Nonlinear modal interactions in clamped-clamped mechanical resonators

A theoretical and experimental investigation is presented on the intermodal coupling between the flexural vibration modes of a single clamped-clamped beam. Nonlinear coupling allows an arbitrary flexural mode to be used as a self-detector for the amplitude of another mode, presenting a method to measure the energy stored in a specific resonance mode. Experimentally observed complex nonlinear dynamics of the coupled modes are quantitatively captured by a model which couples the modes via the beam extension; the same mechanism is responsible for the well-known Duffing nonlinearity in clamped-clamped beams.Comment: 5 pages, 3 figure

Effect of Boundary Constraints on the Nonlinear Flapping of Filaments Animated by Follower Forces

Elastically driven filaments subjected to animating compressive follower forces provide a synthetic way to mimic the oscillatory beating of active biological filaments such as eukaryotic cilia. The dynamics of such active filaments can, under favorable conditions, exhibit stable time-periodic responses that result due to the interplay of elastic buckling instabilities, geometric constraints, boundary conditions, and dissipation due to fluid drag. In this paper, we use a continuum elastic rod model to estimate the critical follower force required for the onset of the stable time-periodic flapping oscillations in pre-stressed rods subjected to fluid drag. The pre-stress is generated by imposing either clamped-clamped or clamped-pinned boundary constraints and the results are compared with those of clamped-free case, which is without pre-stress. We find that the critical value increases with the initial slack--that quantifies the pre-stress, and strongly depends on the type of the constraints at the boundaries. The frequency of oscillations far from the onset, however, depends primarily on the magnitude of the follower force, not on the boundary constraints. Interestingly, oscillations for the clamped-pinned case are observed only when the follower forces are directed towards the clamped end. This finding can be exploited to design a mechanical switch to initiate or quench the oscillations by reversing the direction of the follower force or altering the boundary conditions

Magnetomotive drive and detection of clamped-clamped mechanical resonators in water

We demonstrate magnetomotive drive and detection of doubly clamped string resonators in water. A compact 1.9 T permanent magnet is used to detect the fundamental and higher flexural modes of $\mathrm{200 \mu m}$ long resonators. Good agreement is found between the magnetomotive measurements and optical measurements performed on the same resonator. The magnetomotive detection scheme can be used to simultaneously drive and detect multiple sensors or scanning probes in viscous fluids without alignment of detector beams.Comment: 4 pages, 3 figure

Compressive failure of thick-section composite laminates with and without cutouts subjected to biaxial loading

The composites studied are fiber composite laminate plates made of carbon fibers and a thermoplastic matrix material. Tests and results are given for: the solution convergence for transverse shear in a clamped plate without cutout under compression; the effects of cutout and laminate thickness on maximum shear in buckling and postbuckling response of a clamped plate under biaxial compression; the effects of cutout and laminate thickness on maximum shear in buckling and postbuckling response of a clamped plate under biaxial compression; and the effects of laminate thickness and cutout of the lowest three eigenvalues of a clamped plate under biaxial compression. Additional test results are given

Acoustic plane waves incident on an oblique clamped panel in a rectangular duct

The theory of acoustic plane waves incident on an oblique clamped panel in a rectangular duct was developed from basic theoretical concepts. The coupling theory between the elastic vibrations of the panel (plate) and the oblique incident acoustic plane wave in infinite space was considered in detail, and was used for the oblique clamped panel in the rectangular duct. The partial differential equation which governs the vibrations of the clamped panel (plate) was modified by adding to it stiffness (spring) forces and damping forces. The Transmission Loss coefficient and the Noise Reduction coefficient for oblique incidence were defined and derived in detail. The resonance frequencies excited by the free vibrations of the oblique finite clamped panel (plate) were derived and calculated in detail for the present case

Harmonic-seeded remote laser emissions in N2-Ar, N2-Xe and N2-Ne mixtures: a comparative study

We report on the investigation on harmonic-seeded remote laser emissions at 391 nm wavelength from strong-field ionized nitrogen molecules in three different gas mixtures, i.e., N2-Ar, N2-Xe and N2-Ne. We observed a decrease in the remote laser intensity in the N2-Xe mixture because of the decreased clamped intensity in the filament; whereas in the N2-Ne mixture, the remote laser intensity slightly increases because of the increased clamped intensity within the filament. Remarkably, although the clamped intensity in the filament remains nearly unchanged in the N2-Ar mixture because of the similar ionization potentials of N2 and Ar, a significant enhancement of the lasing emission is realized in the N2-Ar mixture. The enhancement is attributed to the stronger third harmonic seed, and longer gain medium due to the extended filament.Comment: 10 pages, 5 figure

Post clamp

A pair of spaced collars are mounted at right angles on a clamp body by retaining rings which enable the collars to rotate with respect to the clamp body. Mounting posts extend through aligned holes in the collars and clamp body. Each collar can be clamped onto the inserted post while the clamp body remains free to rotate about the post and collar. The clamp body is selectively clamped onto each post

Fabrication of Surface Micromachined AlN Piezoelectric Microstructures and its Potential Apllication to RF Resonators

We report on a novel microfabrication method to fabricate aluminum nitride (AlN) piezoelectric microstructures down to 2 microns size by a surface micromachining process. Highly c-axis oriented AlN thin films are deposited between thin Cr electrodes on polysilicon structural layers by rf reactive sputtering. The top Cr layer is used both as a mask to etch the AlN thin films and as an electrode to actuate the AlN piezoelectric layer. The AlN layer is patterned anisotropically by wet etching using a TMAH (25%) solution. This multilayer stack uses silicon-di-oxide as a sacrificial layer to make free-standing structures. One-port scattering paramenter measurement using a network analyzer show a resonant frequency of 1.781 GHz on a clamped-clamped beam suspended structure. The effective electromechanical coupling factor is calculated as 2.4 % and the measured bandwidth is 13.5 MHz for one such a doubly clamped beam (990x30) μm2

The confined hydrogen atom with a moving nucleus

We study the hydrogen atom confined to a spherical box with impenetrable walls but, unlike earlier pedagogical articles on the subject, we assume that the nucleus also moves. We obtain the ground-state energy approximately by means of first--order perturbation theory and by a more accurate variational approach. We show that it is greater than the one for the case in which the nucleus is clamped at the center of the box. Present approach resembles the well-known treatment of the helium atom with clamped nucleus