Dynamic Stability Of Beam Research Articles

Dynamic stability of CNTs-reinforced non-uniform composite beams under axial excitation loading

This paper presents an analytical study on the dynamic stability of carbon nanotubes (CNTs) reinforced functionally graded composite beams when subjected to axial excitation loading. The composite beams are functionally graded using a I-type CNTs reinforcement. The section properties of the non-uniform functionally graded composite beams are assessed using Halpin–Tsai model. The analysis of dynamic stability of the composite beams is performed by using Bolotin’s method. Analytical expressions of determining free vibration frequency, critical buckling load, and excitation frequency of the non-uniform functionally graded composite beams are derived, in which both the shear deformation and rotary inertia effects are considered. The study demonstrates that the dynamic stability of the beam can be improved significantly when it is functionally graded using the I-type CNTs reinforcement.

Discrete Singular Convolution Method for Dynamic Stability Analysis of Beams under Periodic Axial Forces

AbstractIn the present study, the discrete singular convolution (DSC) method is used to analyze the dynamic stability of beams subjected to different boundary conditions under periodic axial forces. A unified DSC algorithm is established to solve the governing equations of beam motion under different boundary conditions. The regularized Shannon’s delta kernel is selected as singular convolution to illustrate the present algorithm. The matched interface and boundary method is applied to the treatment of elastic restraint boundary conditions. The effects of a constant term in the periodic axial force and damping on dynamic instability regions are also investigated. The obtained numerical results are compared with those of Bolotin’s method. Numerical results indicate that the DSC method is a reliable method for dynamic stability analysis of beams.

Cracks Interaction Effect on the Dynamic Stability of Beams under Conservative and Nonconservative Forces

This study is an extension of the paper by E. Viola and A. Marzani [1] where the eigenfrequencies and critical loads of a single cracked beam subjected to conservative and nonconservative forceshave been investigated. Here the aim is to analyze the dynamic stability of T cross section beams withmultiple cracks. A doubly cracked Euler-Bernoulli beam subjected to triangularly distributed subtangential forces, which are the combination of axial and tangential forces, is considered. The governingequation of the system is derived via the extended Hamilton’s principle in which the kinetic energy, theelastic potential energy, the conservative work and the nonconservative work are taken into account. Thelocal flexibility matrix for a beam with T cross-section is used to model the cracked section. The resultsshow that for given boundary conditions cracked beams become unstable in the form of either flutter ordivergence depending on the crack parameters, the nonconservativeness of the applied load as well as theinteraction of the two cracks.

On the static and dynamic stability of beams with an axial piezoelectric actuation

The present contribution is concerned with the static and dynamic stability of a piezo-laminated Bernoulli-Euler beam subjected to an axial compressive force. Recently, an inconsistent derivation of the equations of motions of such a smart structural system has been presented in the literature, where it has been claimed, that an axial piezoelectric actuation can be used to control its stability. The main scope of the present paper is to show that this unfortunately is impossible. We present a consistent theory for composite beams in plane bending. Using an exact description of the kinematics of the beam axis, together with the Bernoulli-Euler assumptions, we obtain a single-layer theory capable of taking into account the effects of piezoelectric actuation and buckling. The assumption of an inextensible beam axis, which is frequently used in the literature, is discussed afterwards. We show that the cited inconsistent beam model is due to inadmissible mixing of the assumptions of an inextensible beam axis and a vanishing axial displacement, leading to the erroneous result that the stability might be enhanced by an axial piezoelectric actuation. Our analytical formulations for simply supported Bernoulli-Euler type beams are verified by means of three-dimensional finite element computations performed with ABAQUS.

Effect of boundary conditions on the stability of beams under conservative and non-conservative forces

This paper, which is an extension of a previous work by Viola et al. (2002), deals with the dynamic stability of beams under a triangularly distributed sub-tangential forces when the effect of an elastically restrained end is taken into account. The sub-tangential forces can be realised by a combination of axial and tangential follower forces, that are conservative and non-conservative forces, respectively. The studied beams become unstable in the form of either flutter or divergence, depending on the degree of non-conservativeness of the distributed sub-tangential forces and the stiffness of the elastically restrained end. A non-conservative parameter is introduced to provide all possible combinations of these forces. Problems of this kind are usually, at least in the first approximation, reduced to the analysis of beams according to the Bernoulli-Euler theory if shear deformability and rotational inertia are negligible. The equation governing the system may be derived from the extended form of Hamilton`s principle. The stability maps will be obtained from the eigenvalue analysis in order to define the divergence and flutter domain. The passage from divergence to flutter is associated with a noticeable lowering of the critical load. A number of particular cases can be immediately recovered.

Dynamic stability of beams with finite displacements and rotations

The aim of this paper is to find the regions of dynamic stability of systems of beams and frames with finite displacements and rotations. A suitable numerical procedure allows regions of dynamic stability to be obtained for any value of the dynamic force, taking into account the different characteristics of constraints, inertia and stiffness. A set of numerical applications is presented to show the capabilities of the proposed numerical method in the frame of the dynamic stability of beams.

Dynamic stability of beams with shearing strains and rotational inertia

Dynamic stability of beams with shearing strains and rotational inertia