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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 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]

The study focuses quantifying the change in phase speed of waves transmitting through periodically undulated plates under pass band interaction. 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.

A unified method is proposed for screening the ground-transmitted vibrations generated by machine foundations. The method is based on the solid-state phenomenon of Bragg resonance, which leads to the fact that periodic shallow trenches are capable of reflecting a considerable amount of wave energy if they are carefully designed to have a tuned periodicity with the propagating modes. The method of multiple scales is used to derive the coupled-mode equations, describing the interaction of propagating waves with the tuned periodic trenches. Reflection coefficients are calculated to evaluate the effectiveness of the trenches in reducing wave amplitudes.

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]

Six orthotropic film Love elastic modes with multiperiodic surface corrugations and their filtering characteristics at 1.813 MHz are investigated. The use of a stop-band filter enables the imposition of amplitude tapers. The pass-band filter which functions as a tuned circuit with very high Q-factor replace piezoelectric crystal in certain devices. The multiple scale method is used to obtain coupled-mode equations.

Mode localization in a periodic multispan column results in the passive control of the buckling of structures. Incorporation of intermediate torsional springs or displaced intermediate supports enables mode localization. Buckled mode shapes reveal the confinement of buckling to specific sections of the column and that the irregularities in the column do not affect the buckling loads.

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]