Timoshenko beam theory

About: Timoshenko beam theory is a research topic. Over the lifetime, 9426 publications have been published within this topic receiving 200570 citations.

A reformulated flexoelectric theory for isotropic dielectrics

Abstract: In flexoelectricity, a strain gradient can induce polarization and a polarization gradient can induce mechanical stress. In this paper, in order to identify the contributions of each strain gradient component, the flexoelectric theory is reformulated by splitting the strain gradient tensor into mutually independent parts. Two sets of orthogonal higher-order deformation metrics are inherited and perfected to reformulate the internal energy density for isotropic materials. The deviatoric stretch gradient and the symmetric part of the rotation gradient are proved to disappear in the coupling of strain gradient to polarization and, moreover, the independent higher-order constants associated with the coupling of strain gradient to strain gradient reduce from five to three. The constitutive relations are then reformulated in terms of the new deformation and electric field metrics, and the governing equations and boundary conditions are derived according to the variational principle of electric enthalpy. On the basis of the present simplified flexoelectric theory, a flexoelectric Bernoulli–Euler beam theory is specified. Solutions for a cantilever subjected to a force at the free end and a voltage cross the thickness are constructed and the size-dependent direct and inverse flexoelectric effects are captured.

Comparison of modeling of the rotating tapered axially functionally graded Timoshenko and Euler–Bernoulli microbeams

Abstract: The target of this paper is to present an exhaustive study on the small scale effect on vibrational behavior of a rotary tapered axially functionally graded (AFG) microbeam on the basis of Timoshenko and Euler–Bernoulli beam and modified couple stress theories. The variation of the material properties and cross section along the longitudinal direction of the microbeam are taken into consideration as a linear function. Hamilton's principle is used to derive the equations for cantilever and propped cantilever boundary conditions and the generalized differential quadrature method (GDQM) is employed to solve the equations. By parametric study, the effects of small-scale parameter, rates of cross section change of the microbeam and angular velocity on the fundamental and second frequencies of the microbeam are studied. Also, comparison between the frequencies of Timoshenko and Euler–Bernoulli microbeams are presented. The results can be used in many applications such as micro-robots and biomedical microsystems.

Free vibration analysis of viscoelastic nanotubes under longitudinal magnetic field based on nonlocal strain gradient Timoshenko beam model

Abstract: In this paper, the free vibration of viscoelastic nanotube under longitudinal magnetic field is investigated The governing equation is formulated by utilizing Timoshenko beam model and Kelvin-Voigt model based on the nonlocal strain gradient theory The local adaptive differential quadrature method (LADQM) is applied in the analyzing procedure We also investigated the influences of the nonlocal parameter, structural damping coefficient, material length scale parameter and the longitudinal magnetic field on the natural frequencies of the system The results of this research may be helpful for understanding the potential applications of nanotubes in Nano-Electromechanical System

Feedback stabilization of a Timoshenko beam with an end mass

Abstract: The boundary feedback control problem of a Timoshenko beam with an end mass is studied in this paper. First, under some nonlinear boundary feedback controls, the asymptotic stability for the corresponding closed-loop system is shown. Then, with the energy-perturbed approach, it is proved, under some specific linear feedback controls applied to the tip, that the vibration of the beam decays uniformly; finally, in the case when feedback controls are applied to both the beam ends, the uniform decay is also established.