• Geomechanics and Engineering
• /
• v.33 no.4
• /
• pp.381-391
• /
• 2023

The aim of this work is to analyze and predict the wave propagation behavior of the carbon nanotube reinforced composites (CNTRC) beams within the framework of various higher order shear deformation beam theory. Using the Euler-Lagrange principle, the wave equations for CNTRC beams are derived, where the determining factor is to make the determinant equal to zero. Based on the eigenvalue method, the relationship between wave number and circular frequency is obtained. Furthermore, the phase and group velocities during wave propagation are obtained as a function of wave number, and the material properties of CNTRC beams are estimated by the mixture rule. In this paper, various higher order shear beam theory including Euler beam theory, Timoshenko beam theory and other beam theories are mainly adopted to analyze the wave propagation problem of the CNTRC beams, and by this way, we conduct a comparative analysis to verify the correctness of this paper. The mathematical model provided in this paper is verified numerically by comparing it with some existing results. We further investigate the effects of different enhancement modes of CNTs, volume fraction of CNTs, spring factor and other aspects on the wave propagation behaviors of the CNTRC beams.

• Journal of the Korean Society for Nondestructive Testing
• /
• v.20 no.6
• /
• pp.481-489
• /
• 2000

A time-frequency analysis method was developed to analyze the dispersive waves caused by impact loads in structural members such as beams and plates. Stress waves generated by ball drop and pencil lead break were recorded by ultrasonic transducers and acoustic emission (AE) sensors. Wavelet transform (WT) using Gabor function was employed to analyze the dispersive waves in the time-frequency domain, and then to find the arrival time of the waves as a function of frequency. The measured group velocities in the beam and the plate were compared with the predictions based on the Timoshenko beam theory and Rayleigh-Lamb frequency equations, respectively. The agreements were found to be very good.

• Smart Structures and Systems
• /
• v.10 no.2
• /
• pp.111-130
• /
• 2012

Satellites with flexible lightweight solar panels are sensitive to vibration that is caused by internal actuators such as reaction or momentum wheels which are used to control the attitude of the satellite. Any infinitesimal amount of unbalance in the reaction wheels rotors will impose a harmonic excitation which may interact with the solar panels structure. Therefore, quenching the solar panel's vibration is of a practical importance. In the present work, the panels are modeled as laminated composite beam using first-order shear deformation laminated plate theory which accounts for rotational inertia as well as shear deformation effects. The vibration suppression is achieved by bonding patches of piezoelectric material with suitable dimensions at selected locations along the panel. These patches are actuated by driving control voltages. The governing equations for the system are formulated and the dynamic Green's functions are used to present an exact yet simple solution for the problem. A guide lines is proposed for determining the values of the driving voltage in order to suppress the induced vibration.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.12 no.2
• /
• pp.141-149
• /
• 2002

Although the finite element method has become an indispensible tool for the dynamic analysis of structures, difficulty remains to quantify the errors associated with discretization. To improve the modeling accuracy, this paper proposes a method to make a combined use of finite elements and exact dynamic elements. Exact interpolation functions for the Timoshenko beam element are derived using the exact dynamic element modeling (EDEM) and compared with interpolation functions of the finite element method (FEM). The exact interpolation functions are tested with the Laplace variable varied. A combined use of finite element method and exact interpolation functions is presented to gain more accurate mode shape functions. This paper also presents a combined use of finite elements and exact dynamic elements in design/reanalysis problems. Timoshenko flames with tapered sections are tested to demonstrate the design procedure with the proposed method. The numerical study shows that the combined use of finite element model and exact dynamic element model is very useful.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.20 no.6
• /
• pp.719-730
• /
• 2007

This study presents a thin-walled space frame element based on the classical Timoshenko beam theory. The element is derived according to the assumed strain field in order to resolve the shear-locking phenomenon. The shape function is developed in accordance with the strain field which is assumed to be constant at a 2-noded straight frame element. In this study, the geometrically nonlinear analysis applies the Corotational procedure in order to evaluate unbalanced loads. The bowing effect is also considered faithfully. Two numerical examples are given; monosymmetric curved and nonsymmetric straight cantilever. When these example structures behave lateral-torsional bucking, the critical loads are obtained by this study and ABAQUS shell elements. Also, the post-buckling behavior is examined. The results give good agreement between this study and ABAQUS shell.

• Steel and Composite Structures
• /
• v.15 no.5
• /
• pp.481-505
• /
• 2013

This paper focuses on thermal post-buckling analysis of functionally graded beams with temperature dependent physical properties by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. In the case of beams with immovable ends, temperature rise causes compressible forces and therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. Also, the material properties (Young's modulus, coefficient of thermal expansion, yield stress) are temperature dependent: That is the coefficients of the governing equations are not constant in this study. This situation suggests the physical nonlinearity of the problem. Hence, the considered problem is both geometrically and physically nonlinear. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In this study, the differences between temperature dependent and independent physical properties are investigated for functionally graded beams in detail in post-buckling case. With the effects of material gradient property and thermal load, the relationships between deflections, critical buckling temperature and maximum stresses of the beams are illustrated in detail in post-buckling case.

• Journal of the Society of Naval Architects of Korea
• /
• v.39 no.3
• /
• pp.64-74
• /
• 2002

A special purposed program for ship hull strength analysis considering whipping phenomena is developed. In this program, the non-linear hydrodynamic impact force is considered using the momentum slamming theory and the hull girder is modeled as elastic body on the base of Timoshenko's beam theory. The numerical verifications are conducted in the view points that the effect of slamming impact force, the effect of hydro-elastic formulation, and the effect of various design parameters such as ship speed, wave amplitude, wave length and others. By the application of a real ship design process, the availability of the program is proved. This program has a GUI function for many I/O data process as well as the function to show the 2-D ship motion in the graphic window, and has other available functions for the whipping analysis.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.15 no.2
• /
• pp.455-462
• /
• 1991

This paper present an analysis method of crankshaft of four cylinder internal combustion engine for studying dynamic characteristics of the shaft. For simple analysis, uniform sections of journal, pin and arm parts were assumed. Transfer Matrix Method was used, considering branched part and coordinate transformation part. Natural frequencies, natural modes and transfer functions of crank shaft were investigated based upon the Timosenko beam theory: It was shown that the calculated natural frequencies, modeshapes agree well with the experimental results.

• Journal of Ocean Engineering and Technology
• /
• v.17 no.3 s.52
• /
• pp.21-26
• /
• 2003

An iteractive Kantorovich method is presented for the vibration analysis of rectangular orthotropic thick plates. Mindlin plate characteristic functions are derived in general forms using the Kantorovich method. Initially, Timoshenko beam functions consistent with the boundary conditions of the plate were used. Through numerical calculations of natural fairs of appropriate models, it has been confirmed that the method presented is superior to the Rayleigh-Ritz analysis or the finite element analysis in both accuracy and computational efficiency.

• Structural Engineering and Mechanics
• /
• v.35 no.2
• /
• pp.141-173
• /
• 2010

In this paper a boundary element method is developed for the general flexural-torsional buckling analysis of Timoshenko beams of arbitrarily shaped cross section. The beam is subjected to a compressive centrally applied concentrated axial load together with arbitrarily axial, transverse and torsional distributed loading, while its edges are restrained by the most general linear boundary conditions. The resulting boundary value problem, described by three coupled ordinary differential equations, is solved employing a boundary integral equation approach. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross section. To account for shear deformations, the concept of shear deformation coefficients is used. Six coupled boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Several beams are analysed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. The range of applicability of the thin-walled theory and the significant influence of the boundary conditions and the shear deformation effect on the buckling load are investigated through examples with great practical interest.