Finally, some apparently paradoxical results indicating that a reduction in shear stiffness occurs in rare cases if more material is added to a section are discussed and explained as resulting from the use of integrated rather than pointwise deflection measures in the derivation of consistent shear ...
The derivation of Timoshenko beam theory and its applications to the computation of natural frequencies and mode shapes of finite-length beams have been standard material as included in almost all vibration textbooks (e.g., [27]). From the point of view of wave mechanics, considering the waves...
A continuum mechanics-based derivation can be found in [19], where nonlinear effects are considered. The reader is also referred to a recent book [20] where different beam models are treated with a variety of applications. Article [21] promises to be useful for the calculation of natural ...
After the derivation the only nonzero elements are axial strain e XX and the shear strain 2e XY = e XY + e Y X . Under small strain assumption we can finally express strain vector as: e = e 1 e 2 = e XX 2e XY = e −Y κ γ (1) where three strain quantities introduced...
Acta Mechanica N. F. J. van Rensburg, S. du Toit& M. Labuschagne 237Accesses Explore all metrics Abstract In this article, we consider a variant of the Simo–Reissner theory for a rod but restrict the study to two-dimensional motion where the rod undergoes flexure, shear and extension ...
In this section we briefly describe the basic kinematics of a 3D beam, and its subsequent dimensional reduction, for detailed derivation readers are referred to Refs. [26], [27]. Following a Lagrangian description, an arbitrary material point in the un-deformed reference state of a beam can ...
Timoshenko BeamWave Induced ResonanceReferences#The Timoshenko Beam Theory#Derivation of Hamiltonian System#The Method of Separation of Variables#Reciprocal Theorem for Work and Adjoint Symplectic Orthogonality#Solution for Non-Homogeneous Equations#Two-Point Boundary Conditions#Static Analysis of Timoshenko Beam...
Intelligent beam structures: Timoshenko theory vs. Euler-Bernoulli theoryIn this paper, the derivation of the governing equations and boundary conditions of laminated beam smart structures are developed. Sensor and actuator layers are included in the beam so as to facilitate vibration suppression. Two ...
In this paper, the derivation of the governing equations and\nboundary conditions of laminated beam smart structures are developed.\nSensor and actuator layers are included in the beam so as to facilitate\nvibration suppression. Two mathematical models, namely the\nshear-deformable (Timoshenko) ...
Considering a Timoshenko cable-suspended beam structure such as the suspension bridge, where the roadbed has a negligible sectional dimensions in comparison with its length π (span of the bridge), this structure is modeled in Timoshenko theory through a one-dimensional extensible beam, while the ...