Plate and Rod Vibrations With Initial Stress

1966 ◽  
Vol 33 (1) ◽  
pp. 134-140 ◽  
Author(s):  
T. W. Wright
Keyword(s):  
Initial Stress ◽  
Constitutive Relation ◽  
Three Dimensional ◽  
String Tension ◽  
Homogeneous State ◽  
General Frequency ◽  
Bending Modes

The influence of a homogeneous state of initial stress on the frequency of three-dimensional vibrations of plates and rods is considered. A linear constitutive relation is used and only terms to first power of initial stress are retained in all results. General frequency equations are found and various limiting cases are considered. Membrane and string tension terms appear in the bending modes indicating possible instabilities. In all other limiting cases, frequencies are modified only slightly by the presence of initial stress.

Fundamentals of generalized rigidity matrices for multi-layered media

1983 ◽  
Vol 73 (3) ◽  
pp. 749-763
Author(s):  
Maurice A. Biot
Keyword(s):  
Plane Strain ◽  
Initial Stress ◽  
Three Dimensional ◽  
Layered Media ◽  
Mathematical Structure ◽  
Irreversible Thermodynamics ◽  
Initial Stresses ◽  
General Context ◽  
Viscoelastic Media ◽  
Linear Irreversible Thermodynamics

abstract Rigidity matrices for multi-layered media are derived for isotropic and orthotropic layers by a simple direct procedure which brings to light their fundamental mathematical structure. The method was introduced many years ago by the author in the more general context of dynamics and stability of multi-layers under initial stress. Other earlier results are also briefly recalled such as the derivation of three-dimensional solutions from plane strain modes, the effect of initial stresses, gravity, and couple stresses for thinly laminated layers. The extension of the same mathematical structure and symmetry to viscoelastic media is valid as a consequence of fundamental principles in linear irreversible thermodynamics.

scholarly journals STUDIES ON SHELL FORMATION

1961 ◽  
Vol 9 (4) ◽  
pp. 761-771 ◽  
Author(s):  
Norimitsu Watabe ◽  
Karl M. Wilbur
Keyword(s):  
Crystal Growth ◽  
Dendritic Growth ◽  
Three Dimensional ◽  
Outer Part ◽  
Organic Matrix ◽  
Transitional Zone ◽  
Homogeneous State ◽  
Concentration Gradients ◽  
Strong Concentration ◽  
Small Crystals

Details of crystal growth in the calcitostracum of Crassostrea virginica have been studied with the purpose of analyzing the formation of the overlapping rows of oriented tabular crystals characteristic of this part of the shell. Crystal elongation, orientation, and dendritic growth suggest the presence of strong concentration gradients in a thin layer of solution in which crystallization occurs. Formation of the overlapping rows can be explained by three processes observed in the shell: a two-dimensional tree-like dendritic growth in which one set of crystal branchings creeps over an adjacent set of branchings; three-dimensional dendritic growth; and growth by dislocation of crystal surfaces. Multilayers of crystals may thus be formed at one time. This is favored by infrequent secretion of a covering organic matrix which would inhibit crystal growth. The transitional zone covering the outer part of the calcitostracum and the inner part of the prismatic region is generally characterized by aggregates of small crystals with definite orientation. Growth in this zone appears to take place in a relatively homogeneous state of solution without strong concentration gradients. Thin membranes and bands of organic matrix were commonly observed in the transitional zone bordering the prismatic region. The membrane showed a very fine oriented network pattern.

scholarly journals THE EFFECTIVE STRING OF 3D Z2 GAUGE THEORY AS A c = 1 COMPACTIFIED CFT

1993 ◽  
Vol 08 (16) ◽  
pp. 2839-2858 ◽  
Author(s):  
M. CASELLE ◽  
F. GLIOZZI ◽  
S. VINTI ◽  
R. FIORE
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Conformal Field Theory ◽  
Central Charge ◽  
Three Dimensional ◽  
String Tension ◽  
Gauge Model ◽  
Expectation Values ◽  
Monte Carlo Test ◽  
Conformal Field

We report on a high precision Monte Carlo test of the three-dimensional Ising gauge model at finite temperature. The string tension σ is extracted from the expectation values of correlations of Polyakov lines. Agreement with the string tension extracted from Wilson loops is found only if the quantum fluctuations of the flux tube are properly taken into account. The central charge of the underlying conformal field theory is c = 1.

scholarly journals A Mathematical Model for Forced Vibration of Pre-Stressed Piezoelectric Plate-Strip Resting On Rigid Foundation

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 419-431
Author(s):  
Ahmet Daşdemir
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Initial Stress ◽  
Piezoelectric Plate ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rigid Foundation ◽  
Time Harmonic ◽  
Governing System ◽  
Plate Strip

A mathematical model to investigate the dynamic response of a piezoelectric plate-strip with initial stress under the action of a time-harmonic force resting on a rigid foundation is presented within the scope of the three-dimensional linearized theory of electro-elasticity waves in initially stressed bodies (TLTEEWISB). The governing system of equations of motion is solved by employing the Finite Element Method (FEM). The numerical results illustrating the dependencies of different problem parameters are investigated. In particular, the influence of a change in the value of the initial stress parameter on the dynamic response of the plate-strip is discussed.

Vibration Analysis of a Tire Under Static Loading Using Flexible Ring-Based Model

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Aakash Swami ◽  
Ashok Kumar Pandey
Keyword(s):  
Finite Element ◽  
Static Loading ◽  
Contact Region ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Ring Model ◽  
Dimensional Finite Element ◽  
Bending Modes ◽  
Three Dimensional Finite Element ◽  
Flexible Ring

Abstract To address various tire vibration characteristics such as noise, vibration, and harshness, it is necessary to study the tire dynamic performance. In this paper, we focus on investigating the influence of static loading on radial (in-plane) and bending modes and their frequencies of a tire. To model the effect, we first identify important tire parameters, termed as modal parameters, based on three-dimensional ring model and three-dimensional finite element results under free-free conditions without and with temperature variations. After finding the parameters, we have used three-dimensional flexible ring model in which both in-plane and bending modes are considered under static loading. When load is applied, tire behavior changes and it becomes more stiffer. Thus, it fixes the tire to the road and increases the contact region. In this paper, we define this contact region over θf < θ < 2π and the region 0 < θ < θf can be considered free-free. Subsequently, we assume the expression of radial and bending modes in terms of generalized coordinates satisfying the above boundary conditions and obtain kinetic and potential energy by integrating it over 0 < θ < θf. The unknown coordinate is obtained by satisfying the governing conditions. Finally, corresponding mode shapes and frequencies are obtained. The assumed modes and frequencies are validated with three-dimensional finite element model using abaqus. The same procedure can be extended to compute modes and frequencies as a function of temperature under static loading for a constant tire pressure.

Constitutive relation of weakly anisotropic polycrystal with microstructure and initial stress

2007 ◽  
Vol 23 (2) ◽  
pp. 183-198 ◽  
Author(s):  
Mojia Huang ◽  
Hua Zhan ◽  
Xiuqiao Lin ◽  
Hai Tang
Keyword(s):  
Initial Stress ◽  
Constitutive Relation
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