• Coupled systems mechanics
• /
• v.11 no.2
• /
• pp.167-198
• /
• 2022

In this paper we deal with classical instability problems of heterogeneous Euler beam under conservative loading. It is chosen as the model problem to systematically present several possible solution methods from simplest deterministic to more complex stochastic approach, both of which that can handle more complex engineering problems. We first present classical analytic solution along with rigorous definition of the classical Euler buckling problem starting from homogeneous beam with either simplified linearized theory or the most general geometrically exact beam theory. We then present the numerical solution to this problem by using reduced model constructed by discrete approximation based upon the weak form of the instability problem featuring von Karman (virtual) strain combined with the finite element method. We explain how such numerical approach can easily be adapted to solving instability problems much more complex than classical Euler's beam and in particular for heterogeneous beam, where analytic solution is not readily available. We finally present the stochastic approach making use of the Duffing oscillator, as the corresponding reduced model for heterogeneous Euler's beam within the dynamics framework. We show that such an approach allows computing probability density function quantifying all possible solutions to this instability problem. We conclude that increased computational cost of the stochastic framework is more than compensated by its ability to take into account beam material heterogeneities described in terms of fast oscillating stochastic process, which is typical of time evolution of internal variables describing plasticity and damage.

• Steel and Composite Structures
• /
• v.6 no.3
• /
• pp.203-219
• /
• 2006

One of the most promising ways through which a steel moment frame may attain high energy dissipating capability is to trim off a portion of the beam flanges near the column face. This type of moment connection, known as Reduced Beam Section (RBS) connection, has notable superiority in comparison with other moment connection types. As the result of the advantages of RBS moment connection, it has widely being used in practice. In spite of the good hysteretic behaviour, an RBS beam suffers from an undesirable drawback, which is local and lateral instability of the beam. The instability in the RBS beam reduces beam load-carrying capacity. This paper aims to investigate key issues influencing cyclic behaviour of RBS beams. To this end, a numerical analysis was conducted on a series of steel subassemblies with various geometric properties. The obtained results together with the existing experimental data are used to study the instability of RBS beams. A new slenderness concept is presented to control an RBS beam for combined local and lateral instability. This concept is in good agreement with the numerical and experimental results. Finally, a model is developed for the prediction of the magnitude of moment degradation owing to the instability of an RBS beam.

• Steel and Composite Structures
• /
• v.32 no.2
• /
• pp.157-171
• /
• 2019

In this research, the dynamic instability region (DIR) of the sandwich nano-beams are investigated based on nonlocal strain gradient elasticity theory (NSGET) and various higher order shear deformation beam theories (HSDBTs). The sandwich piezoelectric nano-beam is including a homogenous core and face-sheets reinforced with functionally graded (FG) carbon nanotubes (CNTs). In present study, three patterns of CNTs are employed in order to reinforce the top and bottom face-sheets of the beam. In addition, different higher-order shear deformation beam theories such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT) are considered to extract the governing equations for different boundary conditions. The beam is subjected to thermal and electrical loads while is resting on Visco-Pasternak foundation. Hamilton principle is used to derive the governing equations of motion based on various shear deformation theories. In order to analysis of the dynamic instability behaviors, the linear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, nonlocal parameter, strain gradient parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, dimensionless geometric parameters, Visco-Pasternak foundation parameters, applied voltage and temperature change on the dynamic instability characteristics of sandwich piezoelectric nano-beam.

• Laser Solutions
• /
• v.4 no.2
• /
• pp.13-19
• /
• 2001

When a high-power laser beam is irradiated on the surface of material, it is well known that a cavity, called a keyhole induced by the pressure action of the vapor plume, is generated in the molten material. This paper describes the interaction between a pulsed CO$_2$ laser beam and water. The laser-beam is used to generate and maintain a conical depression in the water surface similar to the keyhole created during laser penetration welding. Experimental results show that the depth of laser-beam penetration is limited by hydrodynamic instability. The instability of the surface cavity can be understood by the capillary instability of a hollow jet. Theoretical computation of the steady keyhole shape has been performed. modifying the model suggested by Andrews et al. (1976). The model predicts the qualitative behavior of the keyhole but significantly underestimates the average diameter.

• Coupled systems mechanics
• /
• v.10 no.1
• /
• pp.79-102
• /
• 2021

In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.1 s.173
• /
• pp.232-239
• /
• 2000

The paper describes the parametric instability of free-free beams subjected to a controlled pulsating follower force. The beam has a tip rigid body not a mass point, and the direction of pulsating follower force is controlled by the direction control sensor. Equations of motion are derived by Hamilton's principle and the instability regions are obtained by finite element formulation. The effects of magnitude, rotary inertia, the distance between free end of the beam and the center of gravity of the rigid body on the instability types and regions are investigated by the change of the constant and periodic part of the follower force.

• International Journal of Aeronautical and Space Sciences
• /
• v.14 no.1
• /
• pp.19-29
• /
• 2013

This paper deals with the study of buckling, vibration, and parametric instability characteristics in a damaged cross-ply and angle-ply laminated plate like beam under in-plane harmonic loading, using the finite element approach. Damage is modelled using an anisotropic damage formulation, based on the concept of reduction in stiffness. The effect of damage on free vibration and buckling characteristics of a thin plate like beam has been studied. It has been observed that damage shows a strong orthogonality and in general deteriorates the static and dynamic characteristics. For the harmonic type of loading, analysis was carried out on a thin plate like beam by solving the governing differential equation which is of Mathieu-Hill type, using the method of multiple scales (MMS). The effects of damage and its location on dynamic stability characteristics have been presented. The results indicate that, compared to the undamaged plate like beam, heavily damaged beams show steeper deviations in simple and combination resonance characteristics.

• The Bulletin of The Korean Astronomical Society
• /
• v.37 no.1
• /
• pp.92.2-92.2
• /
• 2012

Previous simulations posed a problem that they used reduced ion to electron mass ratios to save computation time. It was assumed that ion and electron dynamics are sufficiently separated, but it was not clearly verified. In this study, we examine the effect of ion to electron mass ratios on the generation of ion holes by ion beam driven instability. Ion holes are generated via electron holes in an applied electric field with the given initial condition. First, the ion acoustic instability is excited and nonlinearly develops. After the ion acoustic instability nonlinearly develops, the ion two-stream instability is excited and develops into ion holes. This implies that the previously suggested ion beam driven instability is strongly affected by the coupling between ions and electrons and the ion to electron mass ratio is important on the development of the instability. The energy transition and detail variation is different as reduced mass ratio under the same observation value based on FAST satellite. Although, the parameters are rescaled by conserving the kinetic energy to obtain the proper results, the nonlinear evolution is not perfectly identical.

• Structural Engineering and Mechanics
• /
• v.22 no.4
• /
• pp.483-510
• /
• 2006

The dynamic instability characteristics of laminated composite stiffened shell panels subjected to in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented to demonstrate the effects of various parameters like shell geometry, lamination scheme, stiffening scheme, static and dynamic load factors and boundary conditions, on the dynamic instability behaviour of laminated composite stiffened panels subjected to in-plane harmonic loads along the boundaries. The results of free vibration and buckling of the laminated composite stiffened curved panels are also presented.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.17 no.7 s.124
• /
• pp.605-610
• /
• 2007

In this paper a dynamic behavior(natural frequency) of a cracked cantilever beam subjected to follower force is presented. In addition, an analysis of the flutter and buckling instability of a cracked cantilever beam subjected to a follower compressive load is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter instability based on the variation of the first two resonant frequencies of the beam. Besides, the effect of the crack's intensity and location on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.