local potential barrier. The experiments result in a six-fold decrease in the acceleration threshold, to levels comparable to those observed in ambient environmental vibrations. The results are in good agreement with numerical calculations.

In the present contribution, the nonlinear dynamics of beams under axial time-dependent excitation is studied. The beams, which rest on a linear viscoelastic foundation, are assumed as axially graded both in terms of geometrical and material properties. The transversal motion equation is derived under two main hypotheses, namely the beams satisfy the requirements of Euler–Bernoulli theory and undergo moderately large deflections (MLDs).

This paper presents numerical and experimental study of an autoparametric pendulum absorber attached to a vertically moving Duffing oscillator. The absorber can be highly efficient for slightly damped systems, when correctly tuned. In the suspension of pendulum absorber, the magnetorheological damper (MR) is installed to allow control. The influence of system parameters: Viscous and magnetorheological damping, stiffness of the spring, parameter which couples both systems on the suppression effectiveness are studied. Additionally, the influence of system parameters on periodic solutions and stability are analyzed using continuation techniques.

This paper is concerned with the wideband behavior of single-frequency and multi-frequency free-standing thick-film piezoelectric energy harvesters. The energy harvesting devices have been fabricated and brief fabrication information is provided. The individual harvesters have been combined with either symmetric or asymmetric tip masses, with some being connected together to form a harvester array. Testing has been undertaken using harmonic vibrations with a wide range of frequencies and accelerations, and also using a random machinery vibration, and data have been recorded in terms of un-rectified and rectified open-circuit voltage, output power with matched resistive loads, peak-to-peak tip displacement, and even charging rates of capacitors. As a general result, the individual harvesters with asymmetric tip masses have vibrated nonlinearly below and in the vicinity of the resonant frequencies. An individual harvester vibrating at the resonant frequency with 0.5 g acceleration has been able to charge a 1000 μF capacitor to 1 V within 12 min and to 1.5 V within 30 min. Also, the harvester array has exhibited a wideband response, where an open-circuit voltage of above 0.8 V has been provided within a certain range of frequencies. Finally, the harvester array has successfully charged a capacitor on a vibrating test sieve shaker, proving the feasibility of the proposed device in real applications.

We examine the influence of potential energy asymmetry on the power generated by energy harvesting system. We present results for the system consisting of two masses (magnets) attached to piezoelastic oscillators which vibrate in the magnetic field produced by the magnets attached directly to the harvesting device. The nonlinearity of the system is achieved by the variable strength of the magnetic fields produced by the static magnets. We additionally examine the influence of disproportion between piezoelastic beams stiffness, which is described by the mistuning parameter.

The vertical elastic beam with vertical ambient excitation is proposed as an energy harvester. The beam has a tip mass and piezoelectric patches which transduce the bending strains induced by the stochastic force caused by vertical kinematic forcing into electrical charge. We focus on the region with a fairly large amplitude of voltage output where the beam overcomes the potential barrier. Increasing the noise level allows the transition from single well oscillations to inter-well stochastic jumps with more power generation.

A new derivation of Euler's Elastica with transverse shear effects included is presented. The elastic potential energy of bending and transverse shear is set up. The work of the axial compression force is determined. The equation of equilibrium is derived using the variation of the total potential. Using substitution of variables an exact solution is derived. The equation is transcendental and does not have a closed form solution. It is evaluated in a dimensionless form by using a numerical procedure. Finally, numerical examples of laminates made of composite material (fiber reinforced) and sandwich panels are provided.

An autonomous system of energy supplier to low power devices or wireless sensors is one of the most important motivations for energy harvesting based on ambient mechanical vibrations. In traditional approach, harvesters were based on a linear mechanical resonator combined with an electro-mechanical transducer working in the resonance region, i.e. in a relatively small range of frequencies. Here, we study a frequency broadband nonlinear resonator with impact characteristics with the aim of increasing the range of operativity of the system. The excitations are modeled by kinematic forcing possessing periodic and stochastic components, motivated by realistic ambient conditions. We show how the noise component of the excitation influences the stability of the solution.

Cantilever beams have found intensive and extensive uses as underlying mechanisms for energy transduction in sensors as well as in energy harvesters. In magnetoelectric (ME) transduction, the underlying cantilever beam usually will undergo magnetic coupling effect. As the beam itself is either banded with magnetic transducer or magnets, the dynamic motion of the cantilever can be modified due to the magnetic force between the magnets and ME sensors. In this study, the dynamic response of a typical spiral cantilever beam with magnetic coupling is investigated. The spiral cantilever acts as the resonator of an energy harvester with a tip mass in the form of magnets, and a ME transducer is positioned in the air gap and interacts with the magnets. It is expected that this spiral configuration is capable of performing multiple vibration modes over a small frequency range and the response frequencies can be magnetically tunable. The experimental results show that the magnetic coupling between the magnets and the transducer plays a favorable role in achieving tunable resonant frequencies and reducing the frequency spacings. This will benefits the expansion of the response band of a device and is especially useful in energy harvesting.

This paper considers a vibration-based damage assessment approach which is based on the general idea for signal cross-correlation. Here the method is demonstrated and validated on a composite laminate beam and it is applied for the purposes of delamination assessment in composite structures. The method uses two measures of cross-correlation between two vibration signals measured in different points on the structure in order to diagnose the delamination. The linear cross-correlation as well as a new measure for nonlinear cross-correlation, the mutual information, are introduced and applied for the purposes of delamination assessment. The delamination assessment is based on the comparison of the measures for the healthy and the damaged state of the structure. In this study, the method is applied using the free decay responses of the beam. Two delamination indices are introduced and they are used for the purposes of delamination detection and localization.

The recent potential benefit of nonlinearity has been applying in order to improve the effectiveness of energy harvesting devices. For instance, at relatively high excitation levels, both low and high-energy responses can coexist for the same parameter combinations in a hardening type Duffing oscillator, and this provides a wider bandwidth and a higher energy harvesting effectiveness under periodic excitations. However, frequency or amplitude sweeps of the excitation must be used in order to reach a desirable high-energy orbit, and this gives a limitation on practical implementation. This paper presents a stiffness tunable nonlinear vibrational energy harvester which contains a moving magnetic end mass attached to a cantilever beam, whose nonlinearity emerges from the interaction forces with two neighboring permanent magnets facing with opposing poles. The motivating hypothesis has been that the jump from the low-energy orbit to the high-energy orbit can be triggered by tuning the stiffness of the system without changing the frequency or the amplitude of the excitation. Theoretical investigations show a methodology for tuning stiffness, and experimental tests have validated that the proposed method can be used to trigger a jump to the desirable state, and hereby this can broaden the bandwidth of the energy harvester.

The object of the investigation is a honeycomb structure of composite sandwich made of glass-epoxy laminating layers and a honeycomb core of epoxy impregnated paper. Large composite tanks possessing cylindrical shape are produced using the winding process. Therefore, the final products have uneven thickness and fibre orientation lamina layers, and also an unevenly impregnated honeycomb layer. The aim of this research is to develop an economically attractive embedded ultrasonic measurement technique for on-field diagnostics of complex composite structures used for production of large liquid storage tanks. Development of the relatively cheap and easy to operate embedded diagnostic/monitoring technique is important aiming to assure safety of liquid storage tanks (monitoring structural integrity against overpressure, etc.) and detection of accidental defects that may appear during transportation, installation and exploitation of those structures. Typical defects that are aimed to be detected are relatively large delaminations/disbonds (area having diameter of 150–200 mm) of skin layers caused by low energy impacts that cannot be detected visually and show severe influence on the structural strength and safety of liquid tanks. This work presents results of numerical modeling and experimental research in low frequency (50 kHz) ultrasonic guided waves (UGW) propagation in large honeycomb composite structures. Finite element (FE) simulation of UGW propagation has been made aiming to reduce quantity of ultrasonic transducers and optimize their placement on composite structure. The possibilities to place ultrasonic transducers and receivers on both sides (internal or external) of composite structures and to use such a proposed technique for detection of delamination/debonding areas caused by low energy impacts or alternating semi static loads (e.g. filling and draining of liquid from storage tank) and monitoring of partial self-healing of relatively rigid composite structures were proved by experimental testing.

In recent years, the novel lightweight honeycomb sandwich structures have been applied in a wide range of industries. However, daily operational conditions, fatigue, as well as various defects developed during exploitation lead to the risk of structure failure. To meet safety and economical requirements, such structures must be tested. In this paper, an ultrasonic pitch-catch technique based on ultrasonic guided waves (UGW) for detection of defects in honeycomb sandwich structures is proposed. The technique is based on simultaneous scanning of a pair of contact type transmitting and receiving transducers positioned at fixed distance from each other. The proposed technique has been verified by the experiments and simulations on a honeycomb sandwich structure with an aluminium core and carbon fiber skin. The results have shown that different types of internal nonhomogeneities, such as changes in internal multilayered structure, skin delaminations or disbonds between the skin and the core, give the effects of amplitude and phase velocity deviations, which can be detected with accuracy reasonable for practical applications.

The efficiency of linear and nonlinear harvesters with different types of nonlinearity is compared. Narrow band ambient vibrations are modeled by harmonic Gaussian noise. We show that the performance of nonlinear harvesters strongly depends on both the form of nonlinearity and the properties of the noise. Particular forms of nonlinearities which can produce a better than linear response are identified, and these depend on the spectral width of the harmonic noise.

This paper presents a Finite Element Analysis (FEA) of modal energy exchange and harvesting in a simple portal frame structure. We consider both horizontal and vertical support excitations resonant first with the first mode (sway mode) and latter with the second mode (the first symmetrical mode). As 2:1 internal resonance is present between these two modes, the phenomena of mode saturation and energy exchange (modal coupling) may occur. Thus, energy pumped into the system through one of the modes, is partially transferred to the other mode, not directly excited. An evaluation of the energy available for harvesting in each of the considered mode is computed.

We consider the synchronization of n self-excited double pendula. For such pendula hanging on the same beam, different synchronous configurations can be obtained (in-phase and anti-phase states). An approximate analytical analysis allows to derive the synchronization condition and explain the observed types of synchronization for any number of coupled double pendula. The energy balance method is used to show how the energy between the pendula is transferred via the oscillating beam allowing their synchronization. We compute periodic solutions for n = 2, 3, 4, 5 coupled double pendula, based on analytical predictions. For all obtained periodic solutions, we investigate how the stability properties change with the varying natural frequency of the beam.

This paper investigates the uncertainty quantification in structural dynamic problems with spatially random variation in material and damping parameters. Uncertain and locally varying material parameters are represented as stochastic field by means of the Karhunen–Loève (KL) expansion. The stiffness and damping properties of the structure are considered uncertain. Stochastic finite element of structural modal analysis is performed in which modal responses are represented using the generalized polynomial chaos (gPC) expansion. Knowing the KL expansions of the random parameters, the nonintrusive technique is employed on a set of random collocation points where the structure deterministic finite element model is executed to estimate the unknown coefficients of the polynomial chaos expansions. A numerical case study is presented for a cantilever beam with random Young's modulus involving spatial variation. The proportional damping constants are estimated from the experimental modal analysis. The expected value, standard deviation, and probability distribution of the random eigenfrequencies and the damping ratios are evaluated. The results show high accuracy compared to the Monte-Carlo (MC) simulations with 3000 realizations. It is also demonstrated that the eigenfrequencies and the damping ratios are equally affected from material uncertainties.

Compactness is a valuable property in designs of assistive devices and exoskeletons. Current devices are large and stigmatizing in the eyes of the users. The cosmetic appearance will increase by reducing the size. The users want a device that is small enough to be worn underneath the clothes, so it becomes unnoticeable. The goals of this paper are (1) to provide an overview of the shape-changing-material-actuated large-deflection compliant rotational joints, (2) provide new introduced performance indicators that evaluate the designs on performance with respect to volume or weight and (3) design a compact active assistive elbow device as a case study. In order to reach these goals, two evolving fields of study are brought together that have great potential to reduce the size of exoskeletons: smart materials and compliant rotational joints. Smart materials have the ability to change their shape, which make them suitable as actuators. Compliant joints can be compact, since they are made out of one piece of material. An overview of shape-changing-material-actuated large-deflection compliant rotational joints is presented. Performance indicators are proposed to evaluate the existing designs and the prototype. As a case study a compact actuated rotational elbow joint is presented. An antagonistic actuator made from shape memory alloy wires is able to carry an external load and to actuate to move the arm to different positions. The compliant joint is optimized to balance the weight of the arm and to auto-align with the rotational axis of the human elbow joint. A prototype is able to generate a volume specific stall torque of 5.77 ⋅ 10³ Nm/m³, produces a work density of 7.27 ⋅ 10³ J/m³ based on volumes including isolation covers and the half-cycle efficiency of the device is 3.6%. The prototype is able to balance and actuate a torque of 1.1 Nm.

In the present paper, a passive magneto-thermo-mechanical coupling is conceived and developed. The system is designed to engage and disengage auxiliary devices such as a vacuum pump from an internal combustion engine. The coupling increases the transmissible torque of a magnetorheological (MR) clutch, under particular environmental conditions, i.e. for temperature below 20°C. At low temperatures the torque requirements become significantly greater than the nominal operating torque, due to the very low viscosity of the oil in the driven device (vacuum pump). The ON–OFF operation of the thermo-mechanical coupling is the result of two conventional compression springs and two opposing shape memory alloy (SMA) springs. At low temperature the conventional springs keep the coupling engaged, while, if the temperature rises over 90°C, the SMA springs disengages the coupling. At normal operation temperatures, the SMA coupling is disengaged, allowing for the MR clutch to operate as the primary clutch. The SMA springs were designed considering the particular constitutive properties of the material and the equilibrium of the system. A prototype of the mechanical coupling was manufactured considering the geometry of the MR clutch. The experimental results obtained with the prototype, in terms of relative axial position of the two halves of the coupling, appeared in fairly good agreement with the model.

This work discusses the use of chaos control in smart structures. An archetypal model of a shape memory alloy (SMA) two-bar truss is treated. This system exhibits both constitutive and geometrical nonlinearities presenting a complex nonlinear dynamics response including either the snap-through or the chaotic behaviors. A constitutive model that presents a close agreement with experimental data is employed to describe the themomechanical SMA behavior. A variation of the continuous time-delayed feedback method is employed as a control strategy. This variable structure controller is applied to the stabilization of unstable periodic orbits of the SMA structure avoiding the snap-through behavior.