• 소음진동
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• 제9권3호
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• pp.525-534
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• 1999

The present paper proposes a generalized modal analysis procedure for non-uniform, distributed-parameter rotor-bearing systems. An exact element matrix is derived for a Timoshenko shaft model which contains rotary inertia, shear deformation, gyroscopic effect and internal damping. Complex coordinates system is adopted for the convenience in formulation. A generalized orthogonality condition is provided to make the modal decomposition possible. The generalized modal analysis by using a modal decomposition delivers exact and closed form solutions both for frequency and time responses. Two numerical examples are presented for illustrating the proposed method. The numerical study proves that the proposed method is very efficient and useful for the analysis of distributed-parameter rotor-bearing systems.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
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• pp.17-24
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• 2004

This paper established the dynamic model of a flexible Timoshenko beam with geometrical nonlinearities subject to large overall motions by using the finite element method. The equations of motion are derived by using Hamilton principle based on expressing the kinetic and potential energies of the flexible beam in terms of generalized coordinates. The nonlinear constraint equations are adjoined to the system equations of motion by using Lagrange multipliers.

• 한국태양에너지학회 논문집
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• 제36권3호
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• pp.9-16
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• 2016

This paper discusses a refined model for investigating the micro-mechanical behavior of beam-like structures, which are composed of various elastic moduli and complex geometries varying through the cross-section directions and are also periodically-repeated and heterogeneous along the axial direction. Following the previous work (Lee and Yu, 2011), the original three-dimensional static problem is first formulated in a unified and compact form using the concept of decomposition of the rotation tensor. Taking advantage of the smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity, while also performing homogenization along the dimensional reduction simultaneously, the variational asymptotic method is rigorously used to construct a total energy function, which is asymptotically correct up to the second order. Furthermore, through the transformation procedure based on the pure kinematic relations and the linearized equilibrium equations, a generalized Timoshenko model is systematically established. For the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level, this present approach is incorporated into a commercial analysis package. A few examples available in literature are used to demonstrate the consistency and efficiency of this proposed model, especially for the structures, in which the effects of transverse shear deformations are significant.

• 한국기계가공학회지
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• 제19권7호
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• pp.35-40
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• 2020

This work is concerned with various planar deformations of an isotropic sandwich beam, which generally consists of three layers: two stiff skin layers and one soft core layer. When one layer of the sandwich beam is modeled as a beam, the variational-asymptotic method is rigorously used to construct a zeroth-order beam model, which is similar to a generalized Timoshenko beam model capable of capturing the transverse shear deformations but still carries out the zeroth-order approximation. To analyze the planar sandwich beam, the sum of the energies of the two skin layers and one core layer is then formulated with different material and geometric properties and represented by a universal beam model in terms of the core-layer kinematics through interface displacement and stress continuity conditions. As a preliminary validation, two extreme examples are presented to demonstrate the capability and accuracy of this present approach.

• Advances in aircraft and spacecraft science
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• 제3권4호
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• pp.379-397
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• 2016

In this manuscript, free vibrations of a unidirectional composite orthotropic Timoshenko beam based on finite strain have been studied. Using Green-Lagrange strain tensor and comprising all of the nonlinear terms of the tensor and also applying Hamilton's principle, equations of motion and boundary conditions of the beam are obtained. Using separation method in single-harmonic state, time and locative variables are separated from each other and finally, the equations of motion and boundary conditions are gained according to locative variable. To solve the equations, generalized differential quadrature method (GDQM) is applied and then, deflection and cross-section rotation of the beam in linear and nonlinear states are drawn and compared with each other. Also, frequencies of carbon/epoxy and glass/epoxy composite beams for different boundary conditions on the basis of the finite strain are calculated. The calculated frequencies of the nonlinear free vibration of the beam utilizing finite strain assumption for various geometries have been compared to von Karman one.

• 대한기계학회논문집A
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• 제23권11호
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• pp.2058-2066
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• 1999

The present paper proposes a new dynamic analysis method for multi-span Timoshenko beam structures supported by joints with damping subject to moving loads. An exact dynamic element matrix method is adopted to model Timoshenko beam structures. A generalized modal analysis method is applied to derive response formulae for beam structures subject to moving loads. The proposed method offers an exact and closed form solution. Two numerical examples are provided for validating and illustrating the proposed method. In the first numerical example, a single span beam with multiple moving loads is considered. A dynamic analysis on a multi-span beam under a moving load is considered as the second example, in which the flexibility and damping of supporting joints are taken into account. The numerical study proves that the proposed method is useful for the vibration analysis of multi-span beam-hype structures by moving loads.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.838-843
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• 2001

Internal damping plays an important role in some rotor dynamic systems with the use of various materials for shafts, for example, composite material. However, although the effects of internal damping have been investigated for a couple of decades, there are several different internal damping models in use, none of which are accepted as the most reliable model. The purpose of this paper is to compare the results of dynamic analysis of rotor systems with several different internal damping models. The exact dynamic element method is used to formulate and analyze the problem. The simulation results provided in this paper may be useful for the dynamic analysis of high rotor systems subject to significant internal damping.

• International Journal of Aeronautical and Space Sciences
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• 제18권3호
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• pp.467-473
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• 2017

This paper focuses on the investigation of three-dimensional (3D) warping effect on the stiffness constants of composite beams with closed section profiles. A finite element (FE) cross-sectional analysis is developed based on the Reissner's multifield variational principle. The 3D in-plane and out-of-plane warping displacements, and sectional stresses are approximated as linear functions of generalized sectional stress resultants at the global level and as FE shape functions at the local sectional level. The classical elastic couplings are taken into account which include transverse shear and Poisson deformation effects. A generalized Timoshenko level $6{\times}6$ stiffness matrix is computed for closed section composite beams with and without warping. The effect of neglecting the 3D warping on stiffness constants is shown to be significant indicating large errors as high as 93.3%.

• 동력기계공학회지
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• 제19권3호
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• pp.55-62
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• 2015

This paper discusses a new model for investigating the micro-mechanical behavior of beam-like structures composed of various elastic moduli and complex geometries varying through the cross-sectional directions and also periodically-repeated along the axial directions. The original three-dimensional problem is first formulated in an unified and compact intrinsic form using the concept of decomposition of the rotation tensor. Taking advantage of two smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity and performing homogenization along dimensional reduction simultaneously, the variational asymptotic method is used to rigorously construct an effective zeroth-order beam model, which is similar a generalized Timoshenko one (the first-order shear deformation model) capable of capturing the transverse shear deformations, but still carries out the zeroth-order approximation which can maximize simplicity and promote efficiency. Two examples available in literature are used to demonstrate the consistence and efficiency of this new model, especially for the structures, in which the effects of transverse shear deformations are significant.

• Steel and Composite Structures
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• 제21권1호
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• pp.1-36
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• 2016

In the present study, the nonlinear magneto-electro-mechanical free vibration behavior of rectangular double-bonded sandwich microbeams based on the modified strain gradient theory (MSGT) is investigated. It is noted that the top and bottom sandwich microbeams are considered with boron nitride nanotube reinforced composite face sheets (BNNTRC-SB) with electrical properties and carbon nanotube reinforced composite face sheets (CNTRC-SB) with magnetic fields, respectively, and also the homogenous core is used for both sandwich beams. The connections of every sandwich beam with its surrounding medium and also between them have been carried out by considering Pasternak foundations. To take size effect into account, the MSGT is introduced into the classical Timoshenko beam theory (CT) to develop a size-dependent beam model containing three additional material length scale parameters. For the CNTRC and BNNTRC face sheets of sandwich microbeams, uniform distribution (UD) and functionally graded (FG) distribution patterns of CNTs or BNNTs in four cases FG-X, FG-O, FG-A, and FG-V are employed. It is assumed that the material properties of face sheets for both sandwich beams are varied in the thickness direction and estimated through the extended rule of mixture. On the basis of the Hamilton's principle, the size-dependent nonlinear governing differential equations of motion and associated boundary conditions are derived and then discretized by using generalized differential quadrature method (GDQM). A detailed parametric study is presented to indicate the influences of electric and magnetic fields, slenderness ratio, thickness ratio of both sandwich microbeams, thickness ratio of every sandwich microbeam, dimensionless three material length scale parameters, Winkler spring modulus and various distribution types of face sheets on the first two natural frequencies of double-bonded sandwich microbeams. Furthermore, a comparison between the various beam models on the basis of the CT, modified couple stress theory (MCST), and MSGT is performed. It is illustrated that the thickness ratio of sandwich microbeams plays an important role in the vibrational behavior of the double-bonded sandwich microstructures. Meanwhile, it is concluded that by increasing H/lm, the values of first two natural frequencies tend to decrease for all amounts of the Winkler spring modulus.