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 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.

Three-dimensional nonlinear coupled dynamic modeling of a tip-loaded rotating cantilever

2018 ◽  
Vol 24 (22) ◽  
pp. 5366-5378 ◽  
Author(s):  
Mohammed Khair Al-Solihat ◽  
Meyer Nahon ◽  
Kamran Behdinan
Keyword(s):  
Dynamic Response ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Dissipation Function ◽  
Internal Damping ◽  
Symbolic Code ◽  
Mass Position

This paper presents a general three-dimensional flexible dynamic model of a tip-loaded rotating cantilever beam. For generality, the beam tip is assumed to be loaded with a rigid body with an arbitrary center of mass position, and subject to external force and moment. The coupled longitudinal (axial), bending–bending, and twist elastic motions are considered to formulate the system dynamics. The beam structural internal damping is modeled utilizing Rayleigh’s dissipation function. As well, the influence of gravity is considered. A symbolic code is developed to derive the equations of motion, and it is subsequently used to simulate the dynamics of two numerical case studies. The time response results are found to be in an excellent agreement with those reported from the literature. The effects of internal damping and coupling among the elastic motions on the system dynamic response are then investigated.

Time-harmonic dislocations in a multilayered transversely isotropic magneto-electro-elastic half-space

2019 ◽  
Vol 30 (13) ◽  
pp. 1932-1950 ◽  
Author(s):  
Ehsan Moshtagh ◽  
Morteza Eskandari-Ghadi ◽  
Ernian Pan
Keyword(s):  
Analytical Solution ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Effective Property ◽  
Elastic Half Space ◽  
Smart Devices ◽  
Elastic Fields ◽  
Cylindrical System ◽  
Time Harmonic

Modeling layered systems with dislocations is very challenging; yet, it is important since most smart structures are made of multilayers to make best use of the combined effective property. As such, during the manufactures, defects, such as dislocations, could be introduced in the multilayers. In this article, we analytically find, for the first time, the response of three-dimensional multilayered magneto-electro-elastic systems due to time-harmonic dislocations. The dislocations are the most general, containing the elastic dislocations and discontinuity of the electric potential and/or magnetic potential over a circular region in any layer in the medium. The fully coupled partial differential equations of motion and the Gauss law for the magneto-electro-elastic materials are solved in terms of cylindrical system of vector functions, and the dual variable and position method is further introduced to treat the multilayers. Numerical examples are carried out based on the derived analytical solution to demonstrate the effects of the time-harmonic dislocations on the induced magneto-electro-elastic fields. This analytical solution is important in both electrodynamics and elastodynamics, with possible applications in material sciences and physics. The numerical results are useful in design process of smart devices made of magneto-electro-elastic solids applicable to other engineering fields like renewable energy.

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.

Dynamic Response of a Double Articulated Offshore Loading Structure to Noncollinear Waves and Current

1981 ◽  
Vol 103 (1) ◽  
pp. 41-47 ◽  
Author(s):  
R. K. Jain ◽  
C. L. Kirk
Keyword(s):  
Dynamic Response ◽  
Nonlinear Equations ◽  
Relative Motion ◽  
Integration Method ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Governing Equations ◽  
Steady Current ◽  
Highly Nonlinear ◽  
Lagrange’S Method

The three-dimensional dynamic response of a double articulated offshore loading structure to noncollinear waves and a steady current is studied for various waves and varying current directions. The governing equations of motion are derived by the Lagrange’s method where the wave and current forces are computed by a modified form of the Morison’s equation which takes account for the relative motion of the water particles with respect to the oscillating structure. The resulting highly nonlinear equations are solved by using a block integration method. The computed results predict complex whirling oscillations of the structure to noncollinear waves and current.

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