dual integral 
By use of the Fourier transform, the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable was the displacement on the crack surfaces.


To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials.


Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables were the jumps of the displacements across the crack surfaces.


To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials.


This problem is reduced by means of Fourier transforms to the standard set of dual integral equations with two variables.


Application of the Fourier and Laplace transforms technique reduces the problem to that of solving dual integral equations.


The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundaryvalue condition.


By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically.


By using integral transforms and dual integral equations, the local dynamic stress field was obtained.


The solution of this equation under mixed boundary conditions of mode II Griffith crack was obtained in terms of Fourier transform and dual integral equations methods.


The solution of this equation under mixed boundary conditions of modeII Griffith crack was obtained in terms of Fourier transform and dual integral equations methods.


The integral transform method is applied to convert the problem involving an impermeable antiplane crack to dual integral equations.


The analysis relied on the use of integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration of mixed boundaryvalue condition.


The set of dual integral equations are reduced to a Fredholm integral equation of the second kind and solved by numerical procedures.


By using the Fourier transform, the problem can be solved with two pairs of dual integral equations in which the unknown variable is the jump of the diplacement across the crack surfaces.


By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, of which the unknown variables are the jumps of the displacements across the crack surfaces.


By using the Fourier transform, the problem can be solved with a pair of dual integral equations in which the unknown variable was the jump of the displacements across the crack surfaces.


To solve the dual integral equations, the jump of the displacements across the crack surface was expanded in a series of Jacobi polynomials.


By using the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables were the jumps of the displacements across the crack surfaces.


Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundaryvalue problem.

