Variable performance characteristics in a multifunctional structure may be achieved by identifying suitable material candidates, and spatially varying, or grading, their material properties along the structures. Additive manufacturing (e.g. 3D printing) offers various possibilities to fabricate/manufacture such graded structures. The material properties of multifunctional composite structures, such as beams or plates, are often graded along their thickness (laminate/sandwich) or distributed in a material matrix (fibers/nanoparticles). In recent years, it has been demonstrated that by tailoring the materials in other directions (axially/radially), superior mechanical behavior and structural stability can be realized. In this research, the modeling and analyses of axially graded polymeric beams to maximize their vibration performance for a large bandwidth of frequencies and damping is presented. Polymeric materials have frequency and temperature dependent viscoelastic properties (complex modulus, glass transition temperature etc.) which can be leveraged for different applications. The goal is to spatially combine these materials such that desired longitudinal vibration characteristics (natural frequencies, damping and modes) can be achieved. To this end, the modeling for the free and forced vibration of beams with spatially varying properties, is carried out by a piecewise uniform continuous model. The spectral characteristics (natural frequency, damping ratios, and frequency response functions) of the axially graded beams are computed by solving associated transcendental eigenvalues problems. The parametric studies included the grading of polymers which are regularly used for additive manufacturing, such as ABS, PLA, etc. These results demonstrate that the response of the system can be manipulated by axial grading and optimal design/fabrication (3D printing) of multifunctional smart structures may be developed for vibration control applications.

This manuscript investigates the flexural wave propagation behavior of a foldable metamaterial structure. Origami-inspired foldable structures are making inroads into many engineering applications — deployable solar cell arrays, foldable telescope lenses, foldable automotive airbags, to name a few; driven primarily by some of the remarkable mechanical properties (high stiffness, negative Poisson’s ratio, bistability etc.) of these structures. The chief motivation of this research is a comprehensive analysis of flexural wave propagation in such foldable structures. The repeating unit cell of the structure consists of an Euler-Bernoulli beam and a torsion spring. Transfer Matrix (TM) method is used to analyze the vibration attenuation properties of the structure and it is shown that the structure exhibits bandgap behavior. The obtained bandgaps are validated using Finite Element Analysis (FEA). Using the characteristic equation of the transfer matrix, we derive a transcendental equation for the bandgap edge frequencies. We show that for the n th band gap, the second band edge frequency is always equal to the natural frequency of the n th modeshape of the constituent beam under the simply supported condition. This frequency, therefore, is independent of the torsion spring constant. In addition, a detailed parametric study of the variation in band edge frequencies when the geometric and material parameters of the structure (Young’s modulus of beam, torsional spring constant, width and thickness of beam etc.) are varied is conducted. It is concluded that the ratio of flexural rigidity of the beam to the torsion spring constant (EI/k t ) is an important parameter affecting the width of the bandgap. For low values of the ratio, i.e., low beam flexural rigidity and high torsional stiffness, the first band edge frequency is almost equal to the second band edge and, effectively, no bandgap exists. As the stiffness ratio increases, i.e. high flexural rigidity (EI of the beam) and low torsional stiffness k t , the first band edge frequency assumes progressively lower values relative to the second band edge and we obtain a relatively large bandgap over which no flexural waves propagate. This has important ramifications for the design of foldable metamaterial structures.

There has been an increasing demand for force measurement in applications that are portable, wearable, have limited space, low power, or low cost requirements. Such applications cannot support the power and computing requirements of the load cells. Force sensing resistor (FSR) is a passive component that is composed of polymer thick films that change resistance between its terminals due to force applied at its surface. An FSR can provide a suitable alternative to the bulky load cell. However, it inherently exhibits many nonlinear behaviors. This paper evaluates five different FSR sensors (IEE FSR 151 NS, Interlink FSR 402, Sensitronics ShuntMode FSR. FlexiForce A201 FSR, and Sensitorincs ThruMode FSR). The FSRs were evaluated for sensitivity, minimum measurable force, repeatability, creep, and hysteresis. In addition, system identification techniques were used to model each FSR behavior so they can be used as calibrated standalone force sensors. Results show that the Sensitronics ThruMode FSR had the best repeatability and the least hysteresis, while the FlexiForce A201 had the lowest creep, and the Interlinks 402 FSR had the lowest threshold force.

This paper discusses the semi-active control of helicopter ground resonance using magnetorheological (MR) damper. A dynamic model of a MR damper with bi-fold flow mode is built based on the hyperbolic tangent model and experimental data on mechanical properties; and its inverse model is derived for the control. An approximate analytical solution of a linear system is provided and a critical stability area is calculated according to the classical model of ground resonance and the method of determining the linear system stability. Then, Simulations are performed on the helicopter ground resonance model with three semi-active control strategies and the control performance is compared. Simulation results show that the comprehensive performance of the fuzzy skyhook control algorithm is superior to the on-off skyhook and continuous skyhook control algorithms.

This research investigates a quasi-zero stiffness (QZS) property from the pressurized fluidic origami cellular solid, and examines how this QZS property can be harnessed for low-frequency base excitation isolation. The QZS property originates from the nonlinear geometric relations between folding and internal volume change, and it is directly correlated to the design parameters of the constituent Miura-Ori sheets. Two different structures are studied to obtain a design guideline for achieving QZS: one is identical stacked Miura-Ori sheets (ismo) and the other is non-identical stacked Miura-Ori sheets (nismo). Further dynamic analyses based on numerical simulation and harmonic balance method, indicate that the QZS from pressurized fluidic origami can achieve effective base excitation isolation at low frequencies. Results of this study can become the foundation of origami-inspired metamaterials and metastructures with embedded dynamic functionalities.

We consider subset selection and active subspace techniques for parameters in a continuum phase-field polydomain model for ferroelectric materials. This analysis is necessary to mathematically determine the parameter subset or subspace critically affecting the response, prior to model calibration using either experimental or synthetic data constructed using density functional theory (DFT) simulations. For the 180° domain wall model, we employ identifiability analysis using a Fisher information matrix methodology, and subspace selection to determine the active subspace. We demonstrate the implementation and interpretation of techniques that accommodate the model structure and discuss results in the context of identifiable parameter subsets and active subspaces quantifying the strongest influence on the model output. Our results indicate that the governing domain wall gradient energy exchange parameter is most identifiable.

The present study concerns with the performance of a skid landing gear (SLG) system of a rotorcraft impacting the ground at a vertical sink rate of 5.0 m/s. The impact attitude is per chapter 527 of the Airworthiness Manual (AWM) of Transport Canada Civil Aviation and FAR Part 27 of the U.S. Federal Aviation Regulation. A single degree of freedom helicopter model is investigated under two rotor lift factors 0.67 and 1.0. Three Configurations are evaluated: a) A conventional SLG; b) SLG equipped with a passive viscous damper and c) SLG incorporated with a magnetorheological energy absorber. The non-dimensional solutions of the helicopter model show that the passive damper system could reduce the maximum acceleration experienced by the helicopter occupants by 21% and 19.8% in comparison to the undamped system for the above rotor lift factors, respectively. However, the passive damper fails to constrain the non-dimensional energy absorption stroke of the damper within the given 18 cm maximum stroke and a bottoming out of the damper piston was noticed. Therefore, the alternative and successful choice was to employ a magnetorheological energy absorber (MREA). To improve the MREA controllability and to resettle the payload with no oscillations, i.e. in one cycle, two different Bingham numbers for compression stroke and rebound stroke were defined in the non-dimensional solution. Several simulations were conducted for different values of Bingham numbers. Among these numerical simulation results, the solution that implemented the optimum Bingham numbers was found to be the only one feasible solution. In this case the MREA with optimum Bingham number for compression could utilize the full energy absorption stroke to attain soft landing. In the rebound stroke, the generated optimal on-state damping force successfully controls the bounce of the payload until the payload settles down to its original equilibrium position with no oscillations.

Shape memory alloys (SMA) can be used to create actuators for use in mechanical systems that carry pronounced benefits with their low weight, high strength, and low cost when coupled with advancements such as robust self-sensing. However, there exist drawbacks in the form of slow system response and complex material behavior. The design and implementation of controllers that drive SMA actuators successfully can pose a challenge, and accurate modelling of the material in software can help to optimize the system response time and power requirements. We have created a variety of tools to help implement these actuators into simulations that capture accurate thermal and mechanical responses of various SMA systems under a variety of control laws. In particular, thermo-electro-mechanical models of SMA behavior are implemented into software representations of mechanical systems such that the entire temperature, stress, and phase profiles of an SMA actuator can be accurately determined via simulation. Because analytical equations for modelling SMA behavior quickly become so complex to be untenable, we use stable numerical schemes to solve for these profiles. In particular, a finite difference scheme allows for spatial and temporally discretized temperature profiles along a shape memory actuator which can be solved for using empirically derived expressions for the heat transfer coefficient that dictated convective heat transfer. These types of models allow for a variety of boundary conditions to capture a number of SMA geometries, orientations, and applications. This paper presents the results of the numerical schemes for thermal cycling and a sliding mode controller used to drive a simple SMA actuator with varying boundary conditions and compares them to experimental results.

This manuscript investigates one way sound propagation in Magnetorheological fluids (MRF) using spatio-temporal modulation of the applied magnetic field. One-way propagation of waves in a structure can have potential technological applications such as sound isolation, filtering and echo suppression. Several experimental works in the literature have shown that elastic properties of MRF’s (local speed of sound, in particular) are dependent on the applied magnetic field. Therefore, several fascinating possibilities regarding the manipulation of sound waves in MRF, by tailoring the applied magnetic field, exist. A effective medium approximation (previously used in literature) is used to analyze sound propagation in a MRF composed of hydrogen-reduced Iron particles suspended in pure glycerine. Floquet-Bloch theory is used to obtain a quadratic eigenvalue problem that gives the band structure as a function of the material and modulation parameters. When the applied magnetic field is allowed to vary only in space, regular bandgaps are obtained as a result of Bragg scattering. In contrast, the temporal variation of the magnetic field to induce a traveling wave like variation of the modulated parameters, breaks the symmetry of the Brilloouin zones and we obtain directional bandgaps. The theoretical band structure is validated by numerical band diagrams obtained using a Finite Element code. This research has important applications in active sound manipulation.

Creating a multi-variance human pulsation simulator is crucial for deeper understanding of human pulsation system and developing useful medical devices. Current pulsatile systems are bulky, complex, and expensive. In order to address these disadvantages, this project intends to develop a simple and cost-effective pulsatile simulator using Magneto-Rheological fluids whose flow can be controlled by magnetic fields instantly. It also intends to evaluate its effectiveness in generating various arterial blood pulsation patterns. To this end, a test setup consisting of tubing, an electromagnet, and sensors along with MR fluids was constructed. Using Pulse Width Modulation (PWM) techniques, the electromagnet produced control signals to regulate the flow motion. The output pressure changes (perceived human pulsation) were measured using a pressure sensor installed in the tubing. Using the test setup, a series of testing was performed to measure arterial pulsations by varying the duty cycles of PWM signals. The results show that the pulsatile system was capable of replicating various human pulsation waveforms.

In the paper, we discuss the development of a high-fidelity and surrogate model for a PZT bimorph used as an actuator for micro-air vehicles including Robobee. The models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. The actuator dynamics are initially modeled using the homogenized energy model (HEM) framework. This provides a comprehensive high-fidelity model, which can be inverted and implemented in real time for certain control regimes. To improve efficiency, we additionally discuss the development of data-driven models and focus on the implementation of a surrogate model based on a dynamic mode decomposition (DMD). Finally, we detail the design and implementation of a PI controller on the surrogate and high-fidelity models.

Postbuckling response, long considered mainly as a failure limit state is gaining increased interest for smart applications, such as energy harvesting, frequency tuning, sensing, actuation, etc. Cylindrical shells have received less attention as structural form to harness elastic instabilities due to their increased modeling complexity and high imperfection sensitivity. Yet, preliminary experimental and computational evidence indicates that the elastic postbuckling response of cylindrical shells can be controlled and potentially managed. Further, cylindrical shells offer desirable features for the design of mechanical devices and adaptive structures that other forms cannot attain without additional external constraints. This paper presents a study on tailoring the elastic postbuckling response of thin-walled cylindrical shells under compression by means of non-uniform wall stiffness distributions. The pattern of stiffness distribution was designed by discretizing the shell surface into cells and thickening selected cells with respect to a baseline uniform wall thickness. Diverse patterns were characterized in the way of how they affect the postbuckling response through numerical simulations using the finite element method. Results show that the elastic postbuckling response can be tailored into three response types: softening, sustaining, and stiffening; and that number, sequence/time and location/space of localized buckling events can be designed. This work provides new knowledge on the means to design the cylindrical shells with controlled elastic postbuckling behavior for applications in smart materials, mechanical devices, and adaptive structures.

The paper presents results of finite element analysis of architectured iron-based shape memory alloy (SMA) samples consisting of bulk SMA and void combined to different proportions and according to different geometric patterns. The finite element simulation uses a constitutive model for iron-based SMAs that was recently developed by the authors in order to account for the behavior of the bulk material. The simulation of the architectured SMA is then carried out using a unit cell method to simplify calculations and reduce computation time. For each unit cell, periodic boundary conditions are assumed and enforced. The validity of this assumption is demonstrated by comparing the average behavior of one unit cell to that of a considerably larger sample comprising multiple such cells. The averaging procedure used is implemented numerically, by calculating volume averages of mechanical fields such as stress and strain over each finite element model considered as a combination of mesh elements.

Vibrational Resonance (VR) is a nonlinear phenomenon which occurs when a bi-stable system is subjected to a bi-harmonic excitation consisting of a small-amplitude resonant excitation and a large-amplitude high-frequency excitation. The result is that, under some conditions, the high-frequency excitation amplifies the resonant response associated with the slow dynamics. While VR was studied extensively in the open literature, most of the research studies used optical and electrical systems as platforms for experimental investigation. This paper provides experimental evidence that VR can also occur in a mechanical bi-stable twin-well oscillator and discusses the conditions under which VR is possible.

In this communication, we first introduce the concept of programmable boundary conditions, and then use it to design a nonreciprocal acoustic device: an effective, broadband, acoustic diode. Previous works showed that, using sufficiently small transducers, an active acoustic metasurface can be realized: a smart active acoustic skin with tunable acoustic properties. Using distributed control, these properties can be adapted or reconfigured in real-time. Or, it can even depend on the acoustic field itself, allowing for a programming of the (meta)surface properties: a programmable boundary condition. For instance, a partial derivative equation depending on the acoustic quantities can be imposed, in a discretized form, at the surface of such a programmable boundary. This type of non-standard boundary conditions have been shown to provide the necessary basis for nonreciprocal propagation for a plane wave interacting with a boundary with non grazing incidence, ie. for wavevectors that possess a component normal to the boundary. This restriction may appear problematic when the wavevector is then parallel to the boundary, e.g. when dealing with plane waves in a 1D waveguide, as in an acoustic diode. An acoustic diode, or acoustic isolator, is a nonreciprocal device that let acoustic power pass only in one direction, hence breaking the reciprocity of normal acoustic propagation. We propose a new model of acoustic diode, based on active components: a continuous, distributed source inside the domain. However, based on the modeling of parietal sources in ducts, in the low frequency range, we show that the boundary control approach and the distributed domain sources are equivalent. The only difference is that, in the case of the programmable boundary condition, the near-field of the boundary also contains a component normal to the boundary. Hence our acoustic diode can be realized in practice using programmable boundary conditions. Moreover, the acoustic diode is effective on a broad frequency range, since it can work both on the fundamental mode (plane waves) and on higher-order mode of the waveguide.

One of the primary difficulties to implementing NiTi shape memory alloys as robotic actuators is reliably amplifying their low linear strain to large effective displacements. Bowden tubes, called “push-pull cables” in other industries, allow a long length of Shape Memory Alloy (SMA) wire to fit in a small space; this provides a method for increasing effective SMA actuator strain without compromising space or complexity of the entire mechanism. The mechanical advantage of the Bowden tube provides faster actuation speeds, but comes at a cost of increased thermal capacitance resulting in higher power consumption. A feedback control system has been formed comprising the Bowden tube actuator, a rotary platform, and a microcontroller. The controller heats the SMA by passing current through the SMA wire using pulse-width-modulation. After describing the creation of the electro-mechanical system, its capabilities and limitations are discussed. Linear Parameter Varying (LPV) models of SMA are used to determine the range of characteristics the inherently nonlinear SMA system will exhibit. A sliding mode controller is designed based on these characteristics, and implemented in the prototype. Sliding-mode control is shown to be a powerful tool for SMA control even when system parameters are uncertain.

In this paper, we discuss the development and implementation of a 3-D electromechanically coupled homogenized energy model (HEM) for ferroelectric materials. A stochastic-based methodology is introduced and applied to problems involving large scale switching of ferroelectric and ferroelastic materials. Switching criteria for polarization variants are developed using density distributions in three dimensions to accommodate both electrical and mechanical loading and their coupled response. The theory accommodates non-proportional loading and major/minor loop hysteresis. Such formulations are known to accelerate computations for real-time control of nonlinear and hysteretic actuators. The proposed formulation maintains superior computational efficiency in the three dimensional case through the application of density formulations that are based on internal distributions of stress and electric field to produce a distribution of polarization switching events over a range of applied fields and stresses.

Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. We have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. It is usually true that fixed gain controllers are designed for particular applications but these controllers may not be able to stabilize the plant under all variations in the operating domain. Therefore we propose to augment this fixed gain controller with a relatively simple direct adaptive controller that will maintain stability of the full closed loop system over a much larger domain of operation. This can ensure that a flexible structure controller based on a reduced order model will still maintain closed-loop stability in the presence of unmodeled system dynamics. The augmentation approach is also valuable to reduce risk in loss of control situations. First we show that the transmission zeros of the augmented infinite dimensional system are the open loop plant transmission zeros and the eigenvalues (or poles) of the fixed gain controller. So when the open-loop plant transmission zeros are exponentially stable, the addition of any stable fixed gain controller does not alter the stability of the transmission zeros. Therefore the combined plant plus controller is ASD and the closed loop stability when the direct adaptive controller augments this combined system is retained. Consequently direct adaptive augmentation of controlled linear infinite dimensional systems can produce robust stabilization even when the fixed gain controller is based on approximation of the original system. These results are illustrated by application to a general infinite dimensional model described by nuclear operators with compact resolvent which are representative of distributed parameter models of mechanically flexible structures. with a reduced order model based controller and adaptive augmentation.

We propose an analytical model for a superelastic shape memory alloy (SMA) beam. The model considers reversible phase transformation between austenite and a single martensite variant driven by mechanical loading/unloading. In particular, we consider a cantilever beam subjected to a concentrated transverse force acting at the tip. The force is gradually increased from zero to a maximum value sufficient to cause complete transformation of the initially austenitic phase into martensite away from the beam core. The force is then gradually removed, resulting in complete strain recovery. In each stage of the loading/unloading process, an analytical relation is established between bending moment and curvature in terms of position along the axis of the beam. The model is compared to a uniaxial numerical beam model and to finite element analysis (FEA) results for the same beam in 3D, with very good agreement in each case. The moment-curvature relation is then integrated to obtain a nonlinear expression for the deflection and stress distribution in terms of position along the length of the beam. The expression is validated against 3D simulation results.

To alleviate wave and vibration transmission in automotive, aerospace, and civil engineering fields, researchers have investigated periodic metamaterials with especially architected internal topologies. Yet, these solutions employ heavy materials and narrowband, resonant phenomena that are unsuitable for the many applications where broadband frequency vibration energy is a concern, such as that injected by impact forces, and weight is a performance penalty. To overcome these limitations, a new idea for lightweight, elastomeric metamaterials constrained near critical points is recently being explored, such that improved shock and vibration damping is achieved using reduced mass than conventional periodic metamaterials. On the other hand, the internal architectures of these metamaterials have not been explored beyond classical circular designs whereas numerous engineering structures involve square or rectangular geometries that may challenge the ability to realize critical point constraints due to the lack of rotational symmetry. The objectives of this research are to undertake a first study of square cross-section elastomeric metamaterials and to assess the impact tolerance of structures into which these metamaterials are embedded and constrained. Finite element simulations guide attention to design parameters for the metamaterial architectures, while experimental efforts quantify the advantages of constraints on enhancing impact tolerance metrics for engineering structures. It is seen that although the architected metamaterial leads to slightly greater instantaneous acceleration amplitude immediately after impact, it more rapidly attenuates the injected energy when compared to the solid and heavier elastomer mass from which the metamaterial is derived.