James M. Gibert

Effect of height to width ratio on the dynamics of ultrasonic consolidation

Purpose – The purpose of this paper is to focus on the changing dynamics of the ultrasonic consolidation (UC) process due to changes in substrate geometry. Past research points to a limiting height to width ranging from 0.7 to 1.2 on build features.Design/methodology/approach – Resonances of a build feature due to a change in geometry are examined and then a simple non‐linear dynamic model of the UC process is constructed that examines how the geometry change may influence the overall dynamics of the process. This simple model is used to provide estimates of how substrate geometry affects the differential motion at the bonding interface and the amount of energy emitted by friction change due to build height. The trends of changes in natural frequency, differential motion, and frictional energy are compared to experimental limits on build height.Findings – The paper shows that, at the nominal build, dimensions of the feature the excitation caused by the UC approach two resonances in the feature. In additio...

Energy harvesting from aeroelastic vibrations induced by discrete gust loads

This article evaluates the amount of energy that can be extracted from a gust using an aeroelastic energy harvester composed of a flexible wing with attached piezoelectric elements. The harvester operates in a subcritical flow region. It is modeled as a linear Euler–Bernoulli beam sandwiched between two piezoceramics. The extended Hamilton’s principle is used to derive the harvester’s equations of motion and an eigenfunction expansion is used to form a three-degree-of-freedom reduced-order model. The degrees of freedom retained in the model are two flexural degrees for the in-plane and out-of-plane displacements, and a torsional degree for the rotational displacement. Wagner and Küssner functions are used to represent the unsteady aerodynamic and gust loading, respectively. The amount of energy extracted from the system is then compared for two different deterministic gust profiles, 1-COSINE and two sharp-edged gusts forming a square gust, for various magnitudes and durations. The results show that the harvester is able to extract more energy from the square gust profile, although for both profiles the harvester extracts more power after the gust has subsided.

Stick-Slip Dynamics in Ultrasonic Consolidation

Ultrasonic consolidation (UC) is a solid state rapid manufacturing process derived from ultrasonic welding of thin metal foils coupled with contour milling to achieve functional accurate components. Solidica Inc developed the process. The bonding of metal is accomplished by the local application of high frequency vibration energy under pressure producing a metallurgical bond without melting the base material. Its unique nature allows the design and fabrication of structural panels for satellites, production of injection molding tools, functionally graded structures, metal-matrix composites, embedded sensors, armor, and fiber embedded adaptive structures. It is commonly theorized that interfacial motion and friction at the bonding interface play a prominent role in the bonding process by removing surface contaminants, allowing direct metal to metal contact, and producing sufficient stress to induce plastic flow. The substrate’s geometry is also crucial in the bonding process. Researchers have experimentally observed that as the height of build specimen approaches its width, the bonding process degrades, and no further foils may be welded. Numerical simulations indicate that for features built at the nominal width (approximately 0.94 inches) the welding process excites several of the feature’s natural frequencies near the operating frequency of the ultrasonic welder, causing a resonance. This paper presents two modeling approaches to explain the behavior of the substrate as its dimensions approach the critical geometry: a finite element analysis and a lumped parameter model. We compare both models and present preliminary experimental results to verify their respective accuracies.Copyright

Topology Synthesis of Planar Ground Structures for Energy Harvesting Applications

In this manuscript, we investigate the use topology optimization to design planar resonators with modal fre- quencies that occur at 1 : n ratios for kinetic energy scavenging of ambient vibrations that exhibit at least two frequency components. Furthermore, we are interested in excitations with a fundamental component containing large amounts of energy and secondary component with smaller energy content. This phenomenon is often seen in rotary machines; their frequency spectrum exhibits peaks on multiple harmonics, where the energy is primarily contained in the rotation frequency of the device. Several theoretical resonators are known to exhibit modal frequencies that at integer multiples 1:2 or 1:3. However, designing manufacturable resonators for other geometries is still a daunting task. With this goal in mind, we utilize topology optimization to determine the layout of the resonator. We formulate the problem in its non-dimensional form, eliminating the constraint on the allowable frequency. The frequency can be obtained a posteriori by means of linear scaling. Conversely, to previous research, which use the clamped beam as initial guess, we synthesize the final shape starting from a ground structure (or structural universe) and remove of the unnecessary beams from the initial guess by means of a graph-based filtering scheme. The algorithm determines the simplest structure that gives the desired frequency’s ratio. Within the optimization, the structural design is accomplished by a linear FE analysis. The optimization reveals several trends, the most notable being that having members connected orthogonally as in the L-shaped resonator is not the preferred topology of this devices. In order to fully explore the angle of orientation of connected members on the modal characteristics of the device; we derive a reduced-order model that allows a bifurcation analysis on the effect of member orientation on modal frequency. Furthermore, the reduced order approximation is used solve the coupled electro-mechanical equation of a vibration based energy harvester (VEH). Finally, we present the performance of the VEH under various base excitations. These results show an infinite number of topologies that can have integer ratio modal frequencies, and in some cases harvest more power than a nominal L shaped harvester, operating in the linear regime.

Stick-Slip Dynamics in Ultrasonic Additive Manufacturing

Ultrasonic Additive Manufacturing is a solid state manufacturing process that combines ultrasonic welding of layers of thin metal foil with contour milling. Bonding between two foils is accomplished by holding the foils together under pressure and applying high-frequency excitations normal to the pressure direction. The accepted explanation for bonding is that stresses due to both compression and friction stemming from the interfacial motion between the foils result in plasticity and ultimately produce a metallurgical bond. The process however, has been shown to have a critical shortcoming in its operation; namely, the presence of a range of build heights within which bonding cannot be initiated. To better understand the reasons for this anomaly, this paper simplifies the process into a lumped parameter dry friction oscillator and shows that complex stick-slip motions of the build feature near or above its resonance frequency may explain bond degradation. Specifically, it is shown through bifurcation maps obtained for different process parameters that, at the critical build heights, the feature exhibits pure stick motions due to primary resonant interactions between the external excitation and the feature. Furthermore, complex aperiodic responses are observed at build heights above resonance (short features). In such scenarios, bonding cannot be initiated because no or non-uniform interfacial motions occur between the tape and the feature. It is also observed that, once the height of the build feature increases beyond the critical value corresponding to resonance, periodic uniform responses essential for bonding, are recovered. These results corroborates previous experimental findings which demonstrate that bonding can be hard to initiate near or slightly above resonance (at or slightly below a critical height) but can be reinitiated below resonance (above the critical height).Copyright

MDO/MSO of Slender Thin Walled Box Beam Model

This manuscript presents a two steps procedure, useful within preliminary design stages, to optimize High Aspect Ratio composite wing and investigate the effect of different materials on the structural performances. The selection of material is carried out based on structural performances rather than Material Selection Optimization. Notably, the effect of different material is evaluated taking advantage of the objective properties of tensors invariants and by the application of a linear scaling law. Scaled static, dynamic and aeroelastic performances have been compared with those obtained numerically. Through the optimization of the composite wing-box of a High Altitude Long Endurance aircraft, it has been demonstrated that near optimal solutions can be identified for a wide range of composite materials with the procedure presented herein, with no additional request of time and costs.

A Multi-objective Nonlinear Piezoaeroelastic Wing Solution for Energy Harvesting and Load Alleviation: Modeling and Simulation

The model of a geometrically nonlinear wing hosting piezoelectric patches with the dual purpose of suppressing aeroelastic vibration and harvesting vibrational energy is presented in this paper. The nonlinearities are introduced in order to consistently reproduce the behavior of the flexible structure, since moderate to large displacements can occur in response of external loading conditions. A nonlinear shear underfomable 3-D Euler-Bernoulli beam theory is used to model the displacements field and structural nonlinearities up to the third order are retained in the model of a straight untapered composite wing. A linear indicial functional representation of the unsteady aerodynamic loads in an incompressible flowfield is adopted. The extended Hamilton principle is used to derive the aeroelastic equations of motion. The composite cantilever wing includes two piezoelectric elements, perfectly bonded on its lower and upper longitudinal surfaces in the proximity of the wing root, and electrically connected by a resistive load, functioning as energy harvesting devices. During the state of deformation the piezoelectric components induce electric charges to be stored for future use as a supplementary power source. The piezoelectric layers also function as damping elements with desired load alleviation properties. The effectiveness of such a solution, both in terms of the amount of energy harvested and load alleviation characteristics, for a well defined wing configuration have been evaluated in this paper. Numerical results and discussions are followed by pertinent conclusions and directions for future work.

Demonstration of the effect of piezoelectric polarization vector on the performance of a vibration energy harvester

This manuscript is motivated by research that shows the shear, d15, mode energy harvesters offer significant improvement in power generation over the traditional normal, d31, mode based harvesters. The premise behind this study is to examine the effect of expanding the design domain of PZT based energy harvesters by considering an arbitrary poling angle. In the first part of the manuscript, we derive the equation of motions of a harvester based on Timoshenko beam theory in an unimorph configuration. The resulting equations are solved using a Rayleigh Ritz analysis. The electric displacement depends on both the normal and shear strain. Thus the proposed device operates using a combination of shear and normal modes to extract power. The extent to which each mode is used depends on the polarization orientation. We examine the effect of poling on the fundamental short and open circuit frequencies. Next, the poling angle is examined over a range to determine the effect on the power harvested at the fundamental modal frequencies of the system. The study demonstrates that an arbitrary poled piezoelectric increases the power that the harvester produces over traditionally poled devices; however, the performance is highly dependent on the geometry.

New Insights Into Piezoelectric Energy Harvesting Using a Dynamic Magnifier

This manuscript considers the design and performance of a piezoelectric vibration-based energy harvester with a dynamic magnifier (VEHDM) to a traditional single degree-of-freedom harvester (VEHS) using proper metrics. Past research has shown that the addition of the second magnifying mass can increase the peak power harvested by as much as 20 times [1] when compared to the VEHS; however, the metrics of performance comparison were not clearly defined, nor was the comparison carried at optimal loading conditions. For instance, the peak power was compared at different excitation frequencies and power not power per unit mass is used for comparison purposes. Additionally, the VEHDM is designed so that the magnifier mass and stiffness are considered independent of the primary stiffness and mass of the harvester. In this study, we determine the optimal properties of the magnifier, in terms of frequency ratios and resistance that maximizes both power and power density for a fixed frequency harmonic excitation. The optimized VEHDM is compared to a similarly optimized VEHS. Treating the magnifier as a tuned mass damper (TMD), i.e., simply adding the magnifying mass and stiffness to the optimized VEHS and then tuning the magnifier to split the resonance peak of the single mass harvester, increases the peak power harvested for mass ratios greater than one. However, the peak frequencies of excitation of the VEHS and VEHDM differ. Only at large values of the mass ratio does the excitation frequency of the VEHS and VEDHM coincide, making the VEHDM less efficient in terms of power per unit mass. Similarly, simply adding a magnifying stiffness and mass to the optimized VEHS and then tuning both the VEDHM to the VEHS’s to the same excitation frequency by changing the the uncoupled natural frequency of VEHDM’s magnifier components limits the performance of the VEDHM. In this case, the VEHDM generates the same amount of power as the VEHS. Nonetheless, the VEHS is more efficient in terms of power generated per unit mass. In order to match the single mass harvester’s power per unit mass, the optimal magnifier for the VEHDM is a rigid spring of negligible mass acting in series with the stiffness with the VEHDM’s piezoceramic element. However, significant gains in both peak power and peak power per unit mass for a fixed frequency excitation can be obtained by considering all the mass and stiffness elements in the VEHDM, while using the same piezoelectric in the VEHS.Copyright

Exact dynamics of an angle-shaped resonator for energy scavenging applications

This manuscript details the derivation and solution of the equations of motion of angle-shaped resonators, composed of two prismatic members attached at various angles. The first part of the paper is devoted to the derivation of the analytical solution for the dynamic of a two member structure. The governing equation and the boundary conditions are derived by taking the variation of the Hamiltonian. The boundary value problem is then solved analytically giving rise to the characteristic equation of the system. In order to assess the validity of the analytical model presented, the analytical solution is compared against a semi-analytical model, finite element analysis and experiments. In the second part of the manuscript, we derive the electro-mechanical equation of motion of the angle-shaped resonator. The behavior of the harvester when subjected to single and multiple harmonic excitation is investigated along with the sensitivity onto the power harvested due to the folding angle.