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eBook Chapter

Publisher: ASME-Wiley

Published: 2021

ISBN: 9781119393405

Abstract

To understand the coupling between the electrical and mechanical properties of piezoelectric continua, we must supplement the discussion of continuum mechanics and linear elasticity presented in Chapter 3 with the review of continuum electrodynamics in this chapter. The fundamental definitions of charge, current, charge density, current density, bound charge density, and free charge density are discussed in Section 4.1. The electric and magnetic fields are introduced in Section 4.2. The dynamic coupling of the electric and magnetic fields is determined by Maxwell’s equations, which are introduced in Section 4.3. The polarization and electric displacement are discussed in Section 4.3.1, while the magnetization and magnetic field intensity are introduced in Section 4.3.2.

Topics:
Electrodynamics

eBook Chapter

Publisher: ASME-Wiley

Published: 2021

ISBN: 9781119393405

Abstract

This front matter contains the Wiley-ASME Press Series, Contents, Foreword, Preface, Acknowledgments, and List of Symbols. It is available for access by clicking on the PDF icon below. eBook keywords: vibrations of linear piezostructures, piezoelectric effect, ferroelectric piezoelectrics, continuum mechanics, elasticity, electrodynamics, variational calculus, applied mathematics, Newton’s method for piezoelectric systems, Hamilton’s principle for piezoelectricity, vibration, modeling methods.

eBook Chapter

Publisher: ASME-Wiley

Published: 2021

ISBN: 9781119393405

Abstract

In the most general terms, a material is piezoelectric if it transforms electrical into mechanical energy, and vice versa, in a reversible or lossless process. This transformation is evident at a macroscopic scale in what are commonly known as the direct and converse piezoelectric effects. The direct piezoelectric effect refers to the ability of a material to transform mechanical deformations into electrical charge. Equivalently, application of mechanical stress to a piezoelectric specimen induces flow of electricity in the direct piezoelectric effect. The converse piezoelectric effect describes the process by which the application of an electrical potential difference across a specimen results in its deformation. The converse effect can also be viewed as how the application of an external electric field induces mechanical stress in the specimen.

eBook Chapter

Publisher: ASME-Wiley

Published: 2021

ISBN: 9781119393405

Abstract

Piezoelectric materials exhibit coupling between their mechanical and electrical properties that is due to asymmetry in the underlying crystalline structure. These materials are anisotropic when considered at a macroscopic, continuum scale: their electrical and mechanical properties depend on direction. For these reasons it is crucial that we develop a mathematical description that is rich enough to characterize how the mechanical and electrical field variables transform with a change in coordinates. Section 2.1 describes how representations of vectors change when we vary the choice of basis. The transformation equations in this section are applicable to physical observables that are represented by vectors such as electric field, electric displacement, polarization, position, velocity, and acceleration. Section 2.2 generalizes this analysis and derives the transformation laws for nth order tensors . The transformation laws in Section 2.2 are applicable to quantities such as the stress tensor, linear strain tensor, and the higher order tensors that appear in the linear piezoelectric constitutive laws in Chapter 5. Section 2.3 discusses how symmetry properties are described in terms of invariance under transformations, and how symmetry considerations manifest in tensor invariance.

eBook Chapter

Publisher: ASME-Wiley

Published: 2021

ISBN: 9781119393405

Abstract

Since piezoelectric materials exhibit coupling between their mechanical and electrical properties, in this chapter we review elementary principles from the foundations of continuum mechanics and linear elasticity. We present the definition of the stress vector τ in a continuum, the corresponding definition of the stress tensor T := T ij g i ⊗ g j , Cauchy’s formula that relates τ and T , and the equilibrium equations in Section 3.1. The definition of the linear strain tensor S ∶= S ij g i ⊗ g j is given in Section 3.2. The definition of the strain energy density, as well as some example calculations of strain energy for specific common structural elements, is the topic of Section 3.3. Generalized Hooke’s law is presented in Section 3.4, which specifies the constitutive laws that are employed in linear elasticity. Finally, a summary of the initial-boundary value problem that underlies the formulation of mechanics for linearly elastic materials is presented in Section 3.5.

Topics:
Continuum mechanics

eBook Chapter

Publisher: ASME-Wiley

Published: 2021

ISBN: 9781119393405

Abstract

Linear piezoelectric materials transform electrical energy into mechanical energy, and vice versa, in a process that is lossless and reversible. This chapter derives the equations that govern linear piezoelectric materials in three dimensions by synthesizing results from continuum mechanics in Chapter 3 and continuum electrodynamics in Chapter 4. Simple physical experiments described in Section 5.1 illustrate how the piezoelectric effect manifests in one spatial dimension. Section 5.1 introduces the constitutive laws of linear piezoelectricity and shows how they can be interpreted as an extension of the Generalized Hooke’s Law of linear elasticity. The rigorous foundations and assumptions that underly the theory of linear piezoelectricity are presented in Section 5.2. The initial-boundary value problem of linear piezoelectricity introduced in Section 5.2 is shown to be a generalization of the initial-boundary value problem of linear elasticity. Section 5.3 explores the diverse forms that the constitutive laws of linear piezoelectricity can take by using arguments based on thermodynamics.

Topics:
Piezoelectricity

eBook Chapter

Publisher: ASME-Wiley

Published: 2021

ISBN: 9781119393405

Abstract

In principle, the three dimensional equations that constitute the initial-boundary value problem discussed in Section 5.2.2 can be solved to understand the coupled electrical and mechanical response of any linearly piezoelectric body. In practice, however, the number of physical systems for which an analytical solution of these equations can be derived is limited owing to their complexity. Some examples of analytical solutions to the initial-boundary value problem, mostly related to piezoelectric plate vibrations, summarized in Section 5.2.2 can be found in references [44, 47, 48]. In this chapter we show how Newton’s laws of motion can be used directly to derive simple models of common piezostructural systems. This approach closely resembles the strategy employed for linearly elastic bodies that is studied in many texts on advanced strength of materials, vibrations, or structural dynamics. See [11] or [29] for a background on these methods as they are applied in vibrations or structural dynamics.

eBook Chapter

Publisher: ASME-Wiley

Published: 2021

ISBN: 9781119393405

Abstract

The equations of motion for the linearly piezoelectric systems studied in Chapters 5 and 6 are derived by carrying out force and moment summations and applying Newton’s laws. For many structural systems it can be advantageous to formulate the governing equations using variational methods. These techniques are one of the standard tools used in the study of the dynamics or vibrations of linearly elastic structural systems, and this chapter discusses their generalization for linearly piezoelectric systems. We begin with a review of the underlying theory of variational methods in Section 7.1.We next review Hamilton’s principle as it is applied to linearly elastic systems in Section 7.2. Hamilton’s principle for linear piezoelectricity is subsequently presented in Section 7.3.

Topics:
Variational techniques

eBook Chapter

Publisher: ASME-Wiley

Published: 2021

ISBN: 9781119393405

Abstract

Chapters 6 and 7 have derived partial differential equations that govern the time evolution of a variety of typical or canonical piezoelectric structures. In each case the unknowns evolve in an infinite dimensional state space of functions. In practical applications we must use approximations of these governing equations to calculate estimates of the system response. In this chapter we describe two of the most common approaches for deriving approximate solutions: modal or eigenfunction techniques and finite element methods. The chapter begins with a discussion of the classical, strong, and weak solutions of the governing equations in Section 8.1. We then discuss Galerkin approximations of the weak form of the governing equations in Section 8.3. Section 8.3.1 reviews how the eigenfunctions of the spatial differential operators that appear in the governing equations can be used as the basis functions in a Galerkin approximation, while Section 8.3.2 details the construction of the approximating basis from simple finite element shape functions. To make the discussions concrete, numerous examples throughout the chapter outline the fundamentals of building approximations for the composite piezoelectric axial rod and beam.

Topics:
Approximation

eBook Chapter

Publisher: ASME-Wiley

Published: 2021

ISBN: 9781119393405

Abstract

Since this book is intended to be self-contained, several chapters introduce fundamental principles that are essential to a formulation of linear piezoelectricity. Chapters 2, 3, and 4 review the requisite background and supporting principles from mathematics, continuum mechanics, and continuum electrodynamics, respectively. In this section we review topics from the study of vibrations of linear structures that are used throughout Chapters 5, 6, 7, and 8. This review is necessarily brief, and a full account can be found in any of the excellent texts on this classical topic in mechanics. See for example [21, 29, 30], or [11].

eBook Chapter

Publisher: ASME-Wiley

Published: 2021

ISBN: 9781119393405

eBook

Vibrations of Linear Piezostructures is an introductory text that offers a concise examination of the general theory of vibrations of linear piezostructures. This important book brings together in one comprehensive volume the most current information on the theory for modeling and analysis of piezostructures. The authors explore the fundamental principles of piezostructures, review the relevant mathematics, continuum mechanics and elasticity, and continuum electrodynamics as they are applied to electromechanical piezostructures, and include the work that pertains to linear constitutive laws of piezoelectricity. The book addresses modeling of linear piezostructures via Newton’s approach and Variational Methods. In addition, the authors explore the weak and strong forms of the equations of motion, Galerkin approximation methods for the weak form, Fourier or modal methods, and finite element methods. This important book: Covers the fundamental developments to vibrational theory for linear piezostructures Provides an introduction to continuum mechanics, elasticity, electrodynamics, variational calculus, and applied mathematics Offers in-depth coverage of Newton’s formulation of the equations of motion of vibrations of piezo-structures Discusses the variational methods for generation of equations of motion of piezo-structures Written for students, professionals, and researchers in the field, Vibrations of Linear Piezostructures is an up-to-date volume to the fundamental development of linear piezoelectricity for vibrations from initial development to fully modeled systems using various methods. This front matter contains the Wiley-ASME Press Series, Contents, Foreword, Preface, Acknowledgments, and List of Symbols. It is available for access by clicking on the PDF icon below. eBook keywords: vibrations of linear piezostructures, piezoelectric effect, ferroelectric piezoelectrics, continuum mechanics, elasticity, electrodynamics, variational calculus, applied mathematics, Newton’s method for piezoelectric systems, Hamilton’s principle for piezoelectricity, vibration, modeling methods. In the most general terms, a material is piezoelectric if it transforms electrical into mechanical energy, and vice versa, in a reversible or lossless process. This transformation is evident at a macroscopic scale in what are commonly known as the direct and converse piezoelectric effects. The direct piezoelectric effect refers to the ability of a material to transform mechanical deformations into electrical charge. Equivalently, application of mechanical stress to a piezoelectric specimen induces flow of electricity in the direct piezoelectric effect. The converse piezoelectric effect describes the process by which the application of an electrical potential difference across a specimen results in its deformation. The converse effect can also be viewed as how the application of an external electric field induces mechanical stress in the specimen. Piezoelectric materials exhibit coupling between their mechanical and electrical properties that is due to asymmetry in the underlying crystalline structure. These materials are anisotropic when considered at a macroscopic, continuum scale: their electrical and mechanical properties depend on direction. For these reasons it is crucial that we develop a mathematical description that is rich enough to characterize how the mechanical and electrical field variables transform with a change in coordinates. Section 2.1 describes how representations of vectors change when we vary the choice of basis. The transformation equations in this section are applicable to physical observables that are represented by vectors such as electric field, electric displacement, polarization, position, velocity, and acceleration. Section 2.2 generalizes this analysis and derives the transformation laws for nth order tensors . The transformation laws in Section 2.2 are applicable to quantities such as the stress tensor, linear strain tensor, and the higher order tensors that appear in the linear piezoelectric constitutive laws in Chapter 5. Section 2.3 discusses how symmetry properties are described in terms of invariance under transformations, and how symmetry considerations manifest in tensor invariance. Since piezoelectric materials exhibit coupling between their mechanical and electrical properties, in this chapter we review elementary principles from the foundations of continuum mechanics and linear elasticity. We present the definition of the stress vector τ in a continuum, the corresponding definition of the stress tensor T := T ij g i ⊗ g j , Cauchy’s formula that relates τ and T , and the equilibrium equations in Section 3.1. The definition of the linear strain tensor S ∶= S ij g i ⊗ g j is given in Section 3.2. The definition of the strain energy density, as well as some example calculations of strain energy for specific common structural elements, is the topic of Section 3.3. Generalized Hooke’s law is presented in Section 3.4, which specifies the constitutive laws that are employed in linear elasticity. Finally, a summary of the initial-boundary value problem that underlies the formulation of mechanics for linearly elastic materials is presented in Section 3.5. To understand the coupling between the electrical and mechanical properties of piezoelectric continua, we must supplement the discussion of continuum mechanics and linear elasticity presented in Chapter 3 with the review of continuum electrodynamics in this chapter. The fundamental definitions of charge, current, charge density, current density, bound charge density, and free charge density are discussed in Section 4.1. The electric and magnetic fields are introduced in Section 4.2. The dynamic coupling of the electric and magnetic fields is determined by Maxwell’s equations, which are introduced in Section 4.3. The polarization and electric displacement are discussed in Section 4.3.1, while the magnetization and magnetic field intensity are introduced in Section 4.3.2. Linear piezoelectric materials transform electrical energy into mechanical energy, and vice versa, in a process that is lossless and reversible. This chapter derives the equations that govern linear piezoelectric materials in three dimensions by synthesizing results from continuum mechanics in Chapter 3 and continuum electrodynamics in Chapter 4. Simple physical experiments described in Section 5.1 illustrate how the piezoelectric effect manifests in one spatial dimension. Section 5.1 introduces the constitutive laws of linear piezoelectricity and shows how they can be interpreted as an extension of the Generalized Hooke’s Law of linear elasticity. The rigorous foundations and assumptions that underly the theory of linear piezoelectricity are presented in Section 5.2. The initial-boundary value problem of linear piezoelectricity introduced in Section 5.2 is shown to be a generalization of the initial-boundary value problem of linear elasticity. Section 5.3 explores the diverse forms that the constitutive laws of linear piezoelectricity can take by using arguments based on thermodynamics. In principle, the three dimensional equations that constitute the initial-boundary value problem discussed in Section 5.2.2 can be solved to understand the coupled electrical and mechanical response of any linearly piezoelectric body. In practice, however, the number of physical systems for which an analytical solution of these equations can be derived is limited owing to their complexity. Some examples of analytical solutions to the initial-boundary value problem, mostly related to piezoelectric plate vibrations, summarized in Section 5.2.2 can be found in references [44, 47, 48]. In this chapter we show how Newton’s laws of motion can be used directly to derive simple models of common piezostructural systems. This approach closely resembles the strategy employed for linearly elastic bodies that is studied in many texts on advanced strength of materials, vibrations, or structural dynamics. See [11] or [29] for a background on these methods as they are applied in vibrations or structural dynamics. The equations of motion for the linearly piezoelectric systems studied in Chapters 5 and 6 are derived by carrying out force and moment summations and applying Newton’s laws. For many structural systems it can be advantageous to formulate the governing equations using variational methods. These techniques are one of the standard tools used in the study of the dynamics or vibrations of linearly elastic structural systems, and this chapter discusses their generalization for linearly piezoelectric systems. We begin with a review of the underlying theory of variational methods in Section 7.1.We next review Hamilton’s principle as it is applied to linearly elastic systems in Section 7.2. Hamilton’s principle for linear piezoelectricity is subsequently presented in Section 7.3. Chapters 6 and 7 have derived partial differential equations that govern the time evolution of a variety of typical or canonical piezoelectric structures. In each case the unknowns evolve in an infinite dimensional state space of functions. In practical applications we must use approximations of these governing equations to calculate estimates of the system response. In this chapter we describe two of the most common approaches for deriving approximate solutions: modal or eigenfunction techniques and finite element methods. The chapter begins with a discussion of the classical, strong, and weak solutions of the governing equations in Section 8.1. We then discuss Galerkin approximations of the weak form of the governing equations in Section 8.3. Section 8.3.1 reviews how the eigenfunctions of the spatial differential operators that appear in the governing equations can be used as the basis functions in a Galerkin approximation, while Section 8.3.2 details the construction of the approximating basis from simple finite element shape functions. To make the discussions concrete, numerous examples throughout the chapter outline the fundamentals of building approximations for the composite piezoelectric axial rod and beam. Since this book is intended to be self-contained, several chapters introduce fundamental principles that are essential to a formulation of linear piezoelectricity. Chapters 2, 3, and 4 review the requisite background and supporting principles from mathematics, continuum mechanics, and continuum electrodynamics, respectively. In this section we review topics from the study of vibrations of linear structures that are used throughout Chapters 5, 6, 7, and 8. This review is necessarily brief, and a full account can be found in any of the excellent texts on this classical topic in mechanics. See for example [21, 29, 30], or [11]. This back matter contains the Bibliography and Index.

Proceedings Papers

*Proc. ASME*. SMASIS2020, ASME 2020 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, V001T03A002, September 15, 2020

Paper No: SMASIS2020-2225

Abstract

Structure-Borne Traveling Waves (SBTWs) have significant promise as a means of underwater propulsion, drag reduction, and solid-state motion. However, there is poor understanding of how to tailor SBTWs favorable for these applications. This study establishes guidelines and a straight-forward method for generating favorable SBTWs on two-dimensional (2D) surfaces. SBTWs are a novel traveling wave generation method that take advantage of a surface’s inherent structural properties (i.e. mode shapes and natural frequencies). Due to this novel mechanism, SBTWs have significant advantages over other traveling wave methods. This includes active variability (propagation direction, frequency, wavelength), no reliance on complex control mechanisms, and a minimal actuation footprint (small size and weight). SBTWs utilize the two-mode excitation method, whereby a surface is harmonically excited at two locations with a phase offset between them. Due to the phase offset, participating mode shapes superimpose to yield steady-state traveling waves that do not reflect at the boundaries. A SBTW at a given frequency has an optimal phase offset that maximizes the quality; however, high quality does not ensure favorability for a specific application. For propulsion and solid-state motion applications, favorable SBTWs are those that have a uniform propagation direction and consistent amplitude. Using a previously validated electro-mechanical model of a 2D plate, this study demonstrates the generation of SBTWs favorable for such applications. It is shown that the frequency bandwidth can be divided into regions, and each region is classified as generating favorable or unfavorable SBTWs. The favorability of each region is defined by which mode shapes participate. Two guidelines are established that define which combinations of mode shapes yield favorable SBTWs. These guidelines are fundamental in nature, implying that they can be extended to generate favorable SBTWs on any thin-walled surface. This signifies that geometries with tailored SBTWs can be designed to target specific applications (e.g. underwater propulsion, drag reduction, and solid-state motion).

Proceedings Papers

*Proc. ASME*. SMASIS2020, ASME 2020 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, V001T05A010, September 15, 2020

Paper No: SMASIS2020-2334

Abstract

Motivated by its success as a structural health monitoring solution, electromechanical impedance measurements have been utilized as a means for non-destructive evaluation of conventionally and additively manufactured parts. In this process, piezoelectric transducers are either directly embedded in the part under test or bonded to its surface. While this approach has proven to be capable of detecting manufacturing anomalies, instrumentation requirements of the parts under test have hindered its wide adoption. To address this limitation, indirect electromechanical impedance measurement, through instrumented fixtures or testbeds, has recently been investigated for part authentication and non-destructive evaluation applications. In this work, electromechanical impedance signatures obtained with piezoelectric transducers indirectly attached to the part under test, via an instrumented fixture, are numerically investigated. This aims to better understand the coupling between the instrumented fixture and the part under test and its effects ON sensitivity to manufacturing defects. For this purpose, numerical models are developed for the instrumented fixture, the part under test, and the fixture/part assembly. The frequency-domain spectral element method is used to obtain numerical solutions and simulate the electromechanical impedance signatures over the frequency range of 10–50 kHz. Criteria for selecting the frequency range that is most sensitive to defects in the part under test are proposed and evaluated using standard damage metric definitions. It was found that optimal frequency ranges can be preselected based on the fixture design and its dynamic response.

Proceedings Papers

*Proc. ASME*. SMASIS2018, Volume 1: Development and Characterization of Multifunctional Materials; Modeling, Simulation, and Control of Adaptive Systems; Integrated System Design and Implementation, V001T03A026, September 10–12, 2018

Paper No: SMASIS2018-8135

Abstract

Dispersion relations describe the frequency-dependent nature of elastic waves propagating in structures. Experimental determination of dispersion relations of structural components, such as the floor of a building, can be a tedious task, due to material inhomogeneity, complex boundary conditions, and the physical dimensions of the structure under test. In this work, data-driven modeling techniques are utilized to reconstruct dispersion relations over a predetermined frequency range. The feasibility of this approach is demonstrated on a one-dimensional beam where an exact solution of the dispersion relations is attainable. Frequency response functions of the beam are obtained numerically over the frequency range of 0–50kHz. Data-driven dynamical model, constructed by the vector fitting approach, is then deployed to develop a state-space model based on the simulated frequency response functions at 16 locations along the beam. This model is then utilized to construct dispersion relations of the structure through a series of numerical simulations. The techniques discussed in this paper are especially beneficial to such scenarios where it is neither possible to find analytical solutions to wave equations, nor it is feasible to measure dispersion curves experimentally. In the present work, actual experimental data is left for future work, but the complete framework is presented here.

Proceedings Papers

*Proc. ASME*. SMASIS2018, Volume 1: Development and Characterization of Multifunctional Materials; Modeling, Simulation, and Control of Adaptive Systems; Integrated System Design and Implementation, V001T03A030, September 10–12, 2018

Paper No: SMASIS2018-8147

Abstract

Elastic meta-structures, with wave propagation control capabilities, have been widely investigated for mechanical vibrations suppression and acoustics attenuation applications. Periodic architected lattices, combined with mechanical or electromechanical resonators, are utilized to form frequency bands over which the propagation of elastic waves is forbidden, known as bandgaps. The characteristics of these bandgaps, in terms of frequency range and bandwidth, are determined by the local resonators as well as characteristics of the individual cells out of which the structure is composed. In this study, the effectiveness of local stress fields as a tool for bandgap tuning in active, elastic meta-structures is investigated. A finite beam undergoing axial and flexural deformations, with a spatially periodic axial loads acting on it, is chosen to demonstrate the concept. The beam is first divided into several sections where localized stress-fields are varied periodically. Lateral and longitudinal deformations of the beam are described, respectively, by the Timoshenko beam theory and the Elementary rod theory. The Frequency-domain Spectral Element Method is then employed to calculate the forced-vibration response of the structure. The effects of the local state-of-stress on the width and frequency of the resulting bandgaps are investigated.

Proceedings Papers

Charles M. Tenney, Vijaya V. N. Sriram Malladi, Patrick F. Musgrave, Christopher B. Williams, Pablo A. Tarazaga

*Proc. ASME*. SMASIS2018, Volume 1: Development and Characterization of Multifunctional Materials; Modeling, Simulation, and Control of Adaptive Systems; Integrated System Design and Implementation, V001T04A022, September 10–12, 2018

Paper No: SMASIS2018-8189

Abstract

Steady-state traveling waves in structures have been previously investigated for a variety of purposes including propulsion of objects and agitation of a surrounding medium. In the field of additive manufacturing, powder bed fusion (PBF) is a commonly used process that uses heat to fuse regions of metallic or polymer powders within a loose bed. PBF processes require post-process removal of loose powder, which can be difficult when blind holes or complex internal geometry are present in the fabricated part. Here, a preliminary investigation of a simple part is conducted examining the use of traveling waves for post-process de-powdering of additively manufactured specimens. The generation of steady-state traveling waves in a structure is accomplished through excitation at a frequency between two adjacent resonant frequencies of the structure, resulting in two-mode excitation. This excitation can be generated by bonded piezoceramic elements actuated by a sinusoidal voltage signal. The response of the structure is affected by the parameters of the excitation, such as the particular frequency of the voltage signal, the placement of the piezoceramic actuators, and the phase difference in the signals applied to different actuators. Careful selection of these parameters allows adjustment of the quality, wavelength, and wave speed of the resulting traveling waves. In this work, open-top rectangular box specimens composed of sintered nylon powder and coated with fine sand are used to represent freshly fabricated parts yet-to-be cleaned of un-sintered powder. Steady-state traveling waves are excited in the specimens while variations in the frequency content and phase differences between actuation points of the excitation are used to affect the characteristics of the dynamic response. The effectiveness of several response types for the purpose of moving un-sintered nylon powder within the specimens is investigated.

Proceedings Papers

Charles Tenney, Mohammad I. Albakri, Joseph Kubalak, Logan D. Sturm, Christopher B. Williams, Pablo A. Tarazaga

*Proc. ASME*. SMASIS2017, Volume 1: Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Bioinspired Smart Materials and Systems; Energy Harvesting; Emerging Technologies, V001T08A009, September 18–20, 2017

Paper No: SMASIS2017-3856

Abstract

The flexibility offered by additive manufacturing (AM) technologies to fabricate complex geometries poses several challenges to non-destructive evaluation (NDE) and quality control (QC) techniques. Existing NDE and QC techniques are not optimized for AM processes, materials, or parts. Such lack of reliable means to verify and qualify AM parts is a significant barrier to further industrial adoption of AM technologies. Electromechanical impedance measurements have been recently introduced as an alternative solution to detect anomalies in AM parts. With this approach, piezoelectric wafers bonded to the part under test are utilized as collocated sensors and actuators. Due to the coupled electromechanical characteristics of piezoelectric materials, the measured electrical impedance of the piezoelectric wafer depends on the mechanical impedance of the part under test, allowing build defects to be detected. This paper investigates the effectiveness of impedance-based NDE approach to detect internal porosity in AM parts. This type of build defects is uniquely challenging as voids are normally embedded within the structure and filled with unhardened model or supporting material. The impact of internal voids on the electromechanical impedance of AM parts is studied at several frequency ranges.

Proceedings Papers

*Proc. ASME*. SMASIS2017, Volume 2: Modeling, Simulation and Control of Adaptive Systems; Integrated System Design and Implementation; Structural Health Monitoring, V002T05A004, September 18–20, 2017

Paper No: SMASIS2017-3858

Abstract

Current acoustoelastic-based stress measurement techniques operate at the high-frequency, weakly-dispersive portions of the dispersion curves. The weak dispersive effects at such high frequencies allow the utilization of time-of-flight measurements to quantify the effects of stress on wave speed. However, this comes at the cost of lower sensitivity to the state-of-stress of the structure, and hence calibration at a known stress state is required to compensate for material and geometric uncertainties in the structure under test. In this work, the strongly-dispersive, highly stress-sensitive, low-frequency flexural waves are utilized for stress measurement in structural components. A new model-based technique is developed for this purpose, where the acoustoelastic theory is integrated into a numerical optimization algorithm to analyze dispersive waves propagating along the structure under test. The developed technique is found to be robust against material and geometric uncertainties. In the absence of calibration experiments, the robustness of this technique is inversely proportional to the excitation frequency. The capabilities of the developed technique are experimentally demonstrated on a long rectangular beam, where reference-free, un-calibrated stress measurements are successfully conducted.

Proceedings Papers

*Proc. ASME*. SMASIS2015, Volume 1: Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems, V001T03A021, September 21–23, 2015

Paper No: SMASIS2015-9020

Abstract

The focus of this study is to understand traveling wave generation and propagation in reduced order 2D plate models. A plate with all clamped (C-C-C-C) boundary conditions was selected to be the medium through which the wave propagation occurs. The plate is excited at multiple locations by point forces which generates controlled oscillations resulting in net traveling waves. A finite element model is developed and the traveling wave response is simulated. The numerical model is complex with a large number of degrees-of-freedom making a parametric study computationally intensive. In order to overcome this computational burden, balanced truncation based and interpolation-based model reduction techniques are employed to reduce the total number of degrees-of-freedom. The capabilities of these reduction techniques to capture the steady-state frequency-domain characteristics and the steady-state time-domain response have been compared in this paper.