ABSTRACT
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
Resonant elements can generate small amounts of energy that make them pertinent for feeding miniaturized accelerometers with the energy needed. Suitable oscillator candidates are Helmholtz resonators, which have been, for a long time, analyzed and designed within the context of linear vibration. This study focuses on extracting nonlinear characteristics of a dual Helmholtz resonator (HR), with a neck-cavity-neck-cavity configuration, mounted on an acoustic waveguide with harmonically oscillating pressure. The mathematical model used for describing the resonator embraces inherent nonlinear air stiffness and the damping nonlinearity of hydrodynamic origin. Numerical solutions for the resonator's nonlinear oscillations are obtained. Bifurcation diagrams are produced, indicating that the dual HR behaves in a deterministic fashion within the engineering practical limits. Phase portraits are drawn for the system, showing a quasi-periodic motion. Frequency response curves (FRC) are found to shift to the left at the lower resonant frequency indicating a softening behavior. FRC keep generally symmetric curves at the higher resonant frequency indicating a mostly linear behavior.
ABSTRACT
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
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
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.