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 study, the natural frequencies and mode shapes of beams without cracks and cracked Timoshenko beams is calculated with different boundary conditions using finite element method. The energy method is used to solve the equations. Hardness and softness matrices for Timoshenko beam without crack are obtained by solving the potential and kinetic energy equations. Then for investigation of cr...

in this paper, eringen’s nonlocal elasticity and timoshenko beam theories are implemented to analyze the bending vibration for non-uniform nano-beams.  the governing equations and the boundary conditions are derived using hamilton’s principle. a generalized differential quadrature method (gdqm) is utilized for solving the governing equations of non-uniform timoshenko nano-beam for pinned-pinned...

Finite element formulations based generally on classical beam theories such as Euler-Bernoulli or Timoshenko. Sometimes, these two formulations could be problematic expressed in terms of restrictions of Euler-Bernoulli beam theory, in case of thicker beams due to non-consideration of transverse shear; phenomenon that is known as shear locking characterized the Timoshenko beam theory, in case of...

We consider dynamics of the one-dimensional Mindlin-Timoshenko model for beams with a nonlinear external forces and a boundary damping mechanism. We investigate existence and uniqueness of strong and weak solution. We also study the boundary stabilization of the solution, i.e., we prove that the energy of every solution decays exponentially as t → ∞. AMS Subject Classifications. 35L70, 35B40, 7...

In this paper, the dynamic response of a simply supported beam subjected to moving load is reinvestigated. Based on new theory, slope inertia-based Timoshenko (SIBT), governing equations motion are derived. An analytical solution presented by using coupled Fourier and Laplace–Carson integral transformation method. The finite element also developed compared with solution. Then, comparative study...