Michael J. Leamy

A Perturbation Approach for Predicting Wave Propagation in One-Dimensional Nonlinear Periodic Structures

Wave propagation in one-dimensional nonlinear periodic structures is investigated through a novel perturbation analysis and accompanying numerical simulations. Several chain unit cells are considered featuring a sequence of masses connected by linear and cubic springs. Approximate closed-form, first-order dispersion relations capture the effect of nonlinearities on harmonic wave propagation. These relationships document amplitude-dependent behavior to include tunable dispersion curves and cutoff frequencies, which shift with wave amplitude. Numerical simulations verify the dispersion relations obtained from the perturbation analysis. The simulation of an infinite domain is accomplished by employing viscous-based perfectly matched layers appended to the chain ends. Numerically estimated wavenumbers show good agreement with the perturbation predictions. Several example chain unit cells demonstrate the manner in which nonlinearities in periodic systems may be exploited to achieve amplitude-dependent dispersion properties for the design of tunable acoustic devices.

Transient and Steady-State Dynamic Finite Element Modeling of Belt-Drives

In this study, a dynamic finite element model is developed for pulley belt-drive systems and is employed to determine the transient and steady-state response of a prototypical belt-drive. The belt is modeled using standard truss elements, while the pulleys are modeled using rotating circular constraints, for which the driver pulleys angular velocity is prescribed. Frictional contact between the pulleys and the belt is modeled using a penalty formulation with frictional contact governed by a Coulomb-like tri-linear friction law. One-way clutch elements are modeled using a proportional torque law supporting torque transmission in a single direction. The dynamic response of the drive is then studied by incorporating the model into an explicit finite element code, which can maintain time-accuracy for large rotations and for long simulation times. The finite element solution is validated through comparison to an exact analytical solution of a steadily-rotating, two-pulley drive. Several response quantities are compared, including the normal and tangential (friction) force distributions between the pulleys and the belt, the driven pulley angular velocity and the belt span tensions. Excellent agreement is found. Transient response results for a second belt-drive example involving a one-way clutch are used to demonstrate the utility and flexibility of the finite element solution approach.

Nonlinear Periodic Response of Engine Accessory Drives With Dry Friction Tensioners

Belt drives have long been utilized in engine applications to power accessories such as alternators, pumps, compressors and fans. Drives employing a single, flat, serpentine belt tensioned by an automatic tensioner are now common in automotive engine applications. The automatic tensioner helps maintain constant belt tension and to dissipate unwanted belt drive vibration through dry friction. The objective of this study is to predict the periodic rotational response of the entire drive to harmonic excitation from the crankshaft. To this end, a multi-degree of freedom incremental harmonic balance method (IHB) is utilized to compute periodic solutions to the nonlinear equations of motion over a wide range of engine speeds. Computed results illustrate primary and secondary resonances of the accessory drive and tensioner stick-slip motions.

Metamaterial-inspired structures and concepts for elastoacoustic wave energy harvesting

Enhancement of structure-borne wave energy harvesting is investigated by exploiting metamaterial-based and metamaterial-inspired electroelastic systems. The concepts of wave focusing, localization, and funneling are leveraged to establish novel metamaterial energy harvester (MEH) configurations. The MEH systems transform the incoming structure-borne wave energy into electrical energy by coupling the metamaterial and electroelastic domains. The energy harvesting component of the work employs piezoelectric transduction due to the high power density and ease of application offered by piezoelectric materials. Therefore, in all MEH configurations studied in this work, the metamaterial system is combined with piezoelectric energy harvesting for enhanced electricity generation from waves propagating in elastic structures. Experiments are conducted to validate the dramatic performance enhancement in MEH systems as compared to using the same volume of piezoelectric patch in the absence of the metamaterial component. It is shown that MEH systems can be used for both broadband and tuned wave energy harvesting. The MEH concepts covered in this paper are (1) wave focusing using a metamaterial-inspired parabolic acoustic mirror (for broadband energy harvesting), (2) energy localization using an imperfection in a 2D lattice structure (for tuned energy harvesting), and (3) wave guiding using an acoustic funnel (for narrow-to-broadband energy harvesting). It is shown that MEH systems can boost the harvested power by more than an order of magnitude. (Some figures may appear in colour only in the online journal)

Dramatic enhancement of structure-borne wave energy harvesting using an elliptical acoustic mirror

Broadband structure-borne wave energy harvesting is reported by wave focusing using an elliptical acoustic mirror (EAM). The EAM is formed by an array of cylindrical stubs mounted along a semi-elliptical path on the surface of a plate. The array back-scatters incoming guided waves and focuses them at the focal location where a piezoelectric energy harvester is located. Multiple scattering simulations and experiments illustrate the broadband focusing characteristics of the EAM. More than an order of magnitude improvement in piezoelectric power generation is documented for an EAM-based energy harvester with respect to a free harvester over the 30–70 kHz frequency range.

Analysis of Bloch’s Method in Structures with Energy Dissipation

Bloch analysis was originally developed to solve Schrodinger’s equation for the electron wave function in a periodic potential field, such as found in a pristine crystalline solid. In the context of Schrodinger’s equation, damping is absent and energy is conserved. More recently, Bloch analysis has found application in periodic macroscale materials, such as photonic and phononic crystals. In the vibration analysis of phononic crystals, structural damping is present together with energy dissipation. As a result, application of Bloch analysis is not straightforward and requires additional considerations in order to obtain valid results. It is the intent of this paper to propose a general framework for applying Bloch analysis in such systems. Results are presented in which the approach is applied to example phononic crystals. These results reveal the manner in which damping affects dispersion and the presence of band gaps in periodic systems.

Dynamic simulation of a tethered satellite system using finite elements and fuzzy sets

Abstract Dynamic simulations are performed for the NASA planned propulsive small expendable deployer system (ProSEDS) space tether mission using two finite element analysis codes. The first is a specialized code for simulating tethered space systems. The second is an in-house flexible multibody dynamics code adapted herein for modeling tethered satellites. The simulation of the ProSEDS mission is divided into two operations: a tether deployment operation and an electrodynamic operation. The specialized code uses a fixed number of nodes and finite elements in simulating the deployment operation, while the in-house code uses a variable number of nodes and elements. The application of each approach is discussed. A fuzzy-set technique is used in conjunction with the two codes to assess the effect of parameter variations on the deployment and electrodynamic operation of the ProSEDS tether. Detailed numerical simulations reveal that the deployment operation is not sensitive to variations in material parameters, but is sensitive to variations in the initial tether ejection momentum and to controller parameters. The electrodynamic operation is found to be highly sensitive to variations in earths magnetic field and, to a lesser extent, variations in material and plasma parameters.

On a Perturbation Method for the Analysis of Unsteady Belt-Drive Operation

A perturbation method is presented for use in analyzing unsteady belt-drive operation. The method relies on the important assumption that for operating states close to steady operation, the friction state (i.e., whether the bell is creeping or sticking at any location on the pulley) is similar to that of the well-known steady solution in which a lone stick arc precedes a lone slip arc (Johnson, K. L., 1985, Contact Mechanics, Cambridge U.P., London, Chap. 8; Smith, D. P., 1999, Tribol. Int., 31(8), pp. 465-477). This assumption, however, is not used to determine the friction force distribution, and, in fact, the friction forces in the stick zone are found to be nonzero, in direct contrast to the steady solution. The perturbation analysis is used to derive expressions for the span tensions, the pulley tension distributions, the contact forces between the belt and the pulleys, and the angular velocity of the driven pulleys. Validity criteria are developed which determine bounds on the operation state for which the assumed friction state is upheld. Verification of response quantities from the perturbation solution is accomplished through comparison to quantities predicted by an in-house dynamic finite element model and excellent agreement is found. Additionally, the finite element model is used to verify the key assumption that a lone slip arc precedes a lone stick arc.

Acoustic absorption calculation in irreducible porous media: A unified computational approach

A critical task in predicting and tailoring the acoustic absorption properties of porous media is the calculation of the frequency-dependent effective density and compressibility tensors, which are explicitly related to the micro-scale permeability properties. Although these two quantities exhibit strong sensitivity to physics occurring at complex micro-scale geometries, most of the existing literature focuses on employing very limited in-house and oftentimes multiple numerical analysis tools. In order to predict these parameters and acoustic absorption efficiently and conveniently, this article synthesizes multiple disparate approaches into a single unified formulation suitable for incorporation into a commercial analysis package. Numerical results computed herein for four close-packed porous media are compared to similar results available in the literature. These include simple cubic, body-centered cubic, and face-centered cubic structures, and also hexagonal close-packed, which has not appeared in the literature. Together with critical comparisons of a hybrid versus direct numerical approaches, the close agreement demonstrates the capabilities of the unified formulation to analyze and control the acoustic absorption properties at the microscopic level.

Dynamic Programming-Informed Equivalent Cost Minimization Control Strategies for Hybrid-Electric Vehicles

This paper presents a direct mathematical approach for determining the state of charge (SOC)-dependent equivalent cost factor in hybrid-electric vehicle (HEV) supervisory control problems using globally optimal dynamic programming (DP). It therefore provides a rational basis for designing equivalent cost minimization strategies (ECMS) which achieve near optimal fuel economy (FE). The suggested approach makes use of the Pareto optimality criterion that exists in both ECMS and DP, and as such predicts the optimal equivalence factor for a drive cycle using DP marginal cost. The equivalence factor is then further modified with corrections based on battery SOC, with the aim of making the equivalence factor robust to drive cycle variations. Adaptive logic is also implemented to ensure battery charge sustaining operation at the desired SOC. Simulations performed on parallel and power-split HEV architectures demonstrate the cross-platform applicability of the DP-informed ECMS approach. Fuel economy data resulting from the simulations demonstrate that the robust controller consistently achieves FE within 1% of the global optimum prescribed by DP. Additionally, even when the equivalence factor deviates substantially from the optimal value for a drive cycle, the robust controller can still produce FE within 1–2% of the global optimum. This compares favorably with a traditional ECMS controller based on a constant equivalence factor, which can produce FE 20–30% less than the global optimum under the same conditions. As such, the controller approach detailed should result in ECMS supervisory controllers that can achieve near optimal FE performance, even if component parameters vary from assumed values (e.g., due to manufacturing variation, environmental effects or aging), or actual driving conditions deviate largely from standard drive cycles.