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A multiscale model is developed for vertically aligned carbon nanotube (CNT)-based membranes that are made for water purification or gas separation. As a consequence of driving fluids through the membranes, they carry stress waves along the fiber direction. Hence, a continuum mixture theory is established for a representative volume element to characterize guided waves propagating in a periodically CNT-reinforced matrix material. The obtained coupled governing equations for the CNT-based composite are found to retain the integrity of the wave propagation phenomenon in each constituent, while allowing them to coexist under analytically derived multiscale interaction parameters. The influence of the mesoscale characteristics on the continuum behavior of the composite is demonstrated by dispersion curves of harmonic wave propagation. Analytically established continuum mixture theory for the CNT-based composite is strengthened by numerical simulations conducted in COMSOL for visualizing mode shapes and wave propagation patterns. [ABSTRACT FROM AUTHOR]

This study focuses on the nonlinear vibration of a small-size beam hosted in a high-speed moving structure. The equation of the beam's motion is derived using the coordinate transformation. The small-size effect is introduced by applying the modified coupled stress theory. The equation of motion involves quadratic and cubic terms due to mid-plane stretching. Discretization of the equation of motion is achieved via the Galerkin method. The impact of several parameters on the non-linear response of the beam is investigated. Bifurcation diagrams are used to investigate the stability of the response, whereas softening/hardening characteristics of the frequency curves are used as an indication of nonlinearity. Results indicate that increasing the magnitude of the applied force tends to signify the nonlinear hardening behavior. In terms of the periodicity of the response, at a lower amplitude of the applied force, the response appears to be a one-period stable oscillation. Increasing the length scale parameter, the response moves from chaotic to period-doubling to the stable one-period response. The impact of the axial acceleration of the moving structure on the stability as well as on the nonlinearity of the response of the beam is also investigated. [ABSTRACT FROM AUTHOR]

This article presents theoretical dynamic analysis of a vibrating axially moving web of a multi-span / multi-roll microcontact printing system and experimental measurements of the system's frequency response. A unique lab-scale microcontact printing machine with high-speed web handling capabilities is used. The axially moving web is modeled as a string and as a membrane. Then, numerical results of both models are compared with experimentally obtained response. The experiment is run for both case of constant axial speed and varying axial speed with time. Although both models are in good agreement with the experimental results, the values of frequencies obtained from the string model are found to be in closer agreement with those obtained from the experimental findings. It is found that increasing the web tension and decreasing the axial web speed increase the system's frequency. [ABSTRACT FROM AUTHOR]

Because leaks tend to form at joints or welds at the intersection of modular pipes, the occurrence of multiple leaks in a long pipeline is possible. In this study, a multiple-leak detection methodology using an acoustic method was adopted. A mathematical model based on using the transfer matrix method for calculating the sound transmission loss in a pipeline with multiple leaks is presented. It was found that one can clearly differentiate the transmission loss spectrum of multiple leaks from that of a single leak. It was also established that one can distinguish the transmission loss spectra of pipes having two or three concurrent leaks. The transmission loss curves further appear to provide useful indications on the level of leaking severity. [ABSTRACT FROM AUTHOR]

Water leaks from pipelines have large economic and ecological impacts. Minimizing water loss from supply pipelines has favorable effects on the environment as well as on energy consumption. This paper aims to understand the effect of the geometry of a leaking crack in a pipe wall by examining fluid flow characteristics, namely pressure and velocity distributions, inside the pipe. Practical observations show that the cause of wall rupture influences the geometry of cracks formed in a pipe wall, impacting aspects such as excessive pressure, corrosion. Knowledge of fluid flow characteristics could help in detecting and identifying leak characteristics at an early stage and assist in improving the energy and resource efficiency of water supply services. An experimental setup is developed to detect water leakage in a pipe when the leak is at an early stage and is difficult to detect by visual inspection. A computational fluid dynamic (CFD) model is developed using the COMSOL software. A comprehensive analysis of the effect of leak geometry on pressure and velocity distributions along the pipe is carried out while considering factors such as different pipe sizes, leak geometries, and steady-state flow conditions. It is observed that both velocity and pressure magnitudes rapidly fluctuate in the vicinity of leaks. Leaking cracks with slot, circle, and square shapes are found to generate distinguishing pressure and velocity distributions along the pipe. Thus, the geometry of the leaking crack and potentially its root cause(s) could be predicted by measuring velocity and pressure distributions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the analysis of bending edge waves travelling in a thick Kirchhoff-type piezoelectric film resting on a Winkler–Fuss foundation. The electromechanical coupling is accounted for in defining flexural rigidities to embrace piezoelectric and dielectric material constants. Dynamics is solved analytically and demonstrated numerically by assuming harmonic wave propagation. It is observed that an increase of the voltage leads to a decrease of the critical velocity, while an increase of the Winkler's constant leads to an increase of the critical velocity. [ABSTRACT FROM AUTHOR]

Research evidence abounds on the effectiveness of micropillar‐based microelectromechanical systems for the detection of a wide variety of ultrasmall biological objects for clinical and non‐clinical applications. However, the standard micropillar‐based sensing platforms rely on a single‐column micropillar with a spot at the tip for binding of objects. Although this long‐standing form has shown immense potential, performance improvement is hindered by the fundamental limits enforced by physical laws. Moreover, the single‐column micropillar has a lower sensing area and is ill‐suited for a simultaneous differential sensing of chemical/biological objects of different mass. Here, we report a new set of nature‐inspired, branched micropillar‐based sensing resonators to address the highlighted issues. The characteristics of the newly proposed branched micropillars are comprehensively examined with three payloads (Bartonella Bacilliformis, Escherichia coli, and Micro magnetic beads). Anchored on the capability of continuum theoretical framework, the mathematical model of the micropillar is formulated through the synthesis of the modified couple stress, the Rayleigh‐Love, and the Timoshenko theories. The finite element method is employed to shed light on the variability of the structures' resonant response under performance reduction factors (payload's rotary inertia, damaged substrate, and density of a surrounding fluid). The results obtained indicate superior performance indicators for the triply‐branched micropillar: enhanced response sensitivity for multiple payloads and less susceptibility to deterioration in resonant frequencies due to fluid immersion. [ABSTRACT FROM AUTHOR]

Polycarbonate (PC) has a wide range of applications in the electronic, transportation, and biomedical industries. In addition, investigation on the applicability to use PC in superstrate photovoltaic modules is ongoing research. In this paper, PC is envisioned to be used as a material for structural components in renewable energy systems. Usually, structural components have geometrical irregularities, i.e., notches, and are subjected to severe mechanical loading. Therefore, the structural integrity of these components shall consider fracture analysis on notched specimens. In this paper, rectangular PC specimens were machined with straight U-notches having different radii and depths. Eight different notch radii with a depth of 6.0 mm were tested. In addition, three notch depths with a radius of 3.5 mm were considered. Quasi-static fracture tests were performed under displacement-controlled loading with a speed of 5 mm/min. Digital image correlation technique was used to capture the strain fields for un-notched and notched specimens. It was assumed that fracture occurs at the onset of necking. The equivalent material concept (EMC) along with the strain energy density criterion (SED) were employed to estimate the fracture load. The EMC-SED combination is shown to be an effective and practical tool for estimating the fracture load of U-notched PC specimens. [ABSTRACT FROM AUTHOR]

Small size (micro/nano)‐scale beams constitute important building blocks of microelectromechanical systems (MEMS)/nanoelectromechanical systems (NEMS). Emerging roll‐based, high rate, manufacturing processes can make these small size‐beams vibrate, while they are axially moving. In this paper, an analytical‐numerical study on the nonlinear transverse vibration of the representative case of axially moving micro‐beam under an electrostatic force is conducted. The analytical model is realized by employing Hamilton's principle together with Galerkin discretization. The method of multiple time‐scales and Runge‐Kutta based numerical scheme are utilized to investigate the nonlinear dynamic behavior of the micro‐beam. Results are obtained for the influence of axial beam velocity and modified couple stress theory length scale parameter (i) on the values of pull‐in instability voltage of the small‐size beam, and (ii) on the small‐size beam nonlinear softening/hardening characteristics. The effect of axial load on the frequency response is investigated. [ABSTRACT FROM AUTHOR]

In this paper, a model for transverse web vibration in a roll-to-roll system is presented. Web axial tension and web axial speed, decisive parameters in the equation of motion that describes web vibration, are rigorously obtained by considering the two rolls-web coupled system's dynamics, coupled with the equation of motion. According to the present analysis, the idealized simply-supported boundary conditions, commonly used in studies on vibrations of axially moving structures are not needed. Instead, a mathematical model comprised of the governing equation of web transverse vibration and the roll angular velocity -- web axial tension relationship is solved as a coupled system. A finite-difference based algorithm is used for solving the coupled system of differential equations. It is worth noting that the web axial speed and web-transmitted tension are not constants when a certain amount of the web material is transferred from the unwinding roll to the winding roll; they vary nonlinearly after a short transient period. The transverse vibration response at selected points on the web span shows higher (lower) frequency fluctuations corresponding to lower (higher) transport axial speed. This behavior is significantly different from that of a vibrating web under constant axial speed and tension. [ABSTRACT FROM AUTHOR]

Presents a study that analyzed the propagation of thermoelastic harmonic waves in bilaminated waveguide in the context of the generalized theory of thermoelasticity. Development of a continuum mixture theory for waves traversing in the direction parallel to the layering; Background on the mechanical and thermal behavior of composite materials in structural applications; Quasi-elastic and quasi-thermal modes for the cases when thermal relaxation time is either included or neglected.

The vibration of an axially moving beam following a slightly curved path was studied. The simply supported beam was travelling axially on a curved frictionless foundation with nonlinear elastic characteristics. The main objective of this work was to investigate the effect of the moving beam path curvature on its vibration, and the effect of different parameters on the system’s dynamic response. These parameters include axial speed, applied tension, and stiffness of the supporting foundation. A Galerkin decomposition approach with four-term truncation accuracy was used to realize a mathematical model that describes the dynamic behavior of the axially moving beam on a slightly curved foundation. Numerical solutions showed that the natural frequency of the axially moving beam travelling on the curved elastic support was higher than that of an axially moving straight beam for all cases considered of different path curvatures and different degrees of support stiffness. Forced vibrations of an axially moving beam on a curved elastic support were also considered under harmonic excitation. Bifurcation diagrams were obtained for the primary resonance excitation using the excitation amplitude as a controlling parameter, while keeping the excitation frequency fixed. It was found that the amplitude–frequency diagram for the axially moving beam on the curved path exhibited many types of bifurcations, including period doubling bifurcation, period four bifurcation and many jumps, compared to that of an axially moving beam resting on a straight elastic support. [ABSTRACT FROM AUTHOR]

Approximate numerical solutions are obtained for the vibration response of a functionally graded (FG) micro-scale beam entrapped within an axially-directed magnetic field using the differential transformation method (DTM). Idealized as a one-dimensional (1D) continuum with a noticeable microstructural effect and a thickness-directed material gradient, the microbeam's behavior is studied under a range of nonclassical boundary conditions. The immanent microstructural effect of the micro-scale beam is accounted for through the modified couple stress theory (MCST), while the microscopic inhomogeneity is smoothened with the classical rule of mixture. The study demonstrates the robustness and flexibility of the DTM in providing benchmark results pertaining to the free vibration behavior of the FG microbeams under the following boundary conditions: (a) Clamped-tip mass; (b) clamped-elastic support (transverse spring); (c) pinned-elastic support (transverse spring); (d) clamped-tip mass-elastic support (transverse spring); (e) clamped-elastically supported (rotational and transverse springs); and (f) fully elastically restrained (transverse and rotational springs on both boundaries). The analyses revealed the possibility of using functional gradation to adjust the shrinking of the resonant frequency to zero (rigid-body motion) as the mass ratio tends to infinity. The magnetic field is noted to have a negligibly minimal influence when the gradient index is lower, but a notably dominant effect when it is higher. [ABSTRACT FROM AUTHOR]

In this paper, guided ultrasonic wave propagation is analyzed in an elastic plate with sinusoidal surface corrugations. The corrugated area acts as a finite-length grating which corresponds to a 1-D phononic crystal (PC). The multiple-scale perturbation technique is used to derive coupled-mode equations describing the amplitudes of interacting modes. These equations are solved exactly for the two-point boundary-value problem of the PC. The study involves the coupling of the incident symmetric Lamb wave S0 to the reflected antisymmetric Lamb wave A0. The influences of the depth of corrugation and length of the PC are studied. Theoretical results are compared with experimental measurements. [ABSTRACT FROM PUBLISHER]

The effect of spatial harmonics of a square-wave surface grating on the multiband frequency response of ultrasonic SH waves in an elastic plate is investigated. Stopbands are found to occur under simultaneous occurrence of first-order and higher-order Bragg resonances together with co-directional and/or contra-directional mode coupling conditions. The odd harmonic nature of the structure causes stopbands to appear above the cutoff frequencies of the odd-numbered modes. The attenuation within stopbands is found to be greatest when all propagating modes are coupled and reflected. The simultaneous resonance conditions for higher order stopbands must contain at least one co-directional mode coupling condition. The analysis is performed according to the multiple scales scheme, leading to the derivation of coupled mode equations, which are solved numerically using the fundamental matrix method. [ABSTRACT FROM AUTHOR]

This study focuses on quantifying the change in phase speed of waves transmitting through periodically undulated plates under pass band interaction. A perturbation technique is used to analyze the transmission of horizontally polarized guided waves in elastic plates with sinusoidal periodicity at their outerfaces. Phase speed of transmitting modes is presented as a function of various parameters, including outerface wavenumber, undulation amplitude, degree of undulations symmetry about the periodically undulated plate midplane, plate average thickness, and frequency of propagation. [ABSTRACT FROM AUTHOR]

Examines the interaction of Rayleigh surface waves with nonuniform periodic corrugation. Use of the method of multiple scales to derive the coupled-mode equations; Presentation of the filter response in terms of reflection coefficient.

Proposes a unified method for screening the ground-transmitted vibrations generated by machine foundations. Formulation of the problem; Straightforward expansion; Method of multiple scales; Numerical examples; Conclusion.

The mode-localization phenomenon is here proposed as a mechanism for suppressing undesired oscillations of trusses. Sample trusses consisting of repeated unit cells are designed to have weak intermediate member(s) in addition to geometric disorders. These irregularities lead to the confinement of motion to a limited part of the structure. The results of a finite-element analysis show the natural frequencies and the relative amplitudes of mode shapes as functions of a disorder parameter. [ABSTRACT FROM AUTHOR]

The interaction of surface gravity waves on a nonuniformly periodic seabed is considered. The method of multiple scales is used to analyze the interaction leading to two coupled-mode equations. The power reflection coefficient is used as an indicator to evaluate the filter action of the bottom corrugation. The results show that the modes are strongly coupled when the Bragg resonant condition is satisfied. The characteristics of the filtration are found to be enhanced by imposing special types of amplitude and phase modulated periodic nonuniformities, including amplitude taper and chirped periodic variations. [ABSTRACT FROM AUTHOR]

A structure with two periodicities can couple up to six modes under a case of simultaneous resonance resulting in a stop-band interaction. The method of multiple scales is employed to analyze the modal coupling in a two-dimensional acoustic duct with rigid periodically undulated walls as well as in an elastic plate having periodically corrugated outerfaces, leading to the coupled-mode equations. The comparison between the three possible cases of interaction under simultaneous resonance are given in terms of the power reflection coefficient spectrum as a function of frequency. The strength of the stop-band interaction is found to be strongly related to the number of direct couplings between the incident and reflected modes. © 1997 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

This study is concerned with the interaction of six torsional modes in a composite axisymmetric waveguide whose interfaces are sinusoidally corrugated in the axial direction. The modes are interacting when two resonant conditions on the codirectional modes and a Bragg condition occur simultaneously. In light of the weakness of the interface corrugations, the perturbation method of multiple scales is used to derive the mode coupling equations. A novel numerical scheme for two-point boundary-value problems is used to solve the coupled amplitude equations. The power reflection coefficient of a filter section is then calculated for the cases of uniform, tapered, and chirped corrugations. An optimal filter is realized by combining both taper and chirp thus producing a nearly ideal characteristics. [ABSTRACT FROM AUTHOR]

A unified method is proposed to suppress duct acoustic waves. According to this method, a circular cylindrical duct is designed to have a geometric periodicity at its wall in order to act as a wave filter. The filter action of the periodic rigid wall is based on the mode coupling occurring under the Bragg condition resulting in a strong stopband interaction. The problem is attacked using the perturbation method of multiple scales, leading to the derivation of the coupled-mode equations. The performance of the duct as a wave attenuator is presented in terms of the reflection coefficient or the transmission loss factor. Due to the nature of the dispersion curves of the cylindrical duct, many modes could share the same stopband. Hence, a multi-mode acoustic filter could be designed over a certain frequency band. This theoretical study might provide a basis for design concepts of acoustic silencers. [ABSTRACT FROM AUTHOR]