Non-prismatic beams have received great attention from engineers due to their capability in optimizing the strength and weight of the structure. In recent years, many researchers have worked on engineering problems related to static and dynamic analysis of either Euler–Bernoulli [1–3] or Timoshenko [4,5] beams. For short thick beams and rotating machineries, the Timoshenko beam theory presents ...

Analytical relations between the critical buckling load of a functionally graded material (FGM) Timoshenko beam and that of the corresponding homogeneous Euler–Bernoulli beam subjected to axial compressive load have been derived for clamped–clamped (C–C), simply supported–simply supported (S–S) and clamped–free (C–F) edges. However, no such relation is found for clamped–simply supported (C–S) b...

Purpose – To perform the flapwise bending vibration analysis of a rotating cantilever Timoshenko beam. Design/methodology/approach – Kinetic and potential energy expressions are derived step by step. Hamiltonian approach is used to obtain the governing equations of motion. Differential transform method (DTM) is applied to solve these equations. Findings – It is observed that the rIVu term which...

A study of the free vibration of Timoshenko beams and axisymmetric Mindlin plates is presented. The analysis is based on the Chebyshev pseudospectral method, which has been widely used in the solution of fluid mechanics problems. Clamped, simply supported, free and sliding boundary conditions of Timoshenko beams are treated, and numerical results are presented for different thickness-to-length ...

This paper presents the elastic buckling of homogeneous beams with a pair of piezoelectric layers surface bonded on both sides of the beams. The displacement field of beam is assumed based on the Engesser-Timoshenko beam theory. Applying the Hamilton's principle, the equilibrium equation is established. The influences of applied voltage, dimensionless geometrical parameter and piezoelectric thi...

Bending, buckling and vibration behaviors of nonlocal Timoshenko beams are investigated in this research using a variational approach. At first, the governing equations of the nonlocal Timoshenko beams are obtained, and then the weak form of these equations is outlined in this paper. The Ritz technique is selected to investigate the behavior of nonlocal beams with arbitrary boundary conditions ...

This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. N...

In this paper, we introduce a new class of discontinuous Galerkin methods for Timoshenko beams. The main feature of these methods is that they can be implemented in an efficient way through a hybridization procedure which reduces the globally coupled unknowns to approximations to the displacement and bending moment at the element boundaries. After displaying the methods, we obtain conditions un...

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 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...