Vibration of generally orthotropic skew plates

Vibration problem of generally orthotropic plates with particular attention to plates of skew geometry is studied. The formulation is based on orthotropic plate theory with arbitrary orientation of the principal axes of orthotropy. The boundary conditions considered are combinations of simply supported, clamped, and free-edge conditions. Approximate solution for frequencies and modes is obtained by the Ritz method using products of appropriate beam characteristic functions as admissible functions. The variation of frequencies and modes with orientation of the axes of orthotropy is examined for different skew angles and boundary conditions. Features such as "crossings" and "quasi-degeneracies" of the frequency curves are found to occur with variation of the orientation of the axes of orthotropy for a given geometry of the skew plate. It is also found that for each combination of skew angle and side ratio, a particular orientation of the axes gives the highest value for the fundamental frequency of the plate.

Free vibrations of a reservoir-foundation system

The natural frequencies of a reservoir-foundation system are calculated by treating the foundation as a system of linear springs with inertia. The reservoir is treated as consisting of compressible liquid, and the influence of waves at the free surface is included. It is shown that the natural frequencies decrease monotonically as the depth of foundation participating in the motion increases. The influence of waves at the reservoir surface is negligible for the cases normally occurring in practice. It is also shown that the wavelength of motion along the reservoir has no influence on the frequencies when the foundation depth is large compared to the reservoir depth.

Design and analysis of ARROW-based racetrack resonator vibration sensor for inertial navigation application

In this paper we propose and analyze a novel racetrack resonator based vibration sensor for inertial grade application. The resonator is formed with an Anti Resonance Reflecting Optical Waveguide (ARROW) structure which offers the advantage of low loss and single mode propagation. The waveguide is designed to operate at 1310nm and TM mode of propagation since the Photo-elastic co-efficient is larger than TE mode in a SiO2/ Si3N4/ SiO2. The longer side of the resonator is placed over a cantilever beam with a proof mass. A single bus waveguide is coupled to the resonator structure. When the beam vibrates the resonator arm at the foot of the cantilever experiences maximum stress. Due to opto-mechanical coupling the effective refractive index of the resonator changes hence the resonance wavelength shifts. The non uniform cantilever beam has a dimension of 1.75mm X 0.45mm X 0.020mm and the proof mass has a dimension of 3mm X 3mm X 0.380mm. The proof mass lowers the natural frequency of vibration to 410Hz, hence designed for inertial navigation application. The operating band of frequency is from DC to 100Hz and acceleration of less than 1g. The resonator has a Free Spectral Range (FSR) of 893pm and produces a phase change of 22.4mrad/g.

An exact analysis of free vibrations of simply-supported viscoelastic plates

In this paper an exact three-dimensional analysis for free vibrations of a class of simply-supported viscoelastic rectangular plates is given. The characteristic equation defining the eigenvalues is of closed form. Some numerical results are presented for standard linear solids. Results from thin plate and Mindlin theories are also given for the purpose of comparison.

On the use of a coordinate transformation for analysis of axisymmetric vibration of polar orthotropic annular plates

Estimates of natural frequencies corresponding to axisymmetric modes of flexural vibration of polar orthotropic annular plates have been obtained for various combinations of clamped, simply supported and free edge conditions. A coordinate transformation in the radial direction has been used to obtain effective solutions by the classical Rayleigh-Ritz method. The analysis with this transformation has been found to be advantageous in computations, particularly for large hole sizes, over direct analysis. Numerical results have been obtained for various values of hole sizes and rigidity ratio. The eigenvalue parameter has been found to vary more or less linearly with the rigidity ratio. A comparison with the results for isotropic plates has brought out some interesting features.

Effects of high-frequency vibration on critical marangoni number

The influence of vibration on thermocapillary convection and critical Marangoni number in liquid bridge of half floating zone was discussed for the low frequency range 0.4-1.5 Hz and the intermediate frequency range 2.5-15 Hz in our previous papers. This paper extends the study to high frequency range 15-100Hz. This ground based experiment was completed on the deck of an electromagnetic vibration machine. The results of our experiment shows when the frequency of the applied acceleration is high enough, the amplitude of the time varying part of the temperature response is disappear and the shape of the free surface of the liquid bridge exhibits no fluctuations due to inertia. The critical Marangoni number which is defined to describe the transitions from a peroidical convection in response to vibration to an oscillatory convection due to internal instability is nearly the same as the critical Marangoni number for oscillatory flow in the absence of vibration.

Experimental-study of free-surface oscillations of a liquid bridge by optical diagnostics

A non-contact optical method, consisting of a projecting grating technique for the relative measurement of a surface, and a technique of absolute measurement at a fixed point on the surface, are applied to measure the free surface vibration in a liquid bridge of half floating zone with small typical scale of a few of mm for emphasizing the thermocapillary effect in comparison with the effect of buoyancy. The radii variations in both longitudinal and azimuthal directions are obtained, and, then, the feature of surface wave could be analyzed in detail. The results show that there are values of principal oscillatory frequencies at different positions of free surface. The amplitudes of surface waves in longitudinal and azimuthal directions are several mum and several tenths of mum in order of magnitude. The phase of two-dimensional surface waves is different at different height for fixed cross section or at different azimuthal angle for fixed height. The wave features are discussed for the cases of typical parameter ranges.

Nonharmonic transverse vibration of the H-bonded molecules and the THz spectra in ice and water

A nonlinear equation of motion is found for the dimer comprising two charged H2O molecules. The THz dielectric response to nonharmonic vibration of a nonrigid dipole, forming the hydrogen bond (HB), is found in the direction transverse to this bond. An explicit expression is derived for the autocorrelator that governs the spectrum generated by transverse vibration (TV) of such a dipole. This expression is obtained by analytical solution of the truncated set of recurrence equations. The far infrared (FIR) spectra of ice at the temperature - 7 degrees C are calculated. The wideband, in the wavenumber (frequency) v range 0... 100.0 cm(-1), spectra are obtained for liquid water at room temperature and for supercooled water at -5.6 degrees C. All spectra are represented in terms of the complex permittivity epsilon(v) and the absorption coefficient alpha(v). The obtained analytical formula for epsilon comprises the term epsilon(perpendicular to) pertinent to the studied TV mechanism with three additional terms Delta epsilon(q), Delta epsilon(mu), and epsilon(or) arising, respectively, from: elastic harmonic vibration of charged molecules along the H-bond; elastic reorientation of HB permanent dipoles; and rather free libration of permanent dipoles in 'defects' of water/ice structure. The suggested TV-dielectric relaxation mechanism allows us: (a) to remove the THz 'deficit' of loss epsilon" inherent in previous theoretical studies; (b) to explain the THz loss and absorption spectra in supercooled (SC) water; and (c) to describe, in agreement with the experiment, the low- and high-frequency tails of the two bands of ice H2O located in the range 10...300 cm(-1). Specific THz dielectric properties of SC water are ascribed to association of water molecules, revealed in our study by transverse vibration of HB charged molecules. (C) 2006 Published by Elsevier B.V.

Optimal and robust modal control of a flexible structure using an active dynamic vibration absorber

This paper is concerned with feedback vibration control of a lightly damped flexible structure that has a large number of well-separated modes. A single active electrical dynamic absorber is used to reduce a particular single vibration mode selectively or multiple modes simultaneously. The absorber is realized electrically by feeding back the structural acceleration at one position to a collocated piezoceramic patch actuator via a controller consisting of one or several second order lowpass filters. A simple analytical method is presented to design a modal control filter that is optimal in that it maximally flattens the mobility frequency response of the target mode, as well as robust in that it works within a prescribed maximum control spillover of 2 dB at all frequencies. Experiments are conducted with a free-free beam to demonstrate its ability to control any single mode optimally and robustly. It is also shown that an active absorber with multiple such filters can effectively control multiple modes simultaneously.

Robust broadband vibration control of a flexible structure using an electrical dynamic absorber

This paper presents a simple but practical feedback control method to suppress the vibration of a flexible structure in the frequency range between 10 Hz and 1 kHz. A dynamic vibration absorber is designed for this, which has a natural frequency of 100 Hz and a normalized bandwidth (twice the damping ratio) of 9.9. The absorber is realized electrically by feeding back the structural acceleration at one position on the host structure to a collocated piezoceramic patch actuator via an analog controller consisting of a second-order lowpass filter. This absorber is equivalent to a single degree-of-freedom mechanical oscillator consisting of a serially connected mass-spring-damper system. A first-order lowpass filter is additionally used to improve stability at very high frequencies. Experiments were conducted on a free-free beam embedded with a piezoceramic patch actuator and an accelerometer at its center. It is demonstrated that the single absorber can simultaneously suppress multiple vibration modes within the control bandwidth. It is further shown that the control system is robust to slight changes in the plant. The method described can be applied to many other practical structures, after retuning the absorber parameters for the structure under control.

Vibration and oil analysis for monitoring problems related to water contamination in rolling

Trying to reduce particle contamination in lubrication systems, industries of the whole world spend millions of dollars each year on the improvement of filtration technology. In this context, by controlling fluid cleanliness, some companies are able to reduce failures rates up to 85 percent. However, in some industries and environments, water is a contaminant more frequently encountered than solid particles, and it is often seen as the primary cause of component failure. Only one percent of water in oil is enough to reduce life expectancy of a journal bearing by 80 percent. For rolling bearing elements, the situation is worse because water destroys the oil film and, under the extreme temperatures and pressures generated in the load zone of a rolling bearing element, free and emulsified water can result in instantaneous flash-vaporization giving origin to erosive wear. This work studies the effect of water as lubricant contaminant in ball bearings, which simulates a situation that could actually occur in real systems. In a designed bench test, three basic lubricants of different viscosities were contaminated with different contents of water. The results regarding oil and vibration analysis are presented for different bearing speeds.

Numerical and experimental investigation of a vibration system with non-ideal vibration source

An excitation force that is not influenced by the system's states is said to be an ideal energy source. In real situations, a direct and feedback coupling between the excitation source and the system must always exist. This manifestation of the law of conversation of energy is known as Sommerfeld Effect. In the case of obtaining a mathematical model for such system, additional equations are usually necessary to describe the vibration sources and their coupling with the mechanical system. In this work, a cantilever beam and a non-ideal electric DC motor that is fixed to the beam free end is analyzed. The motor has an unbalanced mass that provides excitation to the system proportional to the current applied to the motor. During the motor's coast up operation, as the excitation frequency gets closer to the beam first natural frequency and if the drive power increases further, the DC motor speed remains constant until it suddenly jumps to a much higher value (simultaneously the vibration amplitude jumps to a much lower value) upon exceeding a critical input power. It was found that the Sommerfeld effect depends on some system parameters and the motor operational procedures. These parameters are explored to avoid the resonance capture in Sommerfeld effect. Numerical simulations and experimental tests are used to help insight this dynamic behavior.

DETERMINATION OF THE E/G RATIO OF WOOD LOGS USING TRANSVERSE VIBRATION

The Bernoulli's model for vibration of beams is often used to make predictions of bending modulus of elasticity when using dynamic tests. However this model ignores the rotary inertia and shear. Such effects can be added to the solution of Bernoulli's equation by means of the correction proposed by Goens (1931) or by Timoshenko (1953). But to apply these corrections it is necessary to know the E/G ratio of the material. The objective of this paper is the determination of the E/G ratio of wood logs by adjusting the analytical solution of the Timoshenko beam model to the dynamic testing data of 20 Eucalyptus citriodora logs. The dynamic testing was performed with the logs in free-free suspension. To find the stiffness properties of the logs, the residue minimization was carried out using the Genetic Algorithm (GA). From the result analysis one can reasonably assume E/G = 20 for wood logs.