• Title/Summary/Keyword: free vibration mode shapes

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Dynamic Characteristics and Piezoelectric Effect of Energy Harvesting Block Structures with Different Shapes (다양한 형상 변화에 따른 에너지 수확용 블록 구조의 동적 특성 및 압전 효과)

  • Noh, Myung-Hyun;Lee, Sang-Youl
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.32 no.6A
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    • pp.379-387
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    • 2012
  • This study investigates free vibration characteristics of new energy harvesting multi-layer block structures with different geometrical shapes using solid and shell finite elements and evaluate their piezoelectric effect on experiments. The two and three-dimensional finite element (FE) delamination models for block structures described in this paper is attractive not only because it shows excellent accuracy in analysis but also it shows the entire vibration mode shape. The FE model using ABAQUS is used for studying free vibrations of multi-layer block structures for various tip mass and PZT. In particular, new results reported in this paper are focused on the significant effects of the global and local vibration modes for various parameters, such as size of block shape, existence of tip mass and hole, and location of tip mass and PZT. In addition, we evaluate the power generation capacity of developed energy block structures through a laboratory-scale experiment.

Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method

  • Yesilce, Yusuf;Catal, Seval
    • Structural Engineering and Mechanics
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    • v.31 no.4
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    • pp.453-475
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    • 2009
  • The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko beams on elastic soil is plenty, but the free vibration analysis of Reddy-Bickford beams on elastic soil with/without axial force effect using the Differential Transform Method (DTM) has not been investigated by any of the studies in open literature so far. In this study, the free vibration analysis of axially loaded Reddy-Bickford beam on elastic soil is carried out by using DTM. The model has six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments in this study. The governing differential equations of motion of the rectangular beam in free vibration are derived using Hamilton's principle and considering rotatory inertia. Parameters for the relative stiffness, stiffness ratio and nondimensionalized multiplication factor for the axial compressive force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. At first, the terms are found directly from the analytical solutions of the differential equations that describe the deformations of the cross-section according to the high-order theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The calculated natural frequencies of one end fixed and the other end simply supported Reddy-Bickford beam on elastic soil using DTM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed and the mode shapes are presented in graphs.

Free Vibrations of Tapered Timoshenko Beam by using 4th Order Ordinary Differential Equation (4계 상미분방정식에 의한 변단면 Timoshenko 보의 자유진동)

  • Lee, Byoung-Koo;Park, Kwang-Kyou;Lee, Tae-Eun
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.25 no.3
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    • pp.185-194
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    • 2012
  • This paper deals with free vibrations of the tapered Timoshenko beam in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the rectangular cross section whose depth is constant but breadth is varied with the parabolic function. The fourth order ordinary differential equation with respect the vertical deflection governing free vibrations of such beam is derived based on the Timoshenko beam theory. This governing equation is solved for determining the natural frequencies corresponding with their mode shapes. In the numerical examples, three end constraints of the hinged-hinged, hinged-clamped and clamped-clamped ends are considered. The effects of various beam parameters on natural frequencies are extensively discussed. The mode shapes of both the deflections and stress resultants are presented, in which the composing rates due to bending rotation and shear deformation are determined.

Free vibration analysis of concrete arch dams by quadratic ideal-coupled method

  • Rezaiee-Pajand, Mohammad;Sani, Ahmad Aftabi;Kazemiyan, Mohammad Sadegh
    • Structural Engineering and Mechanics
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    • v.65 no.1
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    • pp.69-79
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    • 2018
  • This paper is devoted to two new techniques for free vibration analysis of concrete arch dam-reservoir systems. The proposed schemes are quadratic ideal-coupled eigen-problems, which can solve the originally non-symmetric eigen-problem of the system. To find the natural frequencies and mode shapes, a new special-purpose eigen-value solution routine is developed. Moreover, the accuracy of the proposed approach is thoroughly assessed, and it is confirmed that the new scheme is very accurate under all practical conditions. It is also concluded that both decoupled and ideal-coupled strategy proposed in the previous works can be considered as special cases of the current more general procedure.

Investigation of natural frequencies of multi-bay and multi-storey frames using a single variable shear deformation theory

  • Bozyigit, Baran;Yesilce, Yusuf
    • Structural Engineering and Mechanics
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    • v.65 no.1
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    • pp.9-17
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    • 2018
  • This study concerns about calculating exact natural frequencies of frames using a single variable shear deformation theory (SVSDT) which considers the parabolic shear stress distribution across the cross section. Free vibration analyses are performed for multi-bay, multi-storey and multi-bay multi-storey type frame structures. Dynamic stiffness formulations are derived and used to obtain first five natural frequencies of frames. Different beam and column cross sections are considered to reveal their effects on free vibration analysis. The calculated natural frequencies are tabulated with the results obtained using Euler-Bernoulli Beam Theory (EBT) and Timoshenko Beam Theory (TBT). Moreover, the effects of inner and outer columns on natural frequencies are compared for multi-bay frames. Several mode shapes are plotted.

A Study of Vibration Characteristics of Cylindrical Composite Shells Manufactured in Present Laboratory (간이 성형장치에 의해 제작된 복합재 원통셸의 진동특성평가)

  • 한병기;유택인;이성희;이재원
    • Composites Research
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    • v.12 no.1
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    • pp.37-46
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    • 1999
  • In this study, the vibration analysis and modal tests of cylindrical composite shells which are manufactured with various stacking sequences in present laboratory were conducted under the free-free and clamped-clamped boundary conditions. Natural frequencies and mode shapes of these specimens were experimentally obtained and their results are compared with theoretical and FEM results. Both results are in good agreement, which confirm the usefulness of proposed manufacturing method for cylindrical composite shells.

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Transverse Vibration of Rectangular Plates Having an Inner Cutout in Water (유공직사각형평판(有孔直四角形平板)의 접수진동(接水振動))

  • H.S.,Lee;K.C.,Kim
    • Bulletin of the Society of Naval Architects of Korea
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    • v.21 no.1
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    • pp.21-34
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    • 1984
  • This paper is concerned with the experimental investigation of transverse vibration characteristics in water of rectangular plates having an inner free cutout. Systematic experiments are carried out to investigate effects of the surrounding water on the added mass and the natural frequency of the plates due to the changes of the aspect ratio, hole size and eccentricity. The main subject is the clamped rectangular plate with a circular hole. For the purpose of comparative evaluations, some other common-type boundary conditions and hole shapes such as ellipses and rectangles are also investigated. Some of the results obtain are as follows; 1) For each given aspect ratio of the plate, there is a hole area ratio which gives a minimum value of the nondimensional frequency parameter for each mode. The hole area ratio increases as the order number of the mode increases. 2) The nondimensinal mass-increment parameter decreases as the aspect ration or the order number of the mode increases. For each given aspect ratio, the parameter the fundamental mode decreases monotonically as the hole area ratio increase. In cases of the second and higher order modes, however, each mode has a hole area ratio which gives a maximum value of the parameter for each aspect ratio more then 2/3. 3) Comparing elliptic holes with rectangular ones with same hole area ratio, nondimensional frequency parameters are almost same for each given ratio of the shorter axises to the longer one. 4) The influences of difference in boundary condion on nondimensional frequency parameters in water are similar to those in air.

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An analytical algorithm for assessing dynamic characteristics of a triple-tower double-cable suspension bridge

  • Wen-ming Zhang;Yu-peng Chen;Shi-han Wang;Xiao-fan Lu
    • Structural Engineering and Mechanics
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    • v.90 no.4
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    • pp.325-343
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    • 2024
  • Triple-tower double-cable suspension bridges have increased confinement stiffness imposed by the main cable on the middle tower, which has bright application prospects. However, vertical bending and torsional vibrations of the double-cable and the girder are coupled in such bridges due to the hangers. In particular, the bending vibration of the towers in the longitudinal direction and torsional vibrations about the vertical axis influence the vertical bending and torsional vibrations of the stiffening girders, respectively. The conventional analytical algorithm for assessing the dynamic features of the suspension bridge is not directly applicable to this type of bridge. This study attempts to mitigate this problem by introducing an analytical algorithm for solving the triple-tower double-cable suspension bridge's natural frequencies and mode shapes. D'Alembert's principle is employed to construct the differential equations of the vertical bending and torsional vibrations of the stiffening girder continuum in each span. Vibrations of stiffening girders in each span are interrelated via the vibrations of the main cables and the bridge towers. On this basis, the natural frequencies and mode shapes are derived by separating variables. The proposed algorithm is then applied to an engineering example. The natural frequencies and mode shapes of vertical bending and torsional vibrations derived by the analytical algorithm agreed well with calculations via the finite element method. The fundamental frequency of vertical bending and first- and second-order torsion frequencies of double-cable suspension bridges are much higher than those of single-cable suspension bridges. The analytical algorithm has high computational efficiency and calculation accuracy, which can provide a reference for selecting appropriate structural parameters to meet the requirements of dynamics during the preliminary design.

A Study on Free Vibration of Steel and Composite Cylindrical Shells with an Oblique Angle (경사단을 갖는 Steel 및 복합재료 원통쉘의 자유진동 특성에 관한 연구)

  • Lee, Jang-Won;Choi, Young-Jin;Lee, Young-Shin
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2004.11a
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    • pp.928-933
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    • 2004
  • The vibration characteristic is a primary design factor. The cylindrical shells are used as a primary components of complex structure. also, The cylindrical shells have oblique angle. In this study, The vibrational characteristics of steel and plain wave GFRP cylindrical shell with an oblique end are given by experimental and finite element method. To be find characteristic of the oblique end, the mass of the cylindrical shell is maintained. Natural frequency and mode shapes of isotropic and plain weave composite shells are obtained by modal test. The results are compared with those of the finite element method. The simply supported boundary conditions with bolts along the circumferential direction of the GFRP shell are well achieved. Also, The clamped boundary conditions is applied to the steel specimen. Those are shown to agree well with the analytical results and finite element analysis results.

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Free Vibration of Mannequins and Car Seat System (마네킹과 자동차 시트 시스템의 진동 해석)

  • Kim, Seong-Keol;Lee, Jae-Hyung;Park, Ki-Hong;Lee, Sin-Young;Davies, Patricia;Bajaj, Anil K.
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2000.06a
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    • pp.1621-1626
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    • 2000
  • A simplified modeling approach for occupied car seats was demonstrated to be feasible. The model, consisting of interconnected masses, springs and dampers, was initially broken down into subsystems and experiments conducted to determine approximate values for model parameters. A short study of the effect of changing model parameters on natural frequencies, mode shapes and resonance locations in frequency response functions was given, highlighting the influence of particular model parameters on features in the mannequin's vibration response. Good agreement between experimental and simulation frequency response estimates was obtained. Future work should include optimization of parameter estimates, the inclusion of viscoelastic and nonlinear elements in addition to the linear springs and dampers, and finally extensions to a 3D model.

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