scholarly journals Three-dimensional exact solutions of homogeneous transversely isotropic coated structures under spherical contact

2019 ◽  
Vol 161 ◽  
pp. 136-173 ◽  
Author(s):  
P.F. Hou ◽  
W.H. Zhang ◽  
Jia-Yun Chen
Keyword(s):  
Exact Solutions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Spherical Contact

Three-dimensional exact solutions of elastic transversely isotropic coated structures under conical contact

2019 ◽  
Vol 369 ◽  
pp. 280-310 ◽  
Author(s):  
Peng-Fei Hou ◽  
Wen-Hua Zhang ◽  
Jian-ping Tang ◽  
Jia-Yun Chen
Keyword(s):  
Exact Solutions ◽  
Three Dimensional ◽  
Transversely Isotropic

scholarly journals The electro-mechanics of a coating/substrate system under charged spherical contact

2019 ◽  
Vol 25 (1) ◽  
pp. 60-96
Author(s):  
PF Hou ◽  
WH Zhang
Keyword(s):  
Coating Thickness ◽  
Three Dimensional ◽  
Optimization Procedure ◽  
Transversely Isotropic ◽  
Dielectric Constants ◽  
Contact Radius ◽  
Total Load ◽  
Spherical Contact ◽  
Theoretical Results ◽  
Piezo Electric

A general theory of the piezo-electric contact mechanics for a transversely isotropic piezo-electric elasticity coated system (TIPECS) under charged spherical contact is presented. Three-dimensional exact solutions for the stresses, displacements, electric displacements and electric potential are derived. The contact radius versus the total load relation is obtained to guide the indentation experiments. The relations of coating thickness versus voltage and coating thickness versus voltage are studied. The optimal thickness can be determined with an optimization procedure. The interfacial delamination area of the TIPECS can be predicted with the interfacial failure criterion. The theoretical results are helpful for the prediction of some transient electrical effects, which can be combined with experiments to estimate some elastic constants, dielectric constants and piezo-electric constants in the indentation process.

Internal-inertia waves in a fluid of variable depth

1973 ◽  
Vol 73 (1) ◽  
pp. 205-213 ◽  
Author(s):  
W. D. McKee
Keyword(s):  
Exact Solutions ◽  
Surface Waves ◽  
Internal Waves ◽  
Vertical Velocity ◽  
General Problem ◽  
Three Dimensional ◽  
Variable Depth ◽  
Internal Inertia ◽  
Perturbation Pressure ◽  
Rotating Stratified Fluid

AbstractWaves in a rotating, stratified fluid of variable depth are considered. The perturbation pressure is used throughout as the dependent variable. This proves to have some advantages over the use of the vertical velocity. Some previous three-dimensional solutions for internal waves in a wedge are shown to be incorrect and the correct solutions presented. A WKB analysis is then performed for the general problem and the results compared with the exact solutions for a wedge. The WKB solution is also applied to long surface waves on a rotating ocean.

Study on soliton solutions of the longitudinal wave equation and magneto-electro-elastic circular rod dynamical model

2021 ◽  
Vol 35 (13) ◽  
pp. 2150168
Author(s):  
Adel Darwish ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
A. L. Elbably ◽  
Mohammed F. Shehab ◽  
...  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Physical Interpretation ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional

In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.

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