Daniel H. Felix

Natural frequencies of a vibrating repaired panel in an ocean structure

Abstract The present work arose from the need of repairing steel plates badly damaged by corrosion in a portion of the structural element of the naval vehicle. The possibility of removing the portion and replacing it by a patch of a composite material was considered. Its dynamic behavior is altered by the introduction of the patch and the prediction of its new behavior is of great interest in many situations. This condition would appear in other real-life situations like as a localized orthotropic effect caused in the panel by a welding procedure or a metallurgical process. The first four natural frequency coefficients of the composite repaired panel with different types of boundary conditions are determined by means of a variational approach. The displacement function is approximated making use of complete sets of beam functions. The eigenvalues have been computed from (225×225) secular determinants. An independent solution is obtained using the finite element method and a reasonably good agreement with the analytical solution is encountered.

Natural vibrations of micro beams with nonrigid supports

The present study aims to provide some new information for the design of micro systems. It deals with free vibrations of Bernoulli–Euler micro beams with nonrigid supports. The study is based on the formulation of the modified couple stress theory. This theory is a nonclassical continuum theory that allows one to capture the small-scale size effects in the vibrational behavior of micro structures. More realistic boundary conditions are represented with elastic edge conditions. The effect of Poisson’s ratio on the micro beam characteristics is also analyzed. The present results revealed that the characterization of real boundary conditions is much more important for micro beams than for macro beams, and this is an assessment that cannot be ignored.

Free Vibration Analysis of Centrifugally Stiffened Non Uniform Timoshenko Beams

Rotating beams – like structures are widely used in many engineering fields and are of great interest as they can be used to model blades of wind turbines, helicopter rotors, robotic manipulators, turbo-machinery and aircraft propellers. The governing differential equations of motion in free vibration of a non-uniform rotating Timoshenko beam, with general elastic restraints at the ends are solved using the differential quadrature method, (Bellman & Roth, 1986; Felix et al., 2008, 2009). The equations of motion are derived to include the effects of shear deformation, rotary inertia, hub radius, ends elastically restrained and non-uniform variation of the cross-sectional area of the beam. The presence of a centrifugal force due to the rotational motion is considered as Banerjee has developed, using Hamilton’s principle to capture the centrifugal stiffening arising in fast rotating structures, (Banerjee, 2001). With the proposed model, a great number of different situations are admitted to be solved. Particular cases with classical restraints can be deduced for limiting values of the rigidities. Also step changes in cross-section are considered (Naguleswaran, 2004).