Efficient inverse frequency design of tapered beams including shear deformations Original Research Article

The purpose of this paper is to develop a new highly efficient numerical method for finding the bending stiffness distribution and the corresponding shear stiffness distribution of a one-dimensional distributed-parameter structure which attains a specified fundamental natural frequency and has a specified lowest-mode curvature distribution. This problem is highly nonlinear with respect to the design variables. The distributed-parameter structure is modeled by a finite-element (FE) system. A cubic displacement function is utilized for bending deformation in the FE system. A bending model and a bending-shear model are introduced. First, the bending stiffness distribution is determined for the bending model taking into account the bending deformation alone. Then additional horizontal displacements, due to shear deformation, of the corresponding bending-shear model are calculated from the shear rigidity. The bending stiffnesses are then updated in terms of the new inertial nodal forces evaluated for the bending-shear model. In order to satisfy the convergence condition, this procedure is implemented recursively. Comparison of numerical results with the results by Toʹs method guarantees the validity and accuracy of this method.