We consider the dynamical one-dimensional Mindlin-Timoshenko system for beams. We analyze how its controllability properties depend on the modulus of elasticity in shear k. In particular we prove that the exact boundary controllability property of the Kirchhoff system may be obtained as singular limit, as k → ∞, of the partial controllability of a sharp subspace of low frequency components of t...

In this paper, we introduce a new class of discontinuous Galerkin methods for Timoshenko beams. The main feature of these methods is that they can be implemented in an efficient way through a hybridization procedure which reduces the globally coupled unknowns to approximations to the displacement and bending moment at the element boundaries. After displaying the methods, we obtain conditions un...

A method is given by which the response of a rotating or non-rotating Timoshenko beam can be determined, subjected to an accelerating fixed direction distributed surface force. The beam mode1 includes the gyroscopically induced displacement transverse to the direction of the load. The solution for pinned supports is set up using multi-integral transforms, and the inversion is expressed in terms...

Continuing in the vein of a recently developed generalization of continuum thermomechanics, in this paper we extend fracture mechanics and beam mechanics to materials described by fractional integrals involving D, d and R. By introducing a product measure instead of a Riesz measure, so as to ensure that the mechanical approach to continuum mechanics is consistent with the energetic approach, sp...

Strain distributions are crucial criteria of cross-beams six-axis force/torque sensors. The conventional method for calculating the criteria is to utilize Finite Element Analysis (FEA) to get numerical solutions. This paper aims to obtain analytical solutions of strains under the effect of external force/torque in each dimension. Genetic mechanical models for cross-beams six-axis force/torque s...

A layered Timoshenko beam (TB) model of a high-rise building is presented and applied to system identification of a full-scale building from recorded seismic response. This model is a new development in a wave method for earthquake damage detection and structural health monitoring being developed by the authors’ research group. The method is based on monitoring changes in the wave properties of...

In this paper, nonlinear vibration analysis of functionally graded piezoelectric (FGP) beam with porosities material is investigated based on the Timoshenko beam theory. Material properties of FG porous beam are described according to the rule of mixture which modified to approximate material properties with porosity phases. The Ritz method is used to obtain the governing equation which is then...

Based on an original interpolation method we develop a beam nite element formulation on the Lie group SEp3q which relies on a mathematically rigorous framework and provides compact notations. We work out the beam kinematics in the SE(3) context, the beam deformation measure and obtain the expression of the internal forces using the virtual work principle. The proposed formulation exhibits impor...

This study introduces the free vibration analysis of multilayered symmetric sandwich Timoshenko beams, made of functionally graded materials with two edge cracked, using the finite element method and linear elastic fracture mechanic theory. The FG beam consists of 50 layers, located symmetrically to the neutral plane, whose material properties distribution change along the beam thickness, accor...

this study introduces the differential transform method (dtm) to analyse the free vibration response of a rotating, closed section, composite, timoshenko beam which features material coupling between flapwise bending and torsional vibrations due to ply orientation. the governing differential equations of motion are derived using hamilton’s principle and solved by applying dtm. the natural frequ...