EIGENFREQUENCIES OF OSCILLATIONS OF A PLATE WHICH SEPARATES A TWO-LAYER IDEAL FLUID WITH A FREE SURFACE IN A RECTANGULAR CHANNEL

The frequency spectrum of plane vibrations of an elastic plate separating a two-layer ideal fluid with a free surface in a rectangular channel is investigated analytically and numerically. For an arbitrary fixing of the contours of a rectangular plate, it is shown that the frequency spectrum of the problem under consideration consists of two sets of frequencies describing the vibrations of the free surface of the liquid and the elastic plate. The equations of coupled vibrations of the plate and the fluid are presented using a system of integro-differential equations with the boundary conditions for fixing the contours of the plate and the condition for the conservation of the volume of the fluid. When solving a boundary value problem for eigenvalues, the shape of the plate deflection is represented by the sum of the fundamental solutions of a homogeneous equation for a loose plate and a partial solution of an inhomogeneous equation by expanding in terms of eigenfunctions of oscillations of an ideal fluid in a rectangular channel. The frequency equation of free compatible vibrations of a plate and a liquid is obtained in the form of a fourth-order determinant. In the case of a clamped plate, its simplification is made and detailed numerical studies of the first and second sets of frequencies from the main mechanical parameters of the system are carried out. A weak interaction of plate vibrations on vibrations of the free surface and vice versa is noted. It is shown that with a decrease in the mass of the plate, the frequencies of the second set increase and take the greatest value for inertialess plates or membranes. A decrease in the frequencies of the second set occurs with an increase in the filling depth of the upper liquid or a decrease in the filling depth of the lower liquid. Taking into account two terms of the series in the frequency equation, approximate formulas for the second set of frequencies are obtained and their efficiency is shown. With an increase in the number of terms in the series of the frequency equation, the previous roots of the first and second sets are refined and new ones appear.

Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties

A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This asymptotic model inherits the dielectric properties of the insulating layer. It involves the electrostatic potential in the device and the deformation of the elastic plate defining the geometry of the device. The electrostatic potential is given by an elliptic equation with mixed boundary conditions in the possibly non-Lipschitz region between the two plates. The deformation of the elastic plate is supposed to be a critical point of an energy functional which, in turn, depends on the electrostatic potential due to the force exerted by the latter on the elastic plate. The energy functional is shown to have a minimizer giving the geometry of the device. Moreover, the corresponding Euler–Lagrange equation is computed and the maximal regularity of the electrostatic potential is established.

Hinge-type FBG acceleration sensor based on double elastic plate

It is critical for the health monitoring of large-scale structures such as bridge, railway and tunnel to acquire the medium-frequency and high-frequency vibration signals. To solve the problems of low sensitivity and poor transverse anti-interference of the medium-frequency and high-frequency fiber acceleration sensor, a hinge-type Fiber Bragg Grating(FBG) acceleration sensor based on double elastic plate has been proposed, and the hinge and elastic plate are used as elastomer to realize the miniaturization and transverse interference suppression of the sensor. The MATLAB and the ANSYS are used for theoretical analysis and optimization of sensor sensitivity and resonance frequency, structural static stress analysis and modal simulation analysis, while the test system is built to test the sensor performance. The results show that the resonance frequency of the sensor is 1300 Hz; the sensor has a flat sensitivity response in the middle-high frequency band of 200–800 Hz; the sensitivity is about 20 pm/g, and the fiber central wavelength drift and acceleration have good linearity and stability, while the transverse anti-interference is about 3.16%, which provides a new idea for monitoring of medium-frequency and high-frequency vibration signals in large-scale structures.

Dynamic Response Measurement of Elastic Structures Through Smart Digital Image Correlation Method and Calculation

Based on the proper improvement and development of the basic principle of digital image correlation method, a 3D-DIC measurement system is built. Its measurement principle and application process can be divided into four steps: camera calibration, image acquisition, image matching and three-dimensional reconstruction. The measurement system can realize non-contact and full-field measurement and has the advantages of not being affected by the test environment, not imposing additional mass on the test model, and high signal-to-noise ratio of the measured data. Taking the elastic plate model as an example, the accuracy and reliability of the measurement system in the measurement of static and dynamic displacement response are verified by using the measurement results of laser displacement meter as a reference. In addition, the tensile strain of the projectile aluminum alloy tail model and the ground mode of the elastic plate are tested to further verify the practicability of the test system.

Hydroelastic waves propagating along a frozen channel with non-uniform thickness of ice

Hydroelastic waves propagating along a channel covered with ice of non-uniform thickness are considered. The channel has a rectangular cross section. The fluid in the channel is inviscid and incompressible. The ice is modeled as a thin elastic plate. The ice thickness changes linearly. The problem is reduced to the problem of the wave profile across the channel, which is solved using the normal modes of an elastic beam with non-uniform thickness. It is shown that with the decrease in the change in the ice thickness, the modes approach the normal modes of an elastic beam with a constant thickness. The behavior of the dispersion relations of the hydroelastic waves depending on the parameter describing the change in the ice thickness is studied.