We formulate large N duality of U(N) refined Chern-Simons theory with a torus knot/link in S3. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the Ω-background. This form enables us to relate refined Chern-Simons invariants of a torus knot/link in S3 to refined BPS invariants in the resolved con...

A Trigonometric Shear Deformation Theory (TSDT) for the analysis of isotropic plate, taking into account transverse shear deformation effect as well as transverse normal strain effect, is presented. The theory presented herein is built upon the classical plate theory. In this displacement-based, trigonometric shear deformation theory, the in-plane displacement field uses sinusoidal function in ...

The effect of a distributed patch mass on the natural frequency of vibration of a laminated rectangular plate with simply supported boundaries is investigated. The third order displacement field of a composite laminated rectangular plate is defined using the two variable refined plate theory. Equations of motion of the plate are obtained with the help of calculus of variation. Parametric study ...

In this paper, an attempt is made for solution of free vibration analysis of annular plate reinforced with carbon nanotubes for Uniformly Distribution (UD), resting on an elastic foundation using a refined theory presented. In this theory, a parabolic distribution of shear stress and strain in the thickness direction and satisfies the boundary conditions of zero shear stress on the upper and lo...