Eric M. Austin

Some design considerations for active and passive constrained layer damping treatments

Active constrained layer damping treatments promise to be an effective means of vibration suppression in structures. Basically, the concept consists in either replacing or augmenting the constraining layer of a constrained viscoelastic material with piezoceramic actuators in an attempt to improve vibration suppression properties by capitalizing on both passive and active damping techniques. An important issue in such configurations is the concept that the actuation ability of the piezoceramic is reduced by the viscoelastic layer, rather than enhanced. On the other hand, an active constraining layer increases the shear in the viscoelastic and thus forms an effective means of enhancing the damping mechanism. Some design considerations for pure passive, pure active control, and active constrained layer damping are discussed here. Several authors have reported comparisons and formulations of active constrained layer damping techniques. The approach presented here differs in that it employs an energy principle for the equations of a beam with partial active/passive constrained layer damping treatments. To simulate a realistic design problem, the optimal sizing, length, and thickness of treatments subject to a total thickness restriction is studied for cases of active constrained layer, passive constrained layer, and pure active control. The results show that the active constrained layer damping treatment provides better vibration suppression than passive damping treatments, and it even out-performs pure active control for low-gain applications.

Some pitfalls of simplified modeling for viscoelastic sandwich beams

It is commonplace in academia to base models of constrained-layer damping treatments on the assumption that the facesheets displace identically during transverse vibrations. This assumption is valid for a large range of problems, particularly for problems common in the era when damping was achieved by applying foil-backed treatments to thin panels. The authors show using a very simple example that oversimplified modeling can skew distributions of modal strain energy, a common indicator of damping.

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...

Time-varying controller for temperature-dependent viscoelasticity

There are internal-variable techniques that account for the frequency-dependent behavior of viscoelastic materials, but the temperature dependence of these materials has received much less attention. Two methods for designing controllers robust to temperature disturbances are given: (1) Modal reference adaptive control and (2) time-varying pole placement control. Examples that demonstrate the strengths and weaknesses of each are given. The results show that it is possible to achieve vibration reduction while simultaneously rejecting the effects of a temperature disturbance. This work shows that both the frequency and temperature dependence of viscoelastic materials can be modeled with internal variables.

Limitations of Using Membrane Theory for Modeling PVDF Patches on Inflatable Structures

An underlying goal in structural modeling is to use the simplest mathematics possible that captures the physics of a problem accurately. Inflatable structures are normally fabricated from thin films, so they are often modeled as membranes, i.e., structural elements that cannot resist bending moments. Researchers have recently been looking at active control of inflated structures, so this raises the question of whether membrane theory can account for the effects of surface-mounted piezopolymer patches used as either sensors or actuators. This work discusses these effects on the dynamic behavior of a flat, rectangular coupon section and assesses the patch’s ability to sense and actuate transverse deflections of the thin film substrate using traditional membrane theory. The Rayleigh-Ritz method was employed to approximate the natural frequencies and mode shapes of this layered system. While including the additional mass of the patch, traditional membrane theory was unable to account for the added stiffness of the patch layer. When the piezoelectric behavior of the patch was considered, membrane theory failed to model the PVDF as a useful sensor. Also, excitation of transverse vibrations was not possible using membrane theory, which does not allow application of bending moments. However, PVDF actuation was modeled as an applied in-plane force, which allowed the patch the ability to suppress out-of-plane disturbances by altering the tension in the base layer as a function of applied voltage. This article discusses the limitations associated with using traditional membrane theory to analyze the dynamic behavior of thin-layered systems as well as model the interaction between an active PVDF patch and the torus substrate.

A C1 finite element capable of interlaminar stress continuity

Abstract This paper extends Lee and Lius [Comput. Struct. 42 (1992) 69–78] zig-zag approach for matching tractions across material boundaries to a more traditional finite element implementation suitable for more general partial-coverage layups. Key quantities from a new C1-capable element are compared with traditional C0 elements and Paganos analytical solution. Comparisons center around interface stresses, as might be used to predict debond of an active or passive damping treatment, and strain energy, the quantity often used to estimate damping is structures. It is shown that traction continuity is important in predicting interface stresses, but not in predicting strain energy distributions.

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

Modeling of Piezoelectric Materials on Rubber Beams

It is common to use piezoelectric materials to reduce vibrations or otherwise alter the dynamics of structures made of metal or composite materials. In contrast, this work addresses modeling of piezoelectric patches applied to a rubber substrate. An underlying goal of modeling, however, is to represent the significant physics of a problem with the simplest model possible. There were several simplified approaches to modeling piezoelectric actuation on classical beam and plate elements developed in the late 1980s and early 1990s. Of these, the pin force, extended pin force, and Euler-Bernoulli methods are assessed in this study. The basic concepts of the three approximation methods are developed, and the curvatures predicted by each is compared to predictions from a special-purpose finite element code. The final conclusion is that the constant-strain approaches (pin force and enhanced pin-force) are not accurate for very soft substrates. Future work includes adding the time dependence of rubber materials as well as the possibility of material of geometric nonlinearities.

Modeling of sandwich structures

Much of the work done on active and passive constrained layer beams is done with models using kinematic assumptions proposed by Kerwin, Mead and Markus, and others. Typically these analyses use low-order Euler-Bernoulli beams and assume the base and constraining layers undergo identical transverse displacements. These assumptions are reasonable for cases where the middle layer (normally a relatively soft viscoelastic material) is thin and the constraining layer is relatively weak in bending, but many practical cases arise where these assumptions are violated. A few authors over the years have done studies with less restrictive kinematic assumptions, but none have specifically studied the effects of doing so in the context of passive or active damping design. The field of composite structures is rich with techniques for analyzing sandwich structures with and without simplifying assumptions, and it is on this body of work that this paper is based. The percentage of modal strain energy in the viscoelastic core is used as the primary measure of the accuracy of different sets of assumptions. Elasticity solutions are available for selected sets of assumptions and boundary conditions, and these solutions provide a basis for some of the preliminary studies. A zig-zag method is used to construct a piecewise continuous displacement field (C1 continuity) that satisfies the appropriate stress continuity between layers in a consistent manner. Finite element analysis provides a versatile way to simulate complicated combinations of boundary conditions, degree of coverage, and kinematic assumptions.

Kinematic assumptions for sandwich beams

Much of the work done on active and passive constrained-layer beams is done with models using kinematic assumptions proposed by Kerwin, Mead and Markus, and others. The key assumption is that the base and constraining layers undergo identical transverse displacements, which is a reasonable assumption when the middle layer (here a viscoelastic material) is thin and the constraining layer is relatively weak. There are, however, many practical cases where an effective passive damping design requires the stiffness of the constraining layer to be on the order of that of the base layer. If the base structure is stiff to begin with, a constraining layer that will produce good damping is likely to violate the above stated assumption by refusing to follow the base layer exactly. The question arises as to how this affects predictions of damping. In this work the facesheets are treated as independently deforming Timoshenko beams, which results in a more general state of strain in the core material. Expressions for the potential and kinetic energies are developed from basic principles of continuum mechanics, and the assumed modes method is used to predict how levels of strain energy in the core are affected by the assumptions on the relative motions of the facesheets.