In this study, flapwise bending vibration analysis of a tapered Timoshenko beam mounted on the periphery of a rotating rigid hub is performed. The governing differential equations of motion for pure bending are derived using the Hamilton’s principle and solved using the Differential Transform Method, DTM. During the derivation of the equations, effects of rotary inertia, shear deformation and h...

We study the implicit time discretization of piano strings governing equations within the Timoshenko prestressed beam model. Such model features two different waves, namely the flexural and shear waves, that propagate with very different velocities. We present a novel implicit time discretization that reduces the numerical dispersion while allowing the use of a large time step in the numerical ...

Für elastische Balken mit Piezoaktuatoren werden flachheitsbasierte Randsteuerungen entworfen, die eine Positionierung in endlicher Einstellzeit gestatten. Dabei werden sowohl Euler-Bernoulli-Balken als auch Timoshenko-Balken untersucht. Steuerungen für Balken mit mehreren Piezoaktuatoren werden durch Superposition berechnet. Die Methoden werden durch die Ergebnisse von Simulationen und eines E...

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...

This article presents an analysis of free vibration of elastically supported Timoshenko beams by using the spectral element method. The governing partial differential equation is elaborated to formulate the spectral stiffness matrix. Effectively, the non classical end boundary conditions of the beam are the primordial task to calibrate the phenomenon of the Timoshenko beam-soil foundation inter...

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...

In this paper, a relatively new method, namely variational iteration method (VIM), is developed for free vibration analysis of a Timoshenko beam with different boundary conditions. In the VIM, an appropriate Lagrange multiplier is first chosen according to order of the governing differential equation of the boundary value problem, and then an iteration process is used till the desired accuracy ...

In this article free vibration of a Timoshenko nanobeam with variable cross-section is investigated using nonlocal elasticity theory within the scope of continuum mechanics. Small scale effects are modelled after Eringen’s nonlocal elasticity theory while the non-uniformity is presented by exponentially varying width through the beam length with constant thickness. Analytical solution is achiev...

In this paper we consider the effect of boundary damping on a cantilevered Timoshenko beam with a rigid body attached to the free end. We establish the efficiency and accuracy of the finite element method for calculating the eigenvalues and eigenmodes. Although no conclusion could be drawn with regard to the stabilization of the system, interesting phenomena concerning the damped vibration spec...

"Well-posedness and stability of a semilinear Mindlin-Timoshenko plate model" I will discuss well-posedness and long-time behavior of Mindlin-Timoshenko plate equations that describe vibrations of thin plates. This system of partial differential equations was derived by R. Mindlin in 1951 (though E. Reissner also considered an analogous model earlier in 1945). It can be regarded as a generaliza...