Boundary and Eigenvalues problems for generally restrained anisotropic plates with internal hinges

RICARDO O. GROSSI Y V. QUINTANA

Facultad de Ingeniería de la Universidad de Buenos Aires,

Congreso; V Congreso Internacional de Matemática Aplicada a la Ingeniería.; 2008

Abstract. This article deals with the free transverse vibration of anisotropic plates with generally restrained boundaries with an internal hinge elastically restrained against rotation and translation. A rigorous and complete development is presented. The Hamilton´s principle is rigorously stated by defining the domain of the action integral and the space of admissible directions. The differential equations, boundary conditions, and particularly the transitions conditions, are obtained. The Ritz method is used to obtain the corresponding eigenvalues. Results are presented for different boundary conditions and restraint conditions in the internal hinge. Tables are given for frequency and three dimensional plots are given for mode shapes. This article deals with the free transverse vibration of anisotropic plates with generally restrained boundaries with an internal hinge elastically restrained against rotation and translation. A rigorous and complete development is presented. The Hamilton´s principle is rigorously stated by defining the domain of the action integral and the space of admissible directions. The differential equations, boundary conditions, and particularly the transitions conditions, are obtained. The Ritz method is used to obtain the corresponding eigenvalues. Results are presented for different boundary conditions and restraint conditions in the internal hinge. Tables are given for frequency and three dimensional plots are given for mode shapes.