Using fourth order element for free vibration parametric analysis of thick plates resting on elastic foundation

Ozdemir, Y.I. Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.3

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin's theory with shear locking free fourth order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency paramerets of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

Precutting of Tunnel Perimeter for Reducing Blasting-Induced Vibration and Damaged Zone – Numerical Analysis

송기일,오태민,조계춘 대한토목학회 2014 KSCE JOURNAL OF CIVIL ENGINEERING Vol.18 No.4

Cost-effective tunnel excavation can be achieved with the blasting method. Unfortunately, blasting technique brings with it blastinginducedvibration and noise, which can cause critical social problems such as public complaints. Thus, the development of a novel tunnelexcavation method, one that can reduce the blasting-induced vibration, is strongly demanded for the effective management of urbanspaces. Thus, this study introduces an innovative vibration-reduced excavation method that combines the conventional blastingtechnique with the precutting process and carries out a feasibility study of the proposed tunnel excavation method using threedimensionalfinite element analyses. The micro-scale study focuses on the stopping holes and contour holes while the macro-scale studydeals with the case of a real scale tunnel. From the micro-scale analyses, it can be deduced that the proposed method is effective for thereduction of blasting-induced vibration compared to the conventional line-drilling method. From the macro-scale simulation, it is foundthat the reduction of blasting-induced vibration is independent of the thickness of the precutting free surface but dependent on the depthof the precutting free surface. As the depth of the precutting free surface increases, blasting-induced vibrations as well as the depth of theexcavation-damaged zone can be significantly reduced. Vibration energy induced by blasting does not transmit through the free surfaceand is trapped inside the target tunnel face. Guided blasting waves cause stress concentration at the target face and maximize the blastingefficiency. It is expected that the construction cost will decrease due to a decrease in the number of drilling holes, the weight of theexplosive charges, the overbreak space, and the excavation-damaged zone. In particular, the reductions of the overbreak space andexcavation-damaged zone enhance the safety of tunnel construction.

Using fourth order element for free vibration parametric analysis of thick plates resting on elastic foundation

Y. I. Özdemir 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.3

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin’s theory with shear locking free fourth order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency paramerets of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

Sn-Ag-Cu-X 무연솔더로 솔더링 된 접합부의 진동파괴 거동

진상훈,강남현,조경목,이창우,홍원식,Jin, Sang-Hun,Kang, Nam-Hyun,Cho, Kyung-Mox,Lee, Chang-Woo,Hong, Won-Sik 대한용접접합학회 2012 대한용접·접합학회지 Vol.30 No.2

Environmental and health concerns over the lead have led to investigation of the alternative Pb-free solders to replace commonly used Pb-Sn solders in microelectronic packaging application. The leading candidates for lead-free solder alloys are presently the near eutectic Sn-Ag-Cu alloys. Therefore, extensive studies on reliability related with the composition have been reported. However, the insufficient drop property of the near eutectic Sn-Ag-Cu alloys has demanded solder compositions of low Ag content. In addition, the solder interconnections in automobile applications like a smart box require significantly improved vibration resistance. Therefore, this study investigated the effect of alloying elements (Ag, Bi, In) on the vibration fatigue strength. The vibration fatigue was conducted in 10~1000Hz frequency and 20Grms. The interface of the as-soldered cross section close to the Cu pad indicated the intermetallic compound ($Cu_6Sn_5$) regardless of solder composition. The type and thickness of IMC was not significantly changed after the vibration test. It indicates that no thermal activities occurred significantly during vibration. Furthermore, as a function of alloying composition, the vibration crack path was investigated with a focus on the IMCs. Vibration crack was initiated from the fillet surface of the heel for QFP parts and from the plating layer of chip parts. Regardless of the solder composition, the crack during a vibration test was propagated as same as that during a thermal fatigue test.

Free-vibration and buckling of Mindlin plates using SGN-FEM models and effects of parasitic shear in models performance

Leilson J. Araujo,João E. Abdalla Filho 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.87 No.3

Free-vibration and buckling analyses of plate problems are investigated with the aid of the strain gradient notation finite element method (SGN-FEM). As SGN-FEM employs physically interpretable polynomials in developing finite elements, parasitic shear sources, which are the cause of shear locking, can be precisely identified and subsequently eliminated. This allows two mutually complementary objectives to be defined in this work, namely, evaluate the efficiency of free-vibration and buckling results provided by corrected models, and study the severity of parasitic shear effects on plate models performance. Parasitic shear are flexural terms erroneously present in shear strain polynomials. It is reviewed here that six parasitic shear terms arise during the formulation of the four-node Mindlin plate element. Two parasitic shear terms have been identified in the in-plane shear strain polynomial while other two have been identified in each of the transverse shear strain polynomials. The element is corrected a-priori, i.e., during development, by simply removing the spurious terms from the shear strain polynomials. The computational implementation of the element in its two versions, namely, containing the parasitic shear terms (PS) and corrected for parasitic shear (SG), allows for assessments of the accuracy of results and of the deleterious effects of parasitic shear in free vibration and buckling analyses. This assessment of the parasitic shear effects is a novelty of this work. Validation of the SG model is done comparing its results with analytical results and results provided by other numerical procedures. Analyses are performed for square plates with different thickness-to-length ratios and boundary conditions. Results for thin plates provided by the PS model do not converge to the correct solutions, which indicates that parasitic shear must be eliminated. That is, analysts should not rely on refinement alone. For thick plates, PS model results can be considered acceptable as deleterious effects are really critical in thin plates. On the other hand, results provided by the SG model converge well for both thin and thick plates. The effectiveness of the SG model is established via high-accuracy results obtained in several examples. It is concluded that corrected SGN-FEM models are efficient alternatives for free-vibration and buckling analysis of Mindlin plate problems, and that precise elimination of parasitic shear is a requirement for sound analyses.

Free vibration analysis of thin rectangular plates with two adjacent edges rotationally-restrained and the others free using finite Fourier integral transform method

Jinghui Zhang,Jiale Lu,Salamat Ullah,Yuanyuan Gao,Dahai Zhao,Arshad Jamal,Ömer Civalek 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.80 No.4

For the first time, the finite Fourier integral transform approach is extended to analytically solve the free vibration problem of rectangular thin plates with two adjacent edges rotationally-restrained and others free. Based on the fundamental transform theory, the governing partial differential equations (PDEs) of the plate is converted to ordinary linear algebraic simultaneous equations without assuming trial function for deflection, which reduces the mathematical complexity caused by both the free corner and rotationally-restrained edges. By coupling with mathematical manipulation, the analytical solutions are elegantly achieved in a straightforward procedure. In addition, the vibration characteristics of plates under classical boundary conditions are also studied by choosing different rotating fixed coefficients. Finally, more than 400 comprehensive analytical solutions were well validated by finite element method (FEM) results, which can be served as reference data for further studies. The advantages of the present method are that it does not need to preselect the deformation function, and it has general applicability to various boundary conditions. The presented approach is promising to be further extended to solve the static and dynamic problems of moderately thick plates and thick plates.

Vibration of two types of porous FG sandwich conical shell with different boundary conditions

Mohsen Rahmani,Younes Mohammadi 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.79 No.4

In this paper, in various boundary conditions, the vibration behavior of the two types of porous FG truncated conical sandwich shells is investigated based on the improved high order sandwich shells theory. Two types of porosity are considered in the power law rule to model the FGM properties. In the first type, FG face sheets cover a homogeneous core, and in the second one, the FG core is covered by the homogeneous face sheets. All materials are temperature dependent. By utilizing the Hamilton’s energy principle, using the nonlinear von Karman strains in the layers and considering the in-plane stresses and thermal stresses in the core and the face sheets, the governing equations are obtained. A Galerkin method is used to solve the equations with clamped-clamped, clamped-free, and free-free boundary conditions. To validate the results, a FEM software is used and some results are validated with the results in the literatures. Also, Some geometrical parameters, temperature variations and porosity effects are studied. By increasing the length to thickness ratio, temperature, the semi-vertex angle and the radius to thickness ratio, the fundamental frequency parameter decreases in all boundary conditions. In both types of sandwiches for both porosity distributions, by increasing the porosity volume fraction, the fundamental frequency parameters increase. Frequency variation of type-II is lower than type-I in the thermal conditions. And the fundamental frequencies of the clamped-clamped (CC) and clamped-free (C-F) boundary conditions have the highest and lowest values, respectively.

왕복동식 수소 압축기의 진동 해석

김효중(H J Kim),구동식(D S Gu),정한얼(H Y Jung),최병근(B K Choi) 한국동력기계공학회 2006 한국동력기계공학회 학술대회 논문집 Vol.- No.-

The reciprocation hydrogen compress has pulsation which is happen noise and vibration. Noise and vibration that happen by pulsation have bed effect machine and working environment. So, must know vibration special quality of compress to decrease these noise and vibration, executed analysis using nastran that is common use program. Find and compared each mode shape when consider Crank case analysis and consider Crank case and cylinder together through free vibration. And to search rejoinder about shock by Crank easel s pulsation 0 ~ 100 ㎐ because do sweep forced oscillation analysis achieve.

A hybrid method for predicting the dynamic response of free-span submarine pipelines

Li, Tongtong,Duan, Menglan,Liang, Wei,An, Chen Techno-Press 2016 Ocean systems engineering Vol.6 No.4

Large numbers of submarine pipelines are laid as the world now is attaching great importance to offshore oil exploitation. Free spanning of submarine pipelines may be caused by seabed unevenness, change of topology, artificial supports, etc. By combining Iwan's wake oscillator model with the differential equation which describes the vibration behavior of free-span submarine pipelines, the pipe-fluid coupling equation is developed and solved in order to study the effect of both internal and external fluid on the vibration behavior of free-span submarine pipelines. Through generalized integral transform technique (GITT), the governing equation describing the transverse displacement is transformed into a system of second-order ordinary differential equations (ODEs) in temporal variable, eliminating the spatial variable. The MATHEMATICA built-in function NDSolve is then used to numerically solve the transformed ODE system. The good convergence of the eigenfunction expansions proved that this method is applicable for predicting the dynamic response of free-span pipelines subjected to both internal flow and external current.

A nonlocal Layerwise theory for free vibration analysis of nanobeams with various boundary conditions on Winkler-Pasternak foundation

Mahsa Najafi,Isa Ahmadi 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.40 No.1

In this study, a nonlocal Layerwise theory is presented for free vibration analysis of nanobeams resting on an elastic foundation. Eringen’s nonlocal elasticity theory is used to consider the small-scale effect on behavior of nanobeam. The governing equations are obtained by employing Hamilton’s principle and Layerwise theory of beams and Eringen’s nonlocal constitutive equation. The presented theory takes into account the in-plane and transverse normal and shear strain in the modeling of the nanobeam and can predict more accurate results. The governing equations of the beam are solved by Navier's method for Simple-Simple boundary conditions and semi-analytical methods to obtain the natural frequency for various boundary conditions including Clamped-Simple (C-S), Clamped-Clamped (C-C) and Free-Free (F-F) boundary conditions. Predictions of the present theory are compared with benchmark results in the literature. Effects of nonlocal parameter, Pasternak shear coefficient, Winkler spring coefficient, boundary conditions, and the aspect ratio on the free vibration of nanobeams are studied. The flexural mode and thickness mode natural frequencies of the nanobeam are predicted. It is shown that the predictions of present method are more accurate than the equivalent single layer theories. The theoretical developments and formulation presented herein should also be served to analyze the mechanical behavior of various nanostructures with various loading and boundary conditions.