Showing papers in "International Journal of Structural Stability and Dynamics in 2004"
TL;DR: In this article, the optimum parameters of multiple tuned mass dampers (MTMD) for suppressing the dynamic response of a base-excited damped main system are investigated by a numerical searching technique.
Abstract: The optimum parameters of multiple tuned mass dampers (MTMD) for suppressing the dynamic response of a base-excited damped main system are investigated by a numerical searching technique. The criterion selected for the optimality is the minimization of the steady state displacement of the main system under harmonic base acceleration. The parameters of the MTMD that are optimized include: the damping ratio, the tuning frequency ratio and the frequency bandwidth. The optimum parameters of the MTMD system and corresponding displacement are obtained for different damping ratios of the main system and different mass ratios of the MTMD system. The explicit formulas for the optimum parameters of the MTMD (i.e. damping ratio, bandwidth and tuning frequency) are then derived using a curve-fitting scheme that can readily be used in engineering applications. The error in the proposed explicit expressions is investigated and found to be negligible. The effectiveness of the optimally designed MTMD system is also compared with that of the optimum single tuned mass damper. It is observed that the optimally designed MTMD system is more effective for vibration control than the single tuned mass damper. Further, the damping in the main system significantly influences the optimum parameters and the effectiveness of the MTMD system.
69 citations
TL;DR: In this article, the buckling and postbuckling behavior of laminated cylindrical shells under axial compression and lateral pressure loading are investigated and a nonlinear theory for thin cylinders incorporating the effects of transverse shear deformation is employed.
Abstract: In the present work the buckling and postbuckling behavior of laminated cylindrical shells under axial compression and lateral pressure loading are investigated. A nonlinear theory for thin cylinders incorporating the effects of transverse shear deformation is employed. A modal solution based on the Koiter theory is utilized to derive the nonlinear equilibrium equations for the postcritical behavior of the shell. The Rayleigh–Ritz method is used to obtain analytical solutions for the critical load through algebraic routines written in Maple. Prebuckling and postbuckling equations are also solved by using symbolic computation. The influence played by geometrical parameters of the cylinder and physical parameters of the laminate (i.e. fiber orientation of each lamina, material properties and number of layers) on the critical and postcritical behavior of the shell is examined. It is noticed that the stability of shells is highly dependent on laminate characteristics and, from these observations, it is concluded that specific configurations of laminates should be designed for each kind of application.
28 citations
TL;DR: In this paper, a special class of closed-form solutions for inhomogeneous beam-columns on elastic foundations is investigated, where a simply-supported beam on elastic foundation is considered and the associated semi-inverse problem is solved that result in the distributions of flexural rigidity that together with a specific law of material density, an axial load distribution and a particular variability of elastic foundation characteristics satisfy the governing eigenvalue problem.
Abstract: In this study, a special class of closed-form solutions for inhomogeneous beam-columns on elastic foundations is investigated. Namely the following problem is considered: find the distribution of the material density and the flexural rigidity of an inhomogeneous beam resting on a variable elastic foundation so that the postulated trigonometric mode shape serves both as vibration and buckling modes. Specifically, for a simply-supported beam on elastic foundation, the harmonically varying vibration mode is postulated and the associated semi-inverse problem is solved that result in the distributions of flexural rigidity that together with a specific law of material density, an axial load distribution and a particular variability of elastic foundation characteristics satisfy the governing eigenvalue problem. The analytical expression for the natural frequencies of the corresponding homogeneous beam-column with a constant characteristic elastic foundation is obtained as a particular case. For comparison the obtained closed-form solution is contrasted with an approximate solution based on an appropriate polynomial shape, serving as trial function in an energy method.
28 citations
TL;DR: In this article, the elastic shear buckling capacity of corrugated plates with edges elastically restrained against rotation is estimated by using the Rayleigh-Ritz method, which is consistent with those as predicted by existing formulas for the limiting cases of simply-supported and clamped edges.
Abstract: This paper presents an estimation of the elastic shear buckling capacity of corrugated plates with edges elastically restrained against rotation. The corrugated plate possesses higher shear buckling capacity compared to an unfolded flat plate. It has been used to replace the concrete web in PC box girders in recent bridge constructions in Japan. In this study, the corrugated plate is modelled as an orthotropic Mindlin plate. Elastically rotational restraint on boundary edges is taken into account in the form of rotational springs in the analysis. The prediction of buckling capacities of corrugated plates is carried out by using the Rayleigh–Ritz method, which was proved to be consistent with those as predicted by existing formulas for the limiting cases of simply-supported and clamped edges. The present study covers the more general case of elastically rotational restraint on the boundary edges showing transition curve of plate buckling capacities from the case of simple support to the case of clamped support.
24 citations
TL;DR: In this article, the fatigue behavior of welded thin-walled T-joints made up of both circular hollow section (CHS) braces and chords, subjected to cyclic in-plane bending, is described.
Abstract: The fatigue behavior of welded thin-walled T-joints made up of both circular hollow section (CHS) braces and chords, subjected to cyclic in-plane bending, is described in this paper. CHS chords and braces are of thicknesses less than 4 mm. Current fatigue design guidelines show that the design of welded tubular nodal joints is restricted to thicknesses greater than or equal to 4 mm. The increased availability and use of thin-walled (t<4 mm) tubes of high-strength steels in recent years, in structures subjected to cyclic loading, means that it is important to study the fatigue behavior of welded thin-walled tubular nodal joints. In this paper, welded thin-walled CHS-CHS T-joints subjected to constant-stress-amplitude cyclic in-plane bending range are studied. The stress concentration factors (SCFs) determined experimentally at the brace and chord crown positions are shown to be about 30% and 40% respectively of the SCFs determined using parametric equations in existing fatigue design guidelines. The fatigue tests showed that in welded thin-walled CHS-CHS T-joints, a through-thickness crack occurs when the surface crack length along the weld toes in the chord has grown to a length equal to about 40% of the circumference of the brace member. An end of test failure criterion was proposed as an alternative to the through-thickness failure criterion, in obtaining data that is suitable for determining fatigue design S-N curves.
22 citations
TL;DR: In this paper, a simple method for adjusting the whole set of normal forces in this kind of structure, based on a combination of influences determined from the unit variations of rest lengths for a reduced set of active cables, is presented.
Abstract: Stress control is a major issue in the development of prestressed structures like the tensegrity systems that gain from it equilibrium and stability. In this paper, we present a simple method for adjusting the whole set of normal forces in this kind of structure, based on a combination of influences determined from the unit variations of rest lengths for a reduced set of active cables. According to an elementary criterion, tension and compression forces are kept in a reduced domain during the implementation stage in order to avoid unwanted transitory stress levels. The process is then simulated to retrieve the modifications for actual lengths that are to be implemented in the correct order. Finally, we describe the application of this method on a 1:1 scale double layer tensegrity grid.
22 citations
TL;DR: In this paper, the postbuckling behavior of beams on a two-parameter elastic foundation subjected to axial forces is investigated, and the critical load and post-buckling characteristics of the beams are altered by ignoring the foundation deflection in the horizontal direction.
Abstract: The postbuckling behavior of beams on a two-parameter elastic foundation subjected to axial forces is investigated. Based on the strain energy expression, a two-node nonlinear beam element is formulated. The element includes the effects of shear deformation, foundation deflection in both the horizontal and vertical directions. The bracketing procedure and the iterative Newton–Raphson method with arc-length control technique are adopted to compute the critical loads and equilibrium paths of the beams with various boundary conditions. The numerical results show that the critical load and the postbuckling behavior are not only governed by the foundation stiffness, but by the foundation deflection in the horizontal direction also. The postbuckling characteristics of the beams are altered by ignoring the foundation deflection in the horizontal direction. A detail investigation is carried out to highlight the influences of the partial support by the foundation and the beam slenderness on the critical load and the postbuckling behavior.
21 citations
TL;DR: In this paper, a one-dimensional finite element formulation for nonlinear analysis of spaced framed structures with thin-walled cross-sections is presented, which accounts for restrained warping as well as the second-order displacement terms due to large rotations.
Abstract: This work presents a one-dimensional finite element formulation for nonlinear analysis of spaced framed structures with thin-walled cross-sections. Within the framework of updated Lagrangian formulation, the nonlinear displacement field of thin-walled cross-sections, which accounts for restrained warping as well as the second-order displacement terms due to large rotations, the equations of equilibrium are firstly derived for a straight beam element. Due to the nonlinear displacement field, the geometric potential of semitangential moment is obtained for both the torsion and bending moments. In such a way, the joint moment equilibrium conditions of adjacent non-collinear elements are ensured. Force recovering is performed according to the external stiffness approach. Material nonlinearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at finite element ends and for this a corresponding plastic reduction matrix is determined. The interaction of element forces at the hinge and the possibility of elastic unloading are taken into account. The effectiveness of the numerical algorithm discussed is validated through the test problem.
20 citations
TL;DR: In this article, three-dimensional (3D) infinite elements for the multi-layered elastodynamics problems were developed using wave functions in function spaces that can simulate real wave problems properly.
Abstract: This paper presents three-dimensional (3D) infinite elements for the multi-layered elastodynamics problems. There are three types of elements, namely horizontal, vertical and corner elements. They have been developed using wave functions in function spaces that can simulate real wave problems properly. The elements are extended forms of the axisymmetric infinite elements developed previously. Since these elements can simulate multiple layers and multiple wave numbers, the response of a 3D general structural system considering soil-structure interaction effect can be determined effectively. Numerical analyses are carried out for a rigid massless disk and square footings on the surface of various layer conditions for verification purposes. The calculated results are compared with existing analytical and numerical data and they were found to be in good agreement.
19 citations
TL;DR: In this article, the authors introduce the use of elastic displacement floor spectra to model the seismic performance behavior of unrestrained components and demonstrate the sensitivity of the displacement floor spectrum to a multitude of modeling uncertainties.
Abstract: This paper introduces the use of elastic displacement floor spectra to model the seismic performance behavior of unrestrained components. The displacement spectrum has the attribute of tracking period-shifts associated with "rocking" behavior. Analyses of the displacement floor spectra in high-rise buildings demonstrate the significance of contributions by the higher modes of vibration. Significantly, such higher mode contributions could not always be captured by established code procedures wherein the seismic demand on a building floor is obtained by linear interpolation between the seismic demand at the roof and ground level. The significant influence of the higher modes in high-rise buildings also precludes the use of simple static models to predict seismic demand. Results are also presented herein to demonstrate the sensitivity of the displacement floor spectrum to a multitude of modeling uncertainties.
14 citations
TL;DR: In this paper, a fiber-based approach is adopted to study the cross-sectional behavior of concrete-filled steel tubes subjected to monotonic and cyclic loading, and a fiber model is also developed to describe the nonlinear response of steel tubes to cyclic load.
Abstract: A fiber-based approach is adopted to study the cross-sectional behavior of concrete-filled steel tubes subjected to monotonic and cyclic loading. Constitutive behavior of the cross-section is formulated by explicitly dividing the section into fibers, and uniaxial stress–strain rules for steel and concrete are defined. Interaction curves, Moment–Thrust–Curvature (M–P–φ) relations and Moment–Thrust–Strain (M–P–e) relations are developed for circular and box-shaped in-filled sections based on fiber analysis. A fiber model is also developed to describe the nonlinear response of concrete-filled steel tubes subjected to cyclic loading. M–P–φ relations are developed for arbitrary loading histories using this simple yet reliable approach. Results are compared with the numerical and experimental data available in published literature, and the accuracy of the proposed model is thus ascertained.
TL;DR: In this paper, the secant stiffness matrix of truss element was derived using a simple co-rotational, total Lagrangian (CR-TL) formulation, and the incremental rotation matrix was derived from geometric principles.
Abstract: To investigate the geometrically nonlinear behavior of space structures using finite elements, the total Lagrangian (TL), updated Lagrangian (UL) and co-rotational (CR) procedures have been used by researchers. For 3D truss structures, the CR formulation has been reported to be computationally more efficient as it possesses the rigid body displacement components during deformations. In this paper, the secant stiffness matrix of truss element will be derived using a simple co-rotational, total Lagrangian (CR–TL) formulation. The incremental rotation matrix, which is the pivotal quantity in the CR formulation, is derived from geometric principles. The secant stiffness matrix is presented in terms of the natural degrees-of-freedom of the truss element. The efficiency and reliability of the present formulation is demonstrated in the solution of several truss problems involving the postbuckling behavior.
TL;DR: In this paper, an analytical model for column analysis of concrete-filled tubular beam-columns subjected to the combined action of axial load and monotonic or cyclic bending is presented.
Abstract: This paper is concerned with an analytical model for column analysis of concrete-filled tubular beam-columns subjected to the combined action of axial load and monotonic or cyclic bending. A method of segmentation is adopted in the analysis of beam-columns. The flexural and axial rigidities of the beam-column segments are derived from M–P–φ and M–P–e relations obtained through fibre-analysis explained in Part 11 of the paper. Geometric and material nonlinearities are taken into account and incremental equilibrium equations are formulated based on an updated Lagrangian formulation. An incremental-iterative Newton–Raphson iteration technique is adopted to obtain the solution of the equations. The limitation of Newton–Raphson technique in approaching the limit points is overcome by using a generalized stiffness parameter, thereby tracing the post-buckling response. The accuracy of the model is verified by comparing the results with the experimental values available in published literature.
TL;DR: In this article, the fundamental dynamic characteristics of an elevated railway subjected to harmonic moving loads are investigated, and the resonant conditions of these three cases are especially emphasized and studied in details.
Abstract: The fundamental dynamic characteristics of an elevated railway subjected to harmonic moving loads are investigated. The elevated ballast railway is analytically modeled as three different cases, with Case A indicating a simply-supported beam, Case B a two-parallel-beam system that is simply supported and inserted with a viscoelastic layer, and Case C an expansion of Case B through addition of two semi-infinite beams with viscoelastic foundation on two sides. The resonant conditions of these three cases are especially emphasized and studied in details. Finally, the resonant curves of an elevated railway to harmonic moving loads are presented, which are useful to railway engineers and may be used as preliminary design aids.
TL;DR: Based on the first-order shear deformation shell theory, an analytical approach was developed to predict the thermal buckling response of an all-edge clamped cylindrical panel.
Abstract: Based on the first-order shear deformation shell theory, an analytical approach is developed to predict the thermal buckling response of an all-edge clamped cylindrical panel. The analytical approach adopts a double Fourier solution method suitable for cylindrical panels. The present solutions are compared with the finite element solutions obtained using ANSYS. The effects of various dimensional parameters are included in the study.
TL;DR: In this paper, the curvature effect of interlayer van der Waals (vdW) forces on an axially compressed double-walled carbon nanotube is studied.
Abstract: The curvature effect of interlayer van der Waals (vdW) forces on an axially compressed double-walled carbon nanotube is studied. Unlike existing models which assume that the interlayer vdW pressure at any point between the inner and outer tubes depends merely on the difference of their deflections at that point, the present model considers the dependence of the interlayer vdW pressure on the curvature of the difference of deflections at that point. A simple formula is derived for the critical axial strain, which clearly indicates the role of the interlayer vdW forces affected by the curvature of deflection. In particular, the critical axial strain predicted by the present model is higher than or equal to that given by the existing models without the curvature effect provided that the coefficient for the curvature dependence of the interlayer vdW pressure is negative. Furthermore, the curvature effect on the critical axial strain is more significant for buckling modes of smaller wavelengths. These results indicate that the curvature effect, which has been neglected in all existing models, could play a significant role in various buckling problems especially for multi-walled carbon nanotubes of smaller radii.
TL;DR: In this paper, the authors presented a simplified, but accurate, numerical procedure for modeling the nonlinear behavior of reinforced concrete, using solid finite elements, which include strain-rate effects.
Abstract: Extensive use of reinforced concrete to build shock-protective structures calls for adequate analytical expertise to facilitate rational and safe structural designs. Although several researchers have studied these problems, there are still some uncertainties, particularly with regard to strain-rate effects. This paper presents a simplified, but accurate, numerical procedure for modeling the nonlinear behavior of reinforced concrete, using solid finite elements, which include strain-rate effects. The details of the material modeling for anisotropic concrete and isotropic steel are presented. A clamped circular plate subjected to uniformly distributed load and a clamped rectangular slab subjected to jet force are analyzed using 8-noded solid finite elements. Strain-rate effects are considered in the analyses.
TL;DR: In this article, a consistent approximation for the strain energy in the vicinity of a pre-deformed state is obtained by starting from the fully geometrically nonlinear deformation model of a 3D elastic body.
Abstract: Starting from the fully geometrically nonlinear deformation model of a 3D elastic body, a consistent approximation for the strain energy in the vicinity of a pre-deformed state is obtained. This allows for the stress (geometric) stiffening effect to be taken into account. Additional terms arise in the strain energy approximation in comparison to the conventional approach, in which stiffening is incorporated in the form of a so-called geometric stiffness matrix. Computational costs of the new model are of the same order as that of the conventional approach. When compared to the fully geometrically nonlinear theory, the numerical analysis shows the suggested model to describe the dynamics of an elastic rotating structure better than the conventional approach. A new strategy is suggested to treat the non-constant pre-deformation, which is important for the flexible multibody simulations when angular velocities and interaction forces vary in time.
TL;DR: The use of hybrid-Trefftz elements for the vibration and stability analysis of thick and thin plates is discussed, focusing on the use of simple and robust triangular elements.
Abstract: This paper discusses the use of hybrid-Trefftz elements for the vibration and stability analysis of thick and thin plates. The approach can be used for elements of arbitrary geometry. However, the paper concentrates on the use of simple and robust triangular elements. Analytical expressions for the required matrices are readily derived for such elements, thereby improving their computational efficiency. Results for various problems are included to demonstrate the accuracy and efficiency of the elements.
TL;DR: In this article, a study using experimental and analytical approaches was carried out to understand the dynamic behavior, failure trigger mechanism, and seismic performance of the chimney that has been rehabilitated.
Abstract: The Chi-Chi Earthquake that struck Taiwan in 1999 damaged a 250 m tall chimney located in central Taiwan To understand the dynamic behavior, failure trigger mechanism, and seismic performance of the chimney that has been rehabilitated, a study using experimental and analytical approaches was carried out The ambient vibration test, together with a system identification approach, was used to evaluate the dynamic characteristics of the chimney A subspace approach with an instrumental variable concept was used in the system identification The dynamic behavior of the chimney was also simulated by a 3D finite element analysis using the commercial software SAP2000 Finally, the design code of ASCE 1975 was adopted to check the buckling capacity of the steel flues in the chimney structure The results indicated that the calculated stresses correspond well with the actual damages observed in the steel flues
TL;DR: Fourier p-elements of trapezoidal and cubical hexahedron shapes for the free vibration analysis of 3D elastic solids are presented in this paper, where trigonometric functions are used as enriching functions to avoid ill-conditioning problems associated with high order polynomials.
Abstract: Fourier p-elements of trapezoidal and cubical hexahedron shapes for the free vibration analysis of 3D elastic solids are presented. Trigonometric functions are used as enriching functions to avoid ill-conditioning problems associated with high order polynomials. The element matrices are analytically integrated in closed form. With the additional Fourier degrees-of-freedom, the accuracy of the computed natural frequencies is greatly improved. As an example, the natural frequencies of a cantilever cube are analyzed by a rectangular hexahedron Fourier p-element, two trapezoidal hexahedron Fourier p-elements and the conventional linear finite elements. The results show that the convergence rate of the present elements is very fast with respect to the number of trigonometric terms. The present elements also produce higher accurate modes than the linear finite elements for the same number of degrees-of-freedom. Furthermore, the first six natural frequencies of a cantilever hexagonal prism and a number of concrete dams with different lengths are given as numerical examples.
TL;DR: In this paper, an empirical relation between modulus of core reaction and the R value is established, which can be directly used in the finite element computation of buckling loads of sandwich panels.
Abstract: This paper deals with the linear stability analysis of sandwich plates modeled as thin plates resting on elastic media. To compute the elastic buckling coefficient of sandwich plates, equations have been presented in the literature by using a coefficient R, which relates the rigidity of facing to the core. In the finite element analysis, if the sandwich plates are to be modeled as plates supported by Winkler elastic springs, the relative rigidity R cannot be directly used to represent the stiffness of the Winkler springs. Instead, the stiffness of the core has to be expressed as a modulus of subgrade/core reaction. Furthermore, the R value cannot be directly used in a finite element postbuckling analysis of sandwich plates. In this study, an empirical relation between modulus of core reaction and the R value is established. This is then used in the finite element computation of buckling loads of sandwich panels. This modulus of core reaction can be directly used in the linear buckling analysis of sandwich plates as well as the postbuckling analysis using finite elements.
TL;DR: In this article, the imperfection sensitivity analysis of structures is carried out by detecting the critical states on the equilibrium path relating to the various imperfections, and a procedure that overcomes the ill-conditioning of the systems defined in the critical points is described.
Abstract: A technique for imperfection sensitivity analysis with reference to the geometrically nonlinear analysis of structures is presented. The paper discusses how detailed information on structural behavior can be obtained with less computational cost. The imperfection sensitivity analysis of structures is carried out by detecting the critical states on the equilibrium path relating to the various imperfections. In fact we can investigate the behavior of imperfect structures without considering the imperfect equilibrium curve. In this work we obtained the fold line, the one-dimensional equilibrium subset of limit points relating to different values of imperfection, by asymptotic extrapolation from a known singular point. The evaluation of this singular point on the perfect equilibrium curve is carried out by a path-following algorithm. A procedure that overcomes the ill-conditioning of the systems defined in the critical points is described. This proves to be highly advantageous in terms of computational cost in comparison with classical methods of analysis. The paper investigates the behavior of cylindrical shell. In particular the sensitivity analysis for load imperfections is carried out. The asymptotic extrapolation algorithm is also compared with continuation methods for the analysis of imperfect cylindrical shell.
TL;DR: In this article, the seismic response of a structure to a seismic activity depends on the characteristics of the structural system and the seismic activity and the difference in lateral stiffness of the two subsystems results in differential response, which is utilized by placing floor-level links between the two sub-systems; these links absorb and dissipate a substantial part of seismic input energy leading to a minimal structural distress.
Abstract: The response of a structure to a seismic activity depends on the characteristics of the structural system and the seismic activity. To improve the seismic response of a structural system, it is bifurcated into two subsystems: a flexible one, catering to the primary function/occupancy of the system and a stiff one, taking care of the lateral strength requirements and housing major services of the system. Low stiffness associated with large mass in the flexible subsystem results in shifting of natural periods of the system to zones of low seismic input energy. The difference in lateral stiffness of the two subsystems results in differential response, which is utilized by placing floor-level links between the two subsystems; these links absorb and dissipate a substantial part of seismic input energy leading to a minimal structural distress. Three types of structural systems, viz. conventional system, seismically bifurcated system with rigid links (SBS-RL) and seismically bifurcated system with damping links (SBS-DL), are analyzed for various parameters. The study shows that seismic bifurcation (SB) helps in controlling the seismic response of tall building structures. The study further shows that SB technique is useful in improving seismic performance of conventionally-designed existing structures by way of seismic retrofitting.
TL;DR: In this paper, the effects of variations in the dynamic modulus and operating speed on the peak dynamic response of a typical framed turbo-generator foundation structure were investigated, and the modal synthesis process adopted in the study included the significant modes in the sub-resonant range and a band of modes around the operating speed to obtain the peak response of the framed structure.
Abstract: Framed type foundation structures supporting turbo-generator machinery in a power plant have stringent vibration limits to ensure proper functioning of turbine generators without any breakdown. Current dynamic analysis methodology for such dynamically sensitive structures involves modal synthesis considering a single value of operating speed for the machinery and a uniform dynamic modulus for the frame material, which cannot be realized in site conditions. Such variations in the dynamic modulus across the whole structure and running speed of the machinery during normal operation have a profound impact on its dynamic performance which may result in alarmingly increasing amplitudes leading to subsequent breakdown of the machinery. A new methodology is outlined that combines the effects of the two variations by way of considering an enhanced range of speeds on either side of the operating speed for the modal synthesis process. This study shows the effects of variations in the dynamic modulus and operating speed on the peak dynamic response of a typical framed turbo-generator foundation structure. The modal synthesis process adopted in the study includes the significant modes in the sub-resonant range and a band of modes around the operating speed to obtain the peak response of the framed structure.
TL;DR: In this paper, the authors derived a relationship between the ratio of the test to theoretical deflection, and a nondimensional parameter to serve as an index for monitoring the structural displacements during testing.
Abstract: Previously, it was found that the analytical deflections computed for towers using computer software are less than those from test results. The present study is aimed at deriving a relationship between the ratio of the test to theoretical deflection, and a nondimensional parameter to serve as an index for monitoring the structural displacements during testing. Currently, structural dynamic evaluation plays little or no role in the design of towers, partly due to the difficulties involved in the analysis and the relatively high cost of field testing. Using the fundamental frequency of a tower, the peak response of the tower to gusty wind and the impact force caused by conductor breakage can be evaluated. Both theoretical and experimental studies have been carried out to evaluate the natural frequencies of the towers tested at TTRS, SERC, Chennai, India. Based on these data, an equation was derived in this paper using the tower geometry and test/theoretical deflection ratios, which allows us to predict the natural frequency of the tower in a way closer to its actual value.
TL;DR: In this paper, the forced vibration of a flexible beam undergoing both global motion and elastic deformation is investigated by its exact linear vibration modes, and the coupled nonlinear equation which takes into account the stiffening effect is derived by applying the Lagrange equation for the moving beam.
Abstract: In this paper, the forced vibration of a flexible beam undergoing both global motion and elastic deformation is investigated. The deformation field of the beam is described by its exact linear vibration modes. The coupled nonlinear equation which takes into account the stiffening effect is derived by applying the Lagrange equation for the moving beam. Based on the Newmark direct integration method and the Newton–Raphson iteration method, the computational procedures of the numerical method for solving the nonlinear equation are given. The simulation result of the rotating blade is compared with the others to demonstrate the efficiency of the present method.
Abstract: A finite element formulation in spherical coordinates is presented for the study of the vibrations of piezoelectric homogeneous and layered hollow spheres. The finite element model is based on nine-node Lagrangian interpolation functions. Representative cases are considered including solid elastic spheres and hollow homogeneous and laminated piezoelectric spheres. The accuracy of the proposed formulation is verified by comparison with existing solutions showing excellent agreement. Several new results are presented for different piezoelectric materials in both tabular and graphical format.
TL;DR: In this article, column-type structures, which are composed of columns and lateral braces attached perpendicular to the columns, are discussed and the sensitivity analysis of the eigenvalues of the tangent stiffness matrix under fixed load condition is carried out with respect to imperfections of the nodal locations.
Abstract: The present paper discusses the design of column-type structures, which are composed of columns and lateral braces attached perpendicular to the columns. Buckling of the braces of this kind of structures directly leads to global buckling of the columns. The brace-buckling modes are successfully detected by considering higher-order geometrically nonlinear relations and by introducing Green's strain into the total potential energy of the structure. Sensitivity analysis of the eigenvalues of the tangent stiffness matrix under fixed load condition is carried out with respect to imperfections of the nodal locations. Furthermore, the critical imperfection that most drastically reduces the eigenvalues are calculated and buckling loads of the imperfect systems are evaluated. The numerical results show that the second or higher eigenmode of the tangent stiffness matrix of the perfect system should be sometimes used for estimating the buckling load of the imperfect system. Design examples are presented using the proposed method, and they are compared with those in accordance with an allowable-stress design standard. The results show a possibility of reducing the sizes of the brace sections.
TL;DR: In this paper, a posteriori error estimation and h-adaptive refinement techniques for transient dynamic analysis of stiffened plates/shells using the finite element method (FEM) are presented.
Abstract: This paper presents a posteriori error estimation and h-adaptive refinement techniques for transient dynamic analysis of stiffened plates/shells using the finite element method (FEM). We furnish the formulation of stiffness and mass matrices for finite element (FE) models, QL9S2 and QUAD4S2 for dynamic analysis of plates/shells with arbitrarily-located concentric/eccentric stiffeners. Procedures for computing a posteriori errors for spatial and temporal errors have been presented for transient dynamic problems. An h-adaptive refinement strategy for stiffened plate/shell panels by employing QL9S2 and QUAD4S2 FE models has been discussed. An adaptive time stepping scheme, which is to be used with the time errors for quality control of the time steps, has also been presented. Numerical studies have been conducted to evaluate the efficacy of the error estimators and the adaptive mesh refinement and time stepping algorithm. The spatial error estimator for transient dynamic analysis is found to exhibit monotonic convergence at all time steps. The temporal error estimator for transient dynamic analysis in association with the adaptive time stepping is able to compute more accurate and reliable time steps to keep the time errors within the specified tolerance limits.