Modes Of Body Research Articles

Heave-Pitch-Roll Dynamics of Flexible Vehicle in Variable Velocity Run

Analysis for response statistics evaluation of a flexible vehicle travelling with variable velocity over nonhomogeneously profiled flexible track is presented with a heave-pitch-roll model. The vehicle body is idealised as a flexible member with variable cross-section, inertia, damping and stiffness distributions. The vehicle may also have variable section slender elastic attachments. Coupled dynamics with rigid body heave-pitch-roll modes and elastic bending-torsion modes of the vehicle body along with coupled bending-torsion modes of the attachments are considered. Equivalent linear suspension system characteristics are employed for developing the analysis. Numerical results are presented for an aircraft with tricycle landing gear arrangements and comparison is made with other models.

An investigation of vibrational and acoustical properties of the violin using MLS and optical holography

In this investigation a multi-channel MLS (maximum length sequence) measurement system is used for vibrational and acoustical measurements on the violin. MLS measurements are useful since both phase and magnitude can be measured with great accuracy. In these measurements, both the phase and magnitude influence of the transducers are corrected. Using this tool, the input admittance, the velocity at the feet of the bridge, and the sound pressure at the far field of the violin are measured simultaneously. These parameters give important information about the vibrational and acoustical properties of the violin. A more extensive investigation is also performed. The sound level pressure and phase are measured in several equally spaced positions in the far field of the violin situated in an anechoic chamber. Radiation patterns are found for each mode and the radiated power is calculated. Optical holography is then used to measure the vibrational pattern for the most important modes of the violin body. These acoustical and vibrational measurements are correlated to determine which modes are most important to the radiated sound power.

Nondestructive assessment of the grain size distribution of SnO2 nanoparticles by low-frequency Raman spectroscopy

A nondestructive methodology is reported to obtain the grain size distribution of SnO2 nanoparticles, with grain sizes below 10 nm, using low-frequency Raman scattering measurements. The position of the main low-frequency Raman bands depends on the grain size and can be correlated with the spheroidal vibration modes of a spherical elastic body with “rigid” boundaries. The grain size distributions deduced from Raman scattering are in agreement with the direct measurements from transmission electron microscopy, especially for the smaller grains.

Unification of the Dirac and Einstein Lagrangians in a tetrad model

In a recent article all classical tensor systems which admit Fermi quantization are characterized as those having unitary Lie–Poisson brackets. Examples include Euler’s tensor equation for a rigid body and Dirac’s equation in tensor form. In this article it is shown that the tensor form of the Dirac Lagrangian can be derived from a tetrad formulation of a Kaluza–Klein model, which unifies the Dirac and Einstein Lagrangians. In this formulation, the isometric modes of the tetrad propagate as fermions, whereas the self-adjoint modes propagate as gravitons. An analogy is made with the rigid and elastic modes of a deformable body, where the rigid modes are Fermi quantized and the elastic modes are Bose quantized. However, unlike a deformable body for which the Euclidean metric is positive definite, fermion and graviton modes are not generally separable, unless the gravitational fluctuations are limited by a certain bound. It is shown that this bound applies whenever bispinors are defined in a general relativistic framework. That is, the bound does not depend on whether bispinors or tensors are used to describe the fermion modes.

043 On the characteristics modes of a rigid body under forces

043 On the characteristics modes of a rigid body under forces

On the Characteristic Modes of a Rigid Body Under Forces

The characteristic modes of a rigid body under forces are determined from its analytical solution. This solution may be expressed in terms of eigenvalues and eigenvectors. The nonlinear feedback control law is deduced from the compatibility conditions of the differential equations

Transonic flow modes of an axisymmetric blunt body

An experimental investigation of transonic flow past a plane-nosed circular cylinder with a plane-nosed circular probe extended coaxially ahead is reported. The possibilities of significant transonic drag reduction and the fluid mechanic phenomena which occur are examined. The probe length and diameter and the approaching flow Mach number are the independent variables. The relations which exist among the probe/cylinder geometry, Mach number, and flow field as revealed by measurements of the drag forces acting on the body are explored.

Limiting stationary modes of a rigid body on a string suspension

The nature of the stationary rotations of an axisymmetric rigid body on a string suspension at high angular velocities is studied. The domain in the space of dimensionless parameters of the system is found where, given the same angular velocity, the maximum number (sixteen) of different permanent rotations is possible. It was shown earlier, see /1/, that as the angular velocity increases without limit, the system tends to a position in which some principal central axis of inertia of the body coincides with the fixed vertical. It was shown in /2/ that there are stationary motions in which an axis of symmetry of the body is horizontal. The different types of permanent rotations have been studied e.g., in/2, 3/

The relationship of degeneration of the intervertebral disc to mechanical loading conditions on lumbar vertebrae.

Degeneration of lumbar intervertebral discs is typical for the aging process and contributes to common low-back problems. It is likely to influence vertebrae by changing the mechanical interaction within each motion segment. This study focuses on the influence of disc degeneration on the mechanism of load transmission through the lumbar vertebral body. Effective stresses, ways of load transmission and failure modes of vertebral body were examined in cases of healthy and degenerated discs. The stress analysis was performed using the Finite Element Method. For healthy discs, the highest effective stresses were found in the center of bony end-plates. For degenerated discs, they were found in the lateral aspects of the end-plates, in the cortical wall, and also in the vertebral body rims. However, regardless of the disc condition, the highest effective stresses do not occupy the whole thickness of the endplate and/or the cortical wall, but are concentrated near the spongy core. Ways of load transmission through the lumbar vertebral body and modes of eventual damage to it are also strongly influenced by the disc condition.

A finite element analysis of the violin body

The normal modes of a violin body were studied using finite element methods. The NASTRAN finite‐element analysis package and PATRAN‐G pre/post‐processor graphics software were the workhorses for this “computer laboratory” investigation. Free finite‐element top and back plates were first “tuned” to generally accepted parameters and were then assembled into a complete body consisting of the plates, bassbar, sound post, and end blocks. The normal modes of the finite‐element body compare favorably with those obtained from an impact hammer modal test on a real violin. Animated graphics of the normal modes, which provide significant insight into the physics of the violin structure, will be presented.

Strains from holographic data

In this paper, reliable derivatives up to second order over a surface are obtained from holographic interferograms. This is done on a large scale, handling an amount of data that would be prohibitive if attempted by hand smoothing. This opens the way for bending and shear-strain determinations in a noncontacting way over large fields of view. The surface need be treated in no special way, in contrast to the preparation required with brittle lacquers and photoelastic coatings. Strains in the microstrain range are readily measured. Holographic interferometry in conjunction with the numerical methods mentioned herein constitutes a noncontacting optical strain gage. Furthermore, it makes possible experimental application of sophisticated modal analysis because the normal modes upon which these techniques are based are directly measured. For example, if the vibratory behavior is known, through a sufficiently large sample of the normal modes, then the static behavior may be calculated. Similarly, if the normal modes of a nonrotating body are known, its behavior in a rotating system can be calculated. Thus, the centrifugal stiffening of a turbine rotor may be predicted from a knowledge of the spectrum of its normal modes.

Network theoretic analysis of transducers

Starting with the open-circuit or short-circuit electroelastic normal modes of a piezoelectric body, one can compute an equivalent electromechanical admittance matrix or hydrid parameter matrix. This matrix effectively transforms the piezoelectric body into an N-port network. One is thus able to bring to bear upon transducer problems the well-developed theory of N-port networks. We have done this for a radially polarized and tangentially polarized (segmented) ferroelectric shell. In particular, we have computed the open-circuit voltage response of the radially polarized shell (assuming it to be in a hydrophone) by utilizing the admittance matrix approach, which is based on the short-circuit normal modes, and the hybrid parameter approach, which is based on the open-circuit normal modes. A comparison of the two approaches is made. In addition, we describe an application of the theory to determining the driving-point (electrical) impedance of a projector consisting of a coaxial array of segmented shells. This is done by treating both the array of shells and the surrounding fluid medium as coupled N-port networks.

Free Vibrations of Reinforced Elastic Shells

A technique is presented for the analysis of a wide class of reinforced, elastic structures undergoing free vibrations while subject to constraints imposed by the reinforcing elements. The technique consists of replacing the constrained structure by an equivalent model, a structure without reinforcing elements, undergoing free vibrations while subject to a loading system which consists of the structure-reinforcing element interaction forces. These forces are introduced as displacement-dependent loads, whose magnitudes reflect the elastic and inertial properties of the reinforcing elements. The displacements of the constrained body are expanded in terms of the normal modes of the unconstrained body. This approach leads to a set of manageable governing equations describing the behavior of the reinforced body exactly. A solution to these equations may then be obtained to any desired degree of accuracy. The technique is illustrated by computations performed for the case of a ring reinforced, circular cylindrical shell.

Surface Magnetostatic Modes and Surface Spin Waves

Examination of the spatial configuration of the magnetostatic modes of a ferromagnetic body shows that those modes whose frequency lies between $\ensuremath{\omega}=\ensuremath{\gamma}{({B}_{i}{H}_{i})}^{\frac{1}{2}}$ and $\ensuremath{\omega}=\ensuremath{\gamma}({H}_{i}+2\ensuremath{\pi}M)$ are surface modes. It is also found that the complete spin-wave spectrum consists of a set of surface spin waves in addition to the spin-wave band usually considered. The magnetostatic mode spectrum thus merges smoothly into the spin-wave spectrum.The characteristic equation for the surface modes on a plane surface at an arbitrary angle to the applied dc field is given. The properties of the surface modes on plane surfaces and on spheroidal bodies are discussed.