The interior and exterior Robin boundary value problems for the model of flexural vibrations of plates with transverse shear deformation are solved by means of layer potentials in conjunction with the integral representation formulas for the solutions.
Thomson, GR , and Constanda, C.Integral equation methods for the Robin problem in stationary oscillations of elastic plates. IMA Journal of Applied Mathematics, 74, 548-558 (2009).
2.
Thomson, GR , and Constanda, C.Scattering of high frequency flexural waves in thin plates. Mathematics and Mechanics of Solids, 4, 461-479 (1999).
3.
Constanda, C.Direct and Indirect Boundary Integral Equation Methods, Chapman & Hall/CRC , Boca Raton, FL, 2002.
4.
Constanda, C.A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation, Longman/ Wiley, New York, 1990.
5.
Schiavone, P., and Constanda, C.Oscillation problems in thin plates with transverse shear deformation. SIAM Journal on Applied Mathematics, 53, 1253-1263 (1993).
6.
Thomson, GR , and Constanda, C.Area potentials for thin plates. Analele Ştiinţifice ale Universităţii ‘‘Alexandru Ioan Cuza’’ din Iaşi. Serie Nouă. Matematică, 44, 235-244 (1998).
7.
Thomson, GR , and Constanda, C.A matrix of fundamental solutions in the theory of plate oscillations. Applied Mathematics Letters, 22, 707-711 (2009).
8.
Constanda, C.Radiation conditions and uniqueness for stationary oscillations in elastic plates. Proceedings of the American Mathematical Society, 126, 827-834 (1998).
9.
Thomson, GR , and Constanda, C.Uniqueness of solution for the Robin problem in high-frequency vibrations of elastic plates. Preprint no. 20, Center for Boundary Integral Methods, University of Tulsa (2008).
10.
Thomson, GR, and Constanda, C.The eigenfrequencies of the Dirichlet and Neumann problems for an oscillating finite plate. Mathematics and Mechanics of Solids, 14, 667-678 (2009).
11.
Thomson, GR, and Constanda, C.Representation theorems for the solution of high frequency harmonic oscillations in elastic plates. Applied Mathematics Letters, 11(5), 55-59 ( 1998).
