scholarly journals Vibrations of thick plate resting on a deformable foundation under impulse load

2017 ◽  
Vol 2017 (9) ◽  
pp. 46-54
Author(s):  
Wacław Szcześniak ◽  
Magdalena Ataman
Keyword(s):  
Analytical Solution ◽  
Thick Plate ◽  
Governing Equations ◽  
Numerical Example ◽  
Deformable Foundation ◽  
Impulse Load ◽  
Winkler’S Foundation ◽  
Winkler's Foundation

The paper deals with vibrations of thick plate resting on generalized Winkler’s foundation. The plate is subjected to the impulse of force. Governing equations of the problem, analytical solution as well as numerical example are presented. Results of calculations are shownin the figures. Solution and diagrams are obtained by means of “Mathematica” code.

scholarly journals An Equal-Strain Analytical Solution for the Radial Consolidation of Unsaturated Soils by Vertical Drains considering Drain Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Feng Zhou ◽  
Zheng Chen ◽  
Xudong Wang
Keyword(s):  
Analytical Solution ◽  
Unsaturated Soils ◽  
Ground Surface ◽  
Matrix Analysis ◽  
Governing Equations ◽  
Vertical Drains ◽  
Ground Surface Settlement ◽  
Parametric Studies ◽  
Strain Model ◽  
Good Agreement

Developing an analytical solution for the consolidation of unsaturated soils remains a challenging task due to the complexity of coupled governing equations for air and water phases. This paper presents an equal-strain model for the radial consolidation of unsaturated soils by vertical drains, and the effect of drain resistance is also considered. Simplified governing equations are established, and an analytical solution to calculate the excess pore-air and pore-water pressures is derived by using the methods of matrix analysis and eigenfunction expansion. The average degrees of consolidation for air and water phases and the ground surface settlement are also given. The solutions of the equal-strain model are verified by comparing the proposed free-strain model with the equal-strain model, and reasonably good agreement is obtained. Moreover, parametric studies regarding the drain resistance effect are graphically presented.

On the Role of Enduring Contact in Powder Lubrication

2005 ◽  
Vol 128 (1) ◽  
pp. 168-175 ◽  
Author(s):  
J. Y. Jang ◽  
M. M. Khonsari
Keyword(s):  
Analytical Solution ◽  
Flow Velocity ◽  
Volume Fraction ◽  
Flow Characteristics ◽  
Kinetic Regime ◽  
Governing Equations ◽  
Wide Range ◽  
Fraction Distribution ◽  
Powder Lubrication

This paper is devoted to a study of the enduring contact between granules of powder lubricants in an effort to better understand the flow characteristics of powder lubricants. Appropriate formulation of the governing equations is reported that can be used for prediction of the flow velocity, pseudo temperature, and volume fraction distribution of powders for a wide range of operating speeds. A set of parametric simulations and a limiting analytical solution is presented for predicting the behavior of a powder lubricant under low operating speeds when the enduring contact tends to dominate the kinetic regime. The limiting solution shows that below a certain sliding speed the volume fraction remains unchanged due to the effect of the enduring contact. It is also shown that below this limiting speed the enduring contact plays a major role and should not be neglected.

scholarly journals Analysis Bending Solutions of Clamped Rectangular Thick Plate

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Yang Zhong ◽  
Qian Xu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Shear Deformation ◽  
Thick Plate ◽  
Plate Theory ◽  
Analytic Solutions ◽  
Higher Order ◽  
Numerical Comparison ◽  
Governing Equations ◽  
Partial Differential

The bending solutions of rectangular thick plate with all edges clamped and supported were investigated in this study. The basic governing equations used for analysis are based on Mindlin’s higher-order shear deformation plate theory. Using a new function, the three coupled governing equations have been modified to independent partial differential equations that can be solved separately. These equations are coded in terms of deflection of the plate and the mentioned functions. By solving these decoupled equations, the analytic solutions of rectangular thick plate with all edges clamped and supported have been derived. The proposed method eliminates the complicated derivation for calculating coefficients and addresses the solution to problems directly. Moreover, numerical comparison shows the correctness and accuracy of the results.

scholarly journals Development of A Process for Predicting the Overall Heat Transfer Coefficient for Transient Heat Transfer in An Exhaust System using CFD

2019 ◽  
Vol 8 (2) ◽  
pp. 2529-2533
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Analytical Solution ◽  
Transfer Coefficient ◽  
Gas Flow ◽  
Transient Flow ◽  
Exhaust System ◽  
Outlet Temperature ◽  
Governing Equations ◽  
Overall Heat Transfer Coefficient

The analysis of heat transfer of automotive exhaust system is most important since their prominence in the design and also in the optimization phase of exhaust after treatment system.This paperdeals with the process which can be useful to predict the overall heat transfer coefficient for the transient flow of pipe in the after treatment system. This considers the convection of heat along gas flow, the convection between gas and wall, conduction through wall, radiation and of course convection to the ambient. Governing equations are obtained for the transient flow in a pipe for calculating gas temperature and wall temperature at distance x and time t. Analytical solution will be computed using CFD techniques for these governing equations. From the obtained analytical solution to the transient flow in pipe an excel tool will be developed which can be able to give the outlet temperature of the pipe in transient flow at length x and time t, total heat loss from pipe to the ambient, overall heat transfer coefficient for the pipe

Dynamic Response of Ground Surface Due to External Disturbance: Analytical Solution

2008 ◽  
Author(s):  
Hamid R. Hamidzadeh
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Wave Equations ◽  
External Disturbance ◽  
Ground Surface ◽  
Equation Of Motion ◽  
Elastic Half Space ◽  
Fourier Domain ◽  
Dynamics Analysis ◽  
Governing Equations

In this investigation the propagation of a harmonic disturbance on the surface of ground is considered. The medium is assumed to be a homogeneous and isotropic, continuous and infinite which can be modeled as an elastic half space medium. Implementing elasto-dynamics analysis, the governing equation of motion for the system is developed. The developed mathematical model formulates the displacement and stresses in the medium in terms of elastic dilatation and rotations and reduces the governing equations into three wave equations in terms of elastic dilatation and rotations. These equations are solved and boundary stresses are satisfied in Fourier domain and the displacement on the surface are provided in this domain.

Dynamic Response of an Electro-Rheological Sandwich Beam with Different Elastic Layers Subjected to Simultaneous Impact Loads

2012 ◽  
Vol 232 ◽  
pp. 117-121 ◽  
Author(s):  
M. Sepehrinour ◽  
M. Nezami
Keyword(s):  
Analytical Solution ◽  
Electric Field ◽  
Dynamic Response ◽  
Material Properties ◽  
Transverse Vibration ◽  
Sandwich Beam ◽  
Impact Loads ◽  
Governing Equations ◽  
Simultaneous Impact ◽  
Elastic Layers

Dynamic response of an electro-rheological sandwich beam subjected to simultaneous Impact loads will be considered. Analytical solution will be used to draw FRF diagram of the beam for different electric field. Upper and lower layers of the beam have different material properties. Coupled governing equations derived from Hamilton Principle will be solved in frequency domain to find transverse vibration of the beam.

scholarly journals A Generalized Analytical Model for Joule Heating of Segmented Wires

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Vivekananthan Balakrishnan ◽  
Toan Dinh ◽  
Hoang-Phuong Phan ◽  
Dzung Viet Dao ◽  
Nam-Trung Nguyen
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Joule Heating ◽  
Numerical Solutions ◽  
Analytical Data ◽  
Experimental Studies ◽  
Governing Equations ◽  
Steady State Temperature ◽  
The One ◽  
Good Agreement

This paper presents an analytical solution for the Joule heating problem of a segmented wire made of two materials with different properties and suspended as a bridge across two fixed ends. The paper first establishes the one-dimensional (1D) governing equations of the steady-state temperature distribution along the wire with the consideration of heat conduction and free-heat convection phenomena. The temperature coefficient of resistance of the constructing materials and the dimension of the each segmented wires were also taken into account to obtain analytical solution of the temperature. COMSOL numerical solutions were also obtained for initial validation. Experimental studies were carried out using copper and nichrome wires, where the temperature distribution was monitored using an IR thermal camera. The data showed a good agreement between experimental data and the analytical data, validating our model for the design and development of thermal sensors based on multisegmented structures.

Power Harvesting Prediction of Piezoelectric Stack Actuator From a Shock Event

2013 ◽  
Author(s):  
Andrew J. Lee ◽  
Ya Wang ◽  
Daniel J. Inman
Keyword(s):  
Space Form ◽  
Test Cases ◽  
Governing Equations ◽  
Power Harvesting ◽  
Single Degree Of Freedom ◽  
Percent Error ◽  
First Case ◽  
Impulse Load ◽  
Shock Event ◽  
Piezoelectric Stack Actuator

In this study, the power harvesting performance of a piezoelectric (PZT) ceramic multilayer stack actuator under a shock event is theoretically and experimentally investigated. The model is derived from the constitutive - 33 mode equations under single degree of freedom (SDOF) assumptions, and then a correction factor is applied onto the resulting electromechanically coupled governing equations. These are represented in state space form and solved in the numerical computation software MATLAB. In order to achieve experimental validation, two test cases are compared to the model prediction when impulses of 20.8 mN·s and 1.70 mN·s are loaded on to the PZT stack actuator. The voltage and power output between the model and the test cases matched well. For the first case, the PZT stack actuator harvested 0.3321 μJ from the shock event while the model’s prediction was 0.3358 μJ, which results in a percent error of only 1.1%. In the second case, the PZT stack actuator harvested 34.64 nJ from the shock event while the model’s prediction was 35.80 nJ, which results in a percent error of 3.2%. This paper achieves its objective of deriving a model that can accurately predict the power harvested when an impulse load is applied onto a PZT stack actuator, and then validating this model with testing.

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