• Journal of KSNVE
• /
• v.9 no.5
• /
• pp.1019-1028
• /
• 1999

Free vibration characteristics of cantilevered laminated composite beams with a transverse non0propagating open carck are investigated. In the present analysis a special ply-angle distribution referred to as asymmetric stiffness configuration inducing the elastic coupling between chord-wise bending and extension is considered. The open crack is modelled as an equivalent rotational spring whose spring constant is calculated on the basis of fracture mechanics of composite material structures. Governing equations of a composite beam with a open crack are derived via Hamilton's Principle and Timoshenko beam theory encompassing transverse shear and rotary inertia effect. the effects of various parameters such as the ply angle, fiber volume fraction, crack depth, crack position and transverse shear on the free vibration characteristics of the beam with a crack is highlighted. The numerical results show that the natural frequencies obtained from Timoshenko beam theory are always lower than those from Euler beam theory. The presence of intrinsic cracks in anisotropic composite beams modifies the flexibility and in turn free vibration characteristics of the structures. It is revealed that non-destructive crack detection is possible by analyzing the free vibration responses of a cracked beam.

• Structural Engineering and Mechanics
• /
• v.62 no.2
• /
• pp.247-258
• /
• 2017

Beam-like structures such as bridge, high building and tower, pipes, flexible connecting rods and some robotic manipulators are often excited by support motions. These structures are important in machines and structures. So, this study proposes an analytic method to accurately predict the dynamic behaviors of the structures during support motions or an earthquake. Using Timoshenko beam theory which is valid even for non-slender beams and for high-frequency responses, the analytic responses of fixed-fixed beams subjected to a real seismic motions at supports are illustrated to show the principled approach to the proposed method. The responses of a slender beam obtained by using Timoshenko beam theory are compared with the solutions based on Euler-Bernoulli beam theory to validate the correctness of the proposed method. The dynamic analysis for the fixed-fixed beam subjected to support motions gives useful information to develop an understanding of the structural behavior of the beam. The bending moment and the shear force of a slender beam are governed by dynamic components while those of a stocky beam are governed by static components. Especially, the maximal magnitudes of the bending moment and the shear force of the thick beam are proportional to the difference of support displacements and they are influenced by the seismic wave velocity.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2004.05a
• /
• pp.315-319
• /
• 2004

Static and dynamic responses of micro cantilever beam structures undertaking electrostatic forces are obtained employing Galerkin's method based on Euler beam theory. Variations of static and dynamic responses as well as resonant frequencies are estimated for several sets of beam properties and applied voltages. It is shown that the applied voltage influences the deflection and the modal characteristics significantly. Such information can be usefully employed for the design of MEMS structures.

• Geomechanics and Engineering
• /
• v.2 no.1
• /
• pp.45-56
• /
• 2010

The current study presents a mathematical model and numerical method for free vibration of tapered piles embedded in two-parameter elastic foundations. The method of Discrete Singular Convolution (DSC) is used for numerical simulation. Bernoulli-Euler beam theory is considered. Various numerical applications demonstrate the validity and applicability of the proposed method for free vibration analysis. The results prove that the proposed method is quite easy to implement, accurate and highly efficient for free vibration analysis of tapered beam-columns embedded in Winkler- Pasternak elastic foundations.

• Structural Engineering and Mechanics
• /
• v.77 no.5
• /
• pp.587-599
• /
• 2021

Based on Euler-Bernoulli beam theory and continuous element method, the free vibration of bi-dimensional functionally graded beams is investigated. It is assumed that the material properties vary exponentially along the beam thickness and length. The characteristic frequency equations of beams with different boundary conditions are obtained by transfer matrix method. The validity of the proposed method is assessed through comparison with available results. Parametric studies are carried out to analyze the influences of the gradient indexes and the beam slenderness ratio on the natural frequencies of bi-dimensional functionally graded beams.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.8
• /
• pp.2123-2138
• /
• 1994

A study on the dynamic mechanical properties of the high strength carbon fiber epoxy composite beam was carried out. The macromechanical model was used for the theoretical analysis of the symmetric laminated composite beam. The anisotropic plate theory and Bernoulli-Euler beam theory were used to predict the effective flexural elastic modulus and the specific damping capacity of laminated composite beam. The free flexural vibration and torsional vibration tests were carried out to determine the specific damping capacities of the unidirectional laminated composite beam. The vibration tests were performed in a vacuum chamber with laser vibrometer system and electromagnetic hammer to obtain accurate experimental data. From the computational and experimental results, it was found that the theoretical values with the macromechanical analysis and the experimental data of symmetric laminated composite beam were in good agreement.

• Structural Engineering and Mechanics
• /
• v.54 no.4
• /
• pp.693-710
• /
• 2015

This paper presents a nonlocal shear deformation beam theory for bending, buckling, and vibration of functionally graded (FG) nanobeams using the nonlocal differential constitutive relations of Eringen. The developed theory account for higher-order variation of transverse shear strain through the depth of the nanobeam, and satisfy the stress-free boundary conditions on the top and bottom surfaces of the nanobeam. A shear correction factor, therefore, is not required. In addition, this nonlocal nanobeam model incorporates the length scale parameter which can capture the small scale effect and it has strong similarities with Euler-Bernoulli beam model in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived from Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam, and the obtained results compare well with those predicted by the nonlocal Timoshenko beam theory.

• Structural Monitoring and Maintenance
• /
• v.4 no.3
• /
• pp.269-299
• /
• 2017

This paper presents a Level III damage evaluation methodology, which simultaneously, identifies the location, the extent, and the severity of stiffness damage in deep beams. Deep beams are structural elements with relatively high aspect (depth-to-length) ratios whose response are no longer based on the simplified Euler-Bernoulli theory. The proposed methodology is developed on the bases of the force-displacement relations of the Timoshenko beam theory and the concept of invariant stress resultants, which states that the net internal force existing at any cross-section of the beam is not affected by the inflicted damage, provided that the external loadings in the undamaged and damaged beams are identical. Irrespective of the aspect ratios, local changes in both the flexural and the shear stiffnesses of beam-type structures may be detected using the approach presented in this paper.

• Proceeding of EDISON Challenge
• /
• 2015.03a
• /
• pp.274-278
• /
• 2015

There are different kinds of aircrafts, such as conventional airplane, rotorcraft, fighter, and unmanned aerial vehicle. Their shape and feature are dependent upon their assigned mission. One of the fundamental analyses during the design of the aircraft is the structural analysis. The structural analysis becomes more complicated and needs more computations because of the on-going complex aircrafts' structure. In order for efficiency in the structural analysis, a simplified approach, such as equivalent beam or plate model, is preferred. However, it is not clear which analysis will be appropriate to analyze the realistic configuration, i.e., an equivalent beam or plate analysis for an aircraft wing. It is necessary to assess the boundary between the one-dimensional beam analysis and the two-dimensional plate theory for an accurate structural analysis. Thus, in this paper, the static structural analysis results obtained by EDISON solvers were compared with the three-dimesional results obtained from MSC NASTRAN. Before that, EDISON program was verified by comparing the results with those from MSC NASTRAN program and analytic solution.

• Structural Engineering and Mechanics
• /
• v.32 no.6
• /
• pp.811-833
• /
• 2009

In the present article bending, buckling and vibration analyses of tapered beams using Eringen non-local elasticity theory are being carried out. The associated governing differential equations are solved employing Rayleigh-Ritz method. Both Euler-Bernoulli and Timoshenko beam theories are considered in the analyses. Present results are in good agreement with those reported in literature. Beam material is considered to be made up of functionally graded materials (fgms). Non-local analyses for tapered beam with simply supported - simply supported, clamped - simply supported and clamped - free boundary conditions are carried out and discussed. Further, effect of length to height ratio on maximum deflections, vibration frequencies and critical buckling loads are studied.