This paper presents an analytical refined beam model taking into account the axial, shear and transverse normal stress distributions. Based on equilibrium equations in local form iterative procedure for solution of bipotential equation, differential axial motion are derived. From a mathematical point view formal structure obtained is identical to Timoshenko but with increased accuracy. achieved...

We consider the problem of minimizing supplied energy infinite-dimensional linear port-Hamiltonian systems and prove that optimal trajectories exhibit turnpike phenomenon towards certain subspaces induced by dissipation dynamics. The theoretical foundations are illustrated means numerical examples concerning a Timoshenko beam heat equation.

The position that the structure of a language has an impact on the cognition of its speakers is a venerable, if controversial, one in both linguistics and anthropology (see Gumperz and Levinson 1996 and Lucy 1992 for recent overviews). Over the last 60 years, a wide range of theories about the relationship between language and thought have been developed and disputed. The theories that posit so...

In this paper we present the first extension of the backstepping methods developed for control of parabolic PDEs (modeling thermal, fluid, and chemical reaction dynamics, including Navier-Stokes equations and turbulence) to secondorder PDE systems (often referred loosely as hyperbolic) which model flexible structures and acoustic. We introduce controller and observer designs capable of adding d...

Euler, Timoshenko and high shear deformation theories to analyze the free vibration of functionally graded (FG) beam were developed. The mechanical properties this assumed differ in thickness direction according model a power-law distribution. principle Hamilton was used find equations motion. For vibration, analytical solution these presented using Navier method. effect power index, aspect rat...

This study introduces the Differential Transform Method (DTM) in the analysis of 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 natura...