Forced Lateral Vibration of a Uniform Cantilever Beam With Internal and External Damping

1960 ◽  
Vol 27 (3) ◽  
pp. 551-556 ◽  
Author(s):  
Ho Chong Lee
Keyword(s):  
Steady State Response ◽  
Lateral Vibration ◽  
Rotatory Inertia ◽  
Stress Strain ◽  
Inertia Effects ◽  
State Response ◽  
Spring Element ◽  
Stress Strain Relation ◽  
Tabular Method ◽  
Strain Relationship

The steady-state response problem of a uniform beam with a sinusoidal shaking force at the base is studied for the case where the beam material is the general linear substance represented by a model having an additional spring element in parallel with the Maxwell elements. In the analysis, the stress-strain relationship is applied only to the longitudinal strain of the beam, leaving the shear stress-strain relation to be that of a perfectly elastic material. The exact solution with a numerical example is given for one case where the shear and rotatory inertia effects are neglected. This result is compared with the solution obtained by a tabular method. The results of both methods are in excellent agreement.

On the Response of a Beam Subjected to a Cyclic Moving Load

1969 ◽  
Vol 91 (4) ◽  
pp. 925-930 ◽  
Author(s):  
P. G. Kessel ◽  
A. L. Schlack
Keyword(s):  
Natural Frequency ◽  
Elastic Foundation ◽  
Infinite Number ◽  
Circular Cylindrical Shell ◽  
Moving Load ◽  
Relative Importance ◽  
Steady State Response ◽  
Rotatory Inertia ◽  
State Response ◽  
Load Movement

A theoretical analysis is presented on the damped steady state response of a simply supported beam on an elastic foundation subjected to a cyclic moving load that oscillates longitudinally along the beam about a fixed point. Loadings of this type have been recently shown to yield an infinite number of load movement frequencies that will excite resonance of a given natural frequency of an elastic member or system of members. It is the purpose of this investigation to introduce damping into the problem in order to determine both the absolute and relative importance of this infinite number of load movement frequencies that will excite a given natural frequency of a beam. The mathematical analogy between the problem of a beam resting on an elastic foundation and that of a long circular cylindrical shell with axial and rotatory inertia neglected is noted. Hence the results obtained are applicable to either problem. Numerical results are presented to illustrate the effects of damping, frequency of oscillation of load movement and amplitude of load movement on the dynamic deflection of the beam.

An Advanced Cap Model for Soil

2003 ◽  
Author(s):  
C. S. Tsai ◽  
Ching-Shyang Chen ◽  
Zhen-Yu Zhang ◽  
Bo-Jen Chen ◽  
J. C. Chen
Keyword(s):  
Failure Surface ◽  
Material Behavior ◽  
Constitutive Law ◽  
Octahedral Plane ◽  
Sensitive Material ◽  
Stress Strain ◽  
Stress Strain Relation ◽  
Highly Nonlinear ◽  
Cap Model ◽  
Strain Relationship

Soil, which is a pressure-sensitive material, is frequently encountered in the engineering profession. To ensure the safety of super-structures, it is prerequisite to fully understand the mechanical behavior of soil. The stress-strain relation of soil is highly nonlinear and complex. Therefore, problems involving soil need an appropriate constitutive model to describe its stress-strain relationship. This paper presents a new cap-type constitutive law for soil. The model is prominent in the sense that it satisfies the compatibility between the failure surface and the yield cap. It has modified the classical cap model to obtain smooth yield surfaces. In addition, the model effectively describes strength variations along various directions on the octahedral plane. The model has shown to realistically simulate soil responses in experiments by 7 parameters. The proposed concept can also be extended to include as many previous models published in the past for describing various observed material behavior as it is required.

Research on Rock Mechanics Characteristics of Mud Sandstone NanTun Formation of HaiLaEr Oilfield

2014 ◽  
Vol 941-944 ◽  
pp. 2606-2610
Author(s):  
Yi Kun Liu ◽  
Yang He ◽  
Feng Jiao Wang ◽  
Yong Ping Wang ◽  
Hui Min Tang ◽  
...  
Keyword(s):  
Rock Mechanics ◽  
Clay Content ◽  
Rock Stress ◽  
Stress Strain ◽  
X Ray ◽  
Stress Strain Relation ◽  
Increasing Trend ◽  
Strain Relationship ◽  
Mechanics Characteristics ◽  
The Ideal

Hailar oilfield Nantun Formation is a set of lacustrine sedimentation, the sedimentation dominated by gravity flow,the rock contains a lot of argillaceous components. This paper analyzes the content of mud in mud sandstone in Nantun Formation by means of X-ray diffractometer, the rock mechanics parameters were measured.The results show that mud content increases with the decrease of the young's modulus, mud content increases with the increase of the Poisson's ratio; at the same time, with the increasing of the shale content, the compressive strength of rock reduce, and the tensile strength showed increasing trend; different clay contents of mud sand rock stress strain relationship is not the same, when the clay content ≤20%, rock stress strain is elastic constitutive relation, the shale content 20%-30%, the stress-strain relationship is approximate to the ideal elastic-plastic, shale content ≥30%, stress strain relation of rock strain hardening and softening of two parts including plastic deformation. Fault mud sandstone first with increasing clay content decreases, when the rock is elastic plasticity, fracture little overall change.

scholarly journals Springback Analysis in Sheet Metal Forming Using Modified Ludwik Stress-Strain Relation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sanjay Kumar Patel ◽  
Radha Krishna Lal ◽  
J. P. Dwivedi ◽  
V. P. Singh
Keyword(s):  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Spring Back ◽  
Stress Strain ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Strain Relationship ◽  
Von Mises ◽  
Strain Hardening Index

This paper deals with the springback analysis in sheet metal forming using modified Ludwik stress-strain relation. Using the deformation theory of plasticity, formulation of the problem and spring back ratio is derived using modified Ludwik stress strain relationship with Tresca and von Mises yielding criteraia. The results have been representing the effect of different value of or ratio, different values of Strain hardening index (), Poisson’s ratio (), and thickness on spring back ratio (). The main aim of this paper is to study the effects of the thickness, ratio, and Poisson’s ratio in spring back ratio.

Isochronous Stress-Strain Relationship in Compressive Stress Relaxation of Vulcanizates

1977 ◽  
Vol 50 (5) ◽  
pp. 915-921 ◽  
Author(s):  
B. Stenberg ◽  
J. F. Jansson
Keyword(s):  
Stress Relaxation ◽  
Mechanical Behavior ◽  
Compressive Stress ◽  
Heterogeneous Systems ◽  
Stress Strain ◽  
Vital Importance ◽  
Suspension Systems ◽  
Stress Strain Relation ◽  
Relaxation Measurements ◽  
Strain Relationship

Abstract The mechanical and other properties of natural and synthetic rubbers can be regulated by the incorporation of fillers. The mechanical behavior of the resulting complicated heterogeneous systems is often difficult to describe theoretically. These vulcanizates have wide and useful applications under conditions of multiaxial stresses. In many cases, however, the stresses act mainly in compression, for instance, in gaskets, seals, suspension systems for vibration insulation, etc. Thus the stress relaxation properties in compression are of vital importance. In spite of this, very few studies have given attention to the stress-strain relations in compression, and the results reported in the literature concentrate mainly on the mechanical behavior of rubbers in tension. We now report a study of the isochronous stress-strain relation in compression for some rubbers at 295 K, based on stress relaxation measurements. A comparison is made between the behavior of samples which have been greased and of samples which have been glued to the deformation plates.

Study on Strain-Sense Property of TiNi and TiNiCu Shape Memory Alloys

2005 ◽  
Vol 8 (6) ◽  
pp. 637-643
Author(s):  
Zhi-Qiang Liu ◽  
Hui Li ◽  
Wen-Li Chen ◽  
Jin-Ping Ou
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Sensing Element ◽  
Stress Strain ◽  
Change Rate ◽  
Stress Strain Relation ◽  
Strain Relationship ◽  
Good Strain ◽  
Relationship Of

Concerning important infrastructures and civil structures, they need real time detection during the service, such as high-rise buildings, cables, bridges and dams. Therefore, it is necessary to study sensing property of shape memory alloy (SMA) for developing a sensing element embedded in the structures to carry out damage detection. In this paper, change rate of resistance-stress-strain relationship of TiNi and TiNiCu shape memory alloys (SMAs) under elongation is examined. Tests are conducted in MTS at room temperature for the mechanical and strain-sense properties. According to the test results, it is concluded that TiNi and TiNiCu in martensitic phase and austenitic TiNi SMA wires have good strain-sense property. The change rate of resistance of SMA wires has a linear relation with the applied strain. Additionally, stress-strain relation is also predicted by Brinson Model. This study is devoted to sensing properties of TiNi and TiNiCu shape memory alloy.

Diastolic stress-strain relation of nonexcised blood-perfused canine papillary muscle

1978 ◽  
Vol 234 (4) ◽  
pp. H416-H420 ◽  
Author(s):  
A. Kitabatake ◽  
H. Suga
Keyword(s):  
Papillary Muscle ◽  
Human Subjects ◽  
Coronary Perfusion ◽  
Stress Strain ◽  
B Values ◽  
Stiffness Constant ◽  
Stress Strain Relation ◽  
Strain Relationship ◽  
Pressure Volume Relationship ◽  
Relationship Of

We studied diastolic stiffness of 10 coronary-perfused twitching papillary muscles of the canine right ventricle. The muscle beat at a regular sinus rhythm of 122 +/- 20 (SD) beats/min at 37 degrees C. They were stretched slowly at a constant rate. Diastolic force increased exponentially with the stretch. Calculating Lagrangian stress (sigma) and strain (epsilon) from diastolic force and length, we found a linear relationship between ln sigma and epsilon within the physiological range of strain (0.025 less than epsilon less than 0.4). This indicates that the diastolic stress-strain relationship of the canine papillary muscle can be approximated by a single exponential curve: sigma = a.exp(b.epsilon). The mean +/- SD of the stiffness constant b was 18.0 +/- 3.2 (dimensionless). Our b values are comparable to those of dogs and human subjects, either indirectly assessed from the ventricular pressure-volume relationship or directly obtained in excised quiescent muscle specimens. Different coronary perfusion pressures (75-125 mmHg) in 10 muscles showed a statistically significant positive correlation to b values.

Transient and Steady-State Response of Constrained Translating Strings

1995 ◽  
Author(s):  
W. D. Zhu ◽  
C. D. Mote
Keyword(s):  
Steady State ◽  
Exact Expression ◽  
Steady State Response ◽  
Constraint Force ◽  
Recording Head ◽  
State Response ◽  
Spring Element ◽  
Function Formulation ◽  
Magnetic Tape Recording ◽  
Transient And Steady State

Abstract The exact expression describing the constraint force in a constrained translating string is derived using the Green’s function formulation. Discontinuity of the initial velocity at a boundary of the string due to a disturbance causes discontinuity in the constraint force history for any constraint that is not modeled by a single spring element. The discontinuities in the constraint force occur at instants when those propagating wave-fronts in the string with non-vanishing slope interact with the constraint. A model of a magnetic tape-recording head system is analyzed. Tape-head contact loss is predicted, depending on the amplitude and frequency of the disturbance, the head location and the preload of the tape against the head. The transient response to a harmonic end excitation is compared at the steady state to the closed-form prediction of a steady forced analysis.

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