Dynamic response of a bi-axially pre-stressed bi-layered plate resting on a rigid foundation under a harmonic force

2019 ◽  
Vol 234 (3) ◽  
pp. 784-795
Author(s):  
Ahmet Daşdemir
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Three Dimensional ◽  
Dimensionless Frequency ◽  
Rigid Foundation ◽  
Layered Plate ◽  
Harmonic Force ◽  
Time Harmonic ◽  
Linearized Theory ◽  
Complete Contact

This study aims to investigate the forced vibrations caused by a time-harmonic force from a pre-stressed bi-layered plate resting on a rigid foundation under the action of a time-harmonic pointwise loading. Our investigation was conducted according to a piecewise homogeneous body model utilizing the three-dimensional linearized theory of elastic waves in initially stressed bodies. Throughout this study, we assumed that there is complete contact between the plate and the rigid foundation. The purpose of this study is threefold: the development of a mathematical model to investigate the dynamic response of the pre-stressed bi-layered plate, the analysis of the frequency response of the plate under consideration, and finally, demonstrating the relationship between the initial stress and the dimensionless frequency of the plate. We solved the mathematical model by employing the finite element method. We present our numerical results on the dynamic behavior of the plate. In particular, we have shown that an increase in the values of the aspect ratio of a plate under fixed thickness leads to a decrease in the normal stress resonance values.

Dynamic response of a pre-stressed bi-layered plate-strip subjected to an arbitrary inclined time-harmonic force

2017 ◽  
Vol 26 (3) ◽  
pp. 255-262
Author(s):  
AHMET DASDEMIR ◽  
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Layered Plate ◽  
Field Problem ◽  
Time Harmonic ◽  
Governing System ◽  
Plate Strip ◽  
Linearized Theory ◽  
Complete Contact

Within the scope of the piecewise homogeneous body model with utilizing of the three dimensional linearized theory of elastic waves in initially stressed bodies the dynamical stress field problem in a bi-layered plate-strip with initial stress under the action of an arbitrary inclined timeharmonic force resting on a rigid foundation is investigated. The concrete materials such as a pair of Aluminum and Steel are selected. It is assumed that there exists a complete contact interaction between the layers. The mathematical modeling of the problem under consideration is carved out, and the governing system of the partial differential equations of motion is approximately solved by employing Finite Element Method. The numerical results related to the influence of certain parameters on the dynamic response of the plate-strip are presented.

scholarly journals Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

2017 ◽  
Vol 22 (3) ◽  
pp. 521-537 ◽  
Author(s):  
A. Daşdemir
Keyword(s):  
Dynamic Response ◽  
Initial Stress ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Layered Plate ◽  
Harmonic Force ◽  
Time Harmonic ◽  
Governing System ◽  
Plate Strip ◽  
Complete Contact

AbstractThe forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

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.

Dynamic Analysis of a Three-Dimensional Poroelastic Beam Using the Boundary-Element Method

2018 ◽  
Vol 769 ◽  
pp. 329-335
Author(s):  
Andrey Petrov ◽  
Leonid A. Igumnov
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Element Solution ◽  
Harmonic Force ◽  
Porosity And Permeability ◽  
Beam Thickness ◽  
Element Method

The problem of the effect of a normal harmonic force on a porous beam in a 3D formulation is solved using the boundary-element method. A homogeneous fully saturated elastic porous medium is described using Biot’s mathematical model. The effect of the porosity and permeability parameters on the deflection of the beam and the distribution of pore pressure over the beam thickness is investigated. The comparison of the boundary-element solution with a 2D numerical-analytical one is given.

Dynamic Response Modeling of Fluid-Solid Coupling for Wet Brake Disc

2013 ◽  
Vol 475-476 ◽  
pp. 1397-1401 ◽  
Author(s):  
Xun Jia Zheng ◽  
Tian Hong Luo ◽  
Ce Jia
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Three Dimensional ◽  
Brake Disc ◽  
Field Variation ◽  
Thermal Stress Field ◽  
Friction Plate ◽  
Transient Thermal ◽  
Response Modeling ◽  
Surface Temperature Field

Due to the poor conditions of wet brake cooling and the high temperature of the working characteristics, this paper intended to introduce the oil film vadose between the brake linings, considered the variation of volume of grooves on the friction plate, and then proposes the three-dimensional transient dynamic response of fluid-solid coupling mathematical model. By numerical analysis of the disc transient thermal stress field distribution on the friction plate, the friction surface temperature field variation is obtained. Finally, the results shows that the mathematical model is effective and feasible.

Forced vibration of a bi-axially pre-stressed plate subjected to a harmonic point force and resting on a rigid foundation

2019 ◽  
Vol 43 (3) ◽  
pp. 333-343
Author(s):  
Ahmet Daşdemir ◽  
Mustafa Eröz
Keyword(s):  
Finite Element Method ◽  
Forced Vibration ◽  
Elastic Waves ◽  
Three Dimensional ◽  
Dynamic Responses ◽  
Rigid Foundation ◽  
The Finite Element Method ◽  
System Parameters ◽  
Linearized Theory ◽  
Stress Influences

This paper models the harmonically forced vibration of a bi-axially pre-stressed plate resting on a rigid foundation using the three-dimensional linearized theory of elastic waves in initially stressed bodies. This model assumes that the material is linearly elastic, homogenous, and isotropic. The model of this system is numerically evaluated using the finite element method simulations. The numerical results illustrate the influence of several system parameters on the dynamic responses of the stresses acting at the interface between the plate and its rigid foundation. The simulations show that the aspect ratio of the plate determines how the initial stress influences the behavior of the system.

Forced Vibration of an Initial Stressed Rectangular Composite Thick Plate With a Cylindrical Hole

2009 ◽  
Author(s):  
Nazmiye Yahnioglu ◽  
Ulku Babuscu Yesil
Keyword(s):  
Thick Plate ◽  
Three Dimensional ◽  
Problem Formulation ◽  
Cylindrical Hole ◽  
Stress Distributions ◽  
Normal Forces ◽  
Time Harmonic ◽  
Upper Face ◽  
Linearized Theory ◽  
Dynamic Time

Within the framework of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies, the influence is studied of the initial stretching of a composite thick plate containing a cylindrical hole on the stress concentration around a hole caused by the action of the additional uniformly distributed dynamic (time-harmonic) normal forces on the upper face of the plane. The corresponding problem formulation is presented and, in order to find the solution to this problem, the finite element method is employed. The numerical results on the concentration of the stress around the hole and the influence of the initial stretching on this concentration are presented. According to these results, in particular it is established that the stress distributions around the cylindrical hole changed significantly with the initial stretching force.

Resonant and non-resonant acoustic properties of elastic panels. I. The radiation problem

1986 ◽  
Vol 406 (1831) ◽  
pp. 139-171 ◽  
Keyword(s):  
Power Flow ◽  
Three Dimensional ◽  
Acoustic Properties ◽  
Dimensional Problem ◽  
Harmonic Force ◽  
Asymptotic Results ◽  
Previous Theory ◽  
Near Resonance ◽  
Time Harmonic ◽  
Transition Formula

An elastic panel is excited by a time harmonic force and the power flow is calculated, averaged over a frequency band and all source positions. The two-dimensional problem is investigated asymptotically, for frequencies that are sufficiently high to ensure that many panel modes are near resonance. The asymptotic results are different according as the frequency is above or below the coincidence value; in the latter case account has to be taken of both resonance and non-resonance contributions to the power flow. A transition formula is given for frequencies near coincidence and the results agree well with numerical calculations. Corresponding results are given for the three-dimensional problem of the rectangular panel and previous theory is justified and extended.

A Real-Time Mathematical Model for Three-Dimensional Tidal Flow and Water Quality

1991 ◽  
Vol 24 (6) ◽  
pp. 171-177 ◽  
Author(s):  
Zeng Fantang ◽  
Xu Zhencheng ◽  
Chen Xiancheng
Keyword(s):  
Mathematical Model ◽  
Water Quality ◽  
Real Time ◽  
Control Volume ◽  
Tidal Flow ◽  
Three Dimensional ◽  
River Estuary ◽  
Pearl River Estuary ◽  
Practical Application ◽  
The Pearl River

A real-time mathematical model for three-dimensional tidal flow and water quality is presented in this paper. A control-volume-based difference method and a “power interpolation distribution” advocated by Patankar (1984) have been employed, and a concept of “separating the top-layer water” has been developed to solve the movable boundary problem. The model is unconditionally stable and convergent. Practical application of the model is illustrated by an example for the Pearl River Estuary.

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