Coupled mode theory for nonlinear piezoelectric plate vibrations

Coupled-mode equations were developed for thickness-longitudinal vibrations of piezoelectric plate resonators. The equations describe the resonator as a parametrically excited nonlinear vibrational system with two degrees of freedom. Thus one can examine the behavior of piezoelectric resonators from a nonlinear dynamic point of view. In the present paper the derivation of the equations is given. As an example of the application of the equations, the behavior of the resonator in the vicinity of primary resonance is discussed. The method of multiple scales is used to solve the coupled-mode equations. An experiment which verises the amplitude-driving voltage relation predicted by the theory is conducted for LiNbO(3) resonators.     

Coupled hygro-thermo-viscoelastic fracture theory

A coupled hygro-thermo-viscoelastic fracture theory is developed for quasi-static and dynamic crack propagation in viscoelastic materials subject to combined mechanical loading and hygrothermal environmental exposure based on fundamental principles of thermodynamics. The Helmholtz free energy is taken to be a functional of the histories of strain, temperature and fluid concentration with the crack parameter being introduced as an internal state variable. A thermodynamically consistent time-dependent fracture criterion for crack propagation in the presence of thermally and mechanically assisted fluid transport is obtained from the global energy balance equation and the requirement of non-negativity of the global energy dissipation rate, which is generally applicable to both quasi-static and dynamic loading and both isothermal/isohumidity and non-isothermal/non-isohumidity conditions with classic fracture criteria as special cases. On the basis of the developed theory, the generalized energy release rate method, the generalized contour integral method and the extended essential work of fracture method are proposed for fracture characterization of load-carrying viscoelastic materials in hygrothermal environments, and the interrelation of these methods and their correlation with conventional methods and existing models, simulations and experiments are discussed.     

Limitations to the large strain theory

In the formulation of a large strain problem, the Euler–Cauchy–Stokes decomposition and the Eulerian objective stress and strain rates used for the formulation of the problem are actually applicable only for some special cases and are not suitable for general large strain and rotation rates. In this paper, the limitations and applicabilities of the conventional large strain formulation under various deformation cases will be studied.     

Coupled theory of thermoelastic plates

Summary In this paper the coupled thermoelastic theory of a thin plate is discussed. Using a perturbation method, the free vibration frequencies of plates under various boundary conditions are found. Furthermore, a solution is given for the problem of a generally loaded thermoelastic plate and thermoelastic dissipations are shown.

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Gekoppelte thermoelastische Plattentheorie

Zusammenfassung In dieser Arbeit wird die gekoppelte thermoclastische Theorie einer dünnen Platte untersucht. Unter Verwendung einer Störungsmethode werden die Frequenzabweichungen der freien Schwingungen einer Platte mit verschiedenen Randbedingungen errechnet. Weiter wird eine Lösung des Problems einer allgemein belasteten Platte angegeben.

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This research is based on a dissertation for the degree of Doctor Engineering Science at The Technical University of Istanbul. The dissertation was supported by the Scientific and Technical Research Council of Turkey.     

Coupled magnetoelastic theory of magnetic and magnetostrictivehysteresis

It is demonstrated that hysteresis in the magnetostriction k is coupled to hysteresis in the magnetization M because of the dependence of the magnetostriction on the magnetization. At the same time, when stress is present, the magnetization is in turn coupled to the behavior of the part of the magnetostriction associated with domain moment rotation. An expression for the magnetostriction is formulated, and numerical modeling results for magnetostriction hysteresis are compared to experimental results. Although some features of the magnetostriction in iron and steel still need additional explanation, the main features of the magnetostriction are accounted for. These include liftoff (failure of the magnetostriction to return to its value in the demagnetized state as the hysteresis loop is cycled) and a magnetostriction increase after flux density B reaches its maximum and starts to decrease. A macromagnetic, multidomain formulation that yields zero magnetostriction in the demagnetized specimen is used     

The radiation mode theory in ultrasonics

This paper describes the history and the state of the art in radiation mode theory (RMT) in ultrasonics. The RMT originates from electromagnetism in which it has proved to be very efficient in the field of wave guides and discontinuities. In ultrasonics, the RMT made its entrance only a decade ago and has already proved to be very efficient in describing the interaction of sound with discontinuities such as a step on a plate, a liquid wedge, the extremity of a plate and much more. It is likely that the development of the RMT for two-dimensional (2-D) isotropic media has come almost to an end. This paper lists the results obtained so far. Further extensions to more complicated media are to be expected in the coming decade.     

On the applicability of tension field theory to a wrinkling instability problem

Summary The wrinkling instability of a pre-stressed annular membrane loaded uniformly along its inner boundary is investigated with the help of a tension field theory. The theoretical solution is shown to capture the essential qualitative features involved in axisymmetric wrinkling, but displays several limitations regarding the quantitative aspects of this issue. The relationship with some related experimental work reported recently in the literature is also discussed.     

Microcontact Printing: Limitations and Achievements

Microcontact printing (µCP) offers a simple and low‐cost surface patterning methodology with high versatility and sub‐micrometer accuracy. The process has undergone a spectacular evolution since its invention, improving its capability to form sub‐100 nm SAM patterns of various polar and apolar materials and biomolecules over macroscopic areas. Diverse development lines of µCP are discussed in this work detailing various printing strategies. New printing schemes with improved stamp materials render µCP a reproducible surface‐patterning technique with an increased pattern resolution. New stamp materials and PDMS surface‐treatment methods allow the use of polar molecules as inks. Flat elastomeric surfaces and low‐diffusive inks push the feature sizes to the nanometer range. Chemical and supramolecular interactions between the ink and the substrate increase the applicability of the µCP process.     

Limitations of the lattice matching theory in predicting GaAs/BeO epitaxy

The atomic arrangements of the GaAs (100) and (111) planes have been compared for fit to the BeO (000$\text{1}$), (10$\text{1}$0), (20$\text{2}$1), (10$\text{1}$1), (10$\text{1}$2), (1$\text{2}$10), (1$\text{2}$11), (1$\text{2}$12) and (1$\text{2}$14) planes. Lattice matching was calculated on both a 1:1 basis and a multiple atom basis for two perpendicular directions in the plane of the film. A figure of merit, formally similar to the elastic strain energy, was defined and used to rank the BeO planes in order of fit to the GaAs planes. Comparison with experimental data subsequently available demonstrated that lattice matching was of relatively little value in predicting the epitaxial relationships observed in the GaAs/BeO system. It was indeed misleading, for some predicted (low mismatch) orientations are not observed whereas some observed orientations have a large mismatch.     

On the applicability of orthotropic fracture theory to the fracture of CFRP laminates

The digital birefringent-coating (DBC) system and finite element method (FEM) were used to study the fracture behavior for laminates of carbonfiber reinforced plastics (CFRPs) containing a central crack. Different crack orientations in different unidirectionally reinforced specimens were tested. The results show that the orthotropic fracture theory cannot adequately describe the fracture behavior of the CFRP laminates. There-fore, the widely used orthotropic fracture theory needs to be re-examined in detail.     

Limitations and possible extensions to a nonlinear finite element shell-of-revolution model based on Reissner's shell theory

A finite element nonlinear shell model has been developed using Reissner's symmetrically loaded shell-of-revolution theory. This model is capable of modelling nonlinear strains, large rotations and nonlinear materials. This paper discusses the limitations of this model by deriving the basic equations and describing the simplifying assumptions used in the theory and the model. Possible extensions of the model are discussed also.     

Consensus building in linguistic failure mode and effect analysis: A perspective based on prospect theory

As one of many scientific and efficient risk assessment approaches, failure mode and effect analysis (FMEA) has been widely applied across various fields. There are two core issues in the FMEA approach: identifying the latent failure modes of the systems, products, processes and services and the risk assessment and the prioritization of those failure modes. Then, corrective measures must be taken in a timely and accessible manner to prevent the occurrence of failure modes with higher risk levels. In practice, several FMEA members from different fields are usually involved in the FMEA implementation process; the risk assessment information given by them may vary greatly. Therefore, it is necessary to integrate a consensus-building process into FMEA. Meanwhile, the psychological behaviours of FMEA members have had a great impact on the final prioritization of failure modes. Prospect theory is an effective approach for describing individual psychological behaviours. Therefore, this paper presents a novel linguistic FMEA approach to address the consensus issue from the perspective of prospect theory. In the proposed linguistic FMEA approach, a consensus measurement approach based on prospect theory is constructed. Then, a novel feedback adjustment mechanism is designed in which FMEA members can adjust not only their assessment information but also their reference points to achieve an acceptable consensus degree. Eventually, a practical application is used to show the validity and applicability of the proposed linguistic FMEA approach.     

Ferroelectric-HTSC Microwave Structures: Fundamental Limitations

Frequency-tunable microwave devices utilizing ferroelectric/HTSC multilayer structures, in which the dielectric constant of the nonlinear dielectric is varied by application of an electric field, have been demonstrated. Significant problems related to losses in the dielectrics have been shown to lead to not insignificant insertion losses in many cases, and fundamental limitations related to these losses are discussed in this paper. Intrinsic and extrinsic losses are described in detail, and some suggestions for reducing these losses are given.     

Open-Ended Coaxial Probe: Model Limitations

We propose a procedure to determine the validity range of any empirical model of the open-ended coaxial probe transition that is used to measure the permittivity of materials. The procedure is illustrated by an application of the method to a standard coaxial cable probe, a permittivity range of interest in the food industry and, as an empirical model, the well-known “lumped capacitor model.”      

Coupled meshfree and fractal finite element method for mixed mode two‐dimensional crack problems

This paper presents a coupling technique for integrating the element‐free Galerkin method (EFGM) with the fractal finite element method (FFEM) for analyzing homogeneous, isotropic, and two‐dimensional linear‐elastic cracked structures subjected to mixed‐mode (modes I and II) loading conditions. FFEM is adopted for discretization of the domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprise both the EFG and the finite element (FE) shape functions, satisfies the consistency condition thus ensuring convergence of the proposed coupled EFGM–FFEM. The proposed method combines the best features of EFGM and FFEM, in the sense that no special enriched basis functions or no structured mesh with special FEs are necessary and no post‐processing (employing any path independent integrals) is needed to determine fracture parameters, such as stress‐intensity factors (SIFs) and T‐stress. The numerical results show that SIFs and T‐stress obtained using the proposed method are in excellent agreement with the reference solutions for the structural and crack geometries considered in the present study. Also, a parametric study is carried out to examine the effects of the integration order, the similarity ratio, the number of transformation terms, and the crack length to width ratio on the quality of the numerical solutions. A numerical example on mixed‐mode condition is presented to simulate crack propagation. As in the proposed coupled EFGM–FFEM at each increment during the crack propagation, the FFEM mesh (around the crack tip) is shifted as it is to the new updated position of the crack tip (such that FFEM mesh center coincides with the crack tip) and few meshless nodes are sprinkled in the location where the FFEM mesh was lying previously, crack‐propagation analysis can be dramatically simplified. Copyright © 2010 John Wiley & Sons, Ltd.     

Limits of applicability of the theory of a single-phase boundary layer using conditions of free-convective frosting

The conditions of applicability of the approximation of a single-phase boundary layer with the formation of a condensate in the form of frost on a vertical flat surface are determined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 2, pp. 222–226, August, 1988.     

Scalar diffraction theory approach to estimating multimode-waveguide field-amplitude mode distributions

We introduce a method to estimate the coupling coefficients of the guided field amplitude and the corresponding angular bandwidth in a multimode slab waveguide. This scalar diffraction theory approach is simpler than the more rigorous electromagnetic treatment and is directly applicable to communications systems that use large (dimensions or numerical aperture) waveguides, as in substrate-mode interconnects. Moreover, this method provides conceptual insight as to a parameter's effect on the field-amplitude mode distribution and angular bandwidth.     

Cost-benefit analysis of road safety measures: applicability and controversies

This paper discusses the applicability of cost-benefit analysis as an aid to policy making for road safety measures. A framework for assessing the applicability of cost-benefit analysis is developed. Five main types of criticism of cost-benefit analysis are identified: 1. rejecting the basic principles of cost-benefit analysis as not applicable to road safety, 2. excluding some types of issues from the scope of calculation of costs and benefits, 3. setting policy objectives that are not amenable to cost-benefit analysis, 4. rejecting the need for maintaining a separation between policy objectives and policy programmes as required for cost-benefit analysis, and 5. rejecting, or denying the possibility of ever obtaining, acceptably valid and reliable economic valuations of the consequences of alternative policy programmes. It is concluded that rejecting the basic principles of cost-benefit analysis is a difficult position to defend, since these principles are simply a re-statement in economic terms of very general principles of rational choice. These principles are part of the normative basis of all formal techniques designed to aid policy making as well as the democratic system of government. Everybody, including those who advocate the use of cost-benefit analysis, agree that some issues are unsuitable for cost-benefit analysis, in particular those that involve basic human rights and fairness in distribution. There may, however, be disagreement with respect to the perception of a specific policy issue in terms of whether it is mainly about rights and fairness or mainly about the effective use of policy instruments to solve a social problem. Politicians may be tempted to set policy objectives that are ill suited for cost-benefit analysis, but this does not imply that cost-benefit analysis makes unreasonable assumptions. Perhaps the most important issue for the applicability of cost-benefit analysis is whether people in general have sufficiently well ordered preferences for economic valuations based on these preferences to make sense.     

Characteristic mode theory of coupled waveguide arrays with periodically varying properties

A method is presented for determining the eigenvalues and eigenvectors (characteristic mode shapes) for coupled waveguide arrays in which the interguide coupling is uniform but where the dephasing varies periodically from guide to guide. It is demonstrated that if the dephasing alternates from guide to guide, a quadratic equation must be solved for the eigenvalues, whatever the number of guides. For dephasing functions of larger period, the eigenvalue equation is of correspondingly higher order. The effect of such functions is to insert additional band gaps into the eigenvalue distribution and to couple together spatial harmonics. Numerical examples illustrating the method are presented where relevant.