Static and Dynamic Analyses of Beam-Columns on Winkler Foundation

1991 ◽  
Author(s):  
T. W. Lee ◽  
W. L. Cleghorn ◽  
B. Tabarrok
Keyword(s):  
Elastic Foundation ◽  
Axial Load ◽  
Natural Frequencies ◽  
Homogeneous Solution ◽  
Time History ◽  
Element Model ◽  
Free Vibrations ◽  
Winkler Foundation ◽  
Static Case ◽  
Minimum Number

Abstract A finite element model is developed for static, free and forced vibration analyses of a compressed beam resting on a Winkler-type elastic foundation and subjected to transverse loads. The homogeneous solution of the governing differential equation of static equilibrium is used as shape functions when deriving the load vector, the stiffness and mass matrices. For the static case, a procedure is outlined for improving the internal distributions of deflections, rotations, bending moments and shear forces of the structure. In this procedure, exact results are obtained for concentrated, uniform and ramp distributed loads with a minimum number of elements. When considering free vibrations, natural frequencies converge rapidly with increasing numbers of elements, and are shown to agree with results obtained by other analytical methods. The effects of the axial load and elastic foundation on the natural frequencies are also illustrated. For forced vibrations, the Newmark β Method is employed for obtaining the time history response of a beam-column on an elastic foundation subjected to lateral time-dependent excitations and constant axial load.

Dynamic Parameters Identification of Structural Laminated Glass

2015 ◽  
Author(s):  
Francesco Clementi ◽  
Laura Consolini ◽  
Stefano Lenci
Keyword(s):  
Natural Frequencies ◽  
Theoretical Models ◽  
Element Model ◽  
Free Vibrations ◽  
Laminated Glass ◽  
Beam Model ◽  
Dynamical Characteristics ◽  
Time Histories ◽  
Dynamical Properties

In this work, we address experimentally the determination of the dynamical properties, in particular natural frequencies and damping factors, of laminated structural glass. Various specimens, coming from different productions and manufactures, are investigated. Damped free vibrations experiments are performed, where the excitation is provided by an instrumented hammer. The boundary conditions are free-free (the specimens lay on a very flexible sponge substrate). The dynamical characteristics are determined by last squares fitting of time histories, a technique that is very simple, fast and provides very good results. Finally, two theoretical models (a two-layer beam model and a 2D finite element model) are employed to interpret the experimental results.

scholarly journals An Inverse Method to Predict NEMS Beam Properties From Natural Frequencies

2020 ◽  
Vol 87 (6) ◽  
Author(s):  
Alyssa T. Liem ◽  
Atakan B. Ari ◽  
J. Gregory McDaniel ◽  
Kamil L. Ekinci
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Boundary Conditions ◽  
Finite Element Model ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Element Model ◽  
Normalized Error ◽  
Beam Parameters

Abstract This paper presents a method to simultaneously predict the elastic modulus, axial load, and boundary conditions of a nanoelectromechanical system (NEMS) beam from a minimum of two measured natural frequencies. The proposed method addresses the challenges of the inverse problem at the nano scale, which include high natural frequencies, small geometric beam dimensions, and measurements limited to natural frequencies. The method utilizes a finite element model of an Euler–Bernoulli beam under axial loading to predict the response of the beam with axial loading and flexible boundary conditions. By expressing the finite element model in terms of dimensionless beam parameters, the proposed method may be applied to nano scale beams while maintaining numerical stability of the finite element equation of motion. With the stabilized finite element model, the NEMS beam properties are predicted by iterating through values of dimensionless beam parameters until the normalized error between predicted and measured natural frequencies is minimized. A key feature of the proposed method is the simultaneous prediction of the elastic modulus during the iterative search, resulting in a reduction of the search space and significant computational savings. Additionally, the proposed method readily accommodates an arbitrary number of measured natural frequencies without the reformulation of procedures and analyses. Numerical examples are presented to illustrate the proposed method’s ability to predict the elastic modulus, axial load, and boundary conditions. The proposed method is applied to experimental measurements of a NEMS beam, where the normalized error between predicted and measured natural frequencies is reduced below 10−3.

A Scheme of a Knowledge Based System for Optimal Modelling and Design of Robots

1994 ◽  
Author(s):  
Michael Lawo
Keyword(s):  
Structural Model ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Time History ◽  
Element Model ◽  
Identification Problem ◽  
Optimization Method ◽  
Knowledge Based System ◽  
Knowledge Based ◽  
History Of

Abstract Based on a finite element model the deformations and vibrations of a robot structure are calculated for different configurations (layouts). The results of the analysis are verified by measuring the corresponding deformations and velocities. The time history of velocities at different points of the structure in test positions is recorded. Out of the time history by modal analysis the natural frequencies are determined. The structural model is checked by the comparison of corresponding analysed and measured values A nonlinear optimization method with the structural parameters as variables of the model is used for the solution of this identification problem. The result is a verified and sufficient structural model of the real structure. Out of the experiences a knowledge based system for the modelling and simulation of robot structures is conceived. The concept of the system is presented.

Buckling and Free Vibration of a Single Pile Considering the Effect of Soil–Structure Interaction

2018 ◽  
Vol 18 (04) ◽  
pp. 1850061 ◽  
Author(s):  
Jianjun Ma ◽  
Fengjun Liu ◽  
Xiaojuan Gao ◽  
Mengqiang Nie
Keyword(s):  
Critical Load ◽  
Elastic Foundation ◽  
Axial Load ◽  
Soil Structure ◽  
Natural Frequencies ◽  
Soil Structure Interaction ◽  
Single Pile ◽  
Structure Interaction ◽  
Post Buckling ◽  
Foundation Parameter

The buckling response and free vibration characteristics of a single pile in the elastic foundation are investigated. Considering the effect of soil–structure interaction and geometric nonlinearity, the nonlinear equation of motion for a single pile is derived by Hamilton’s principle. Then, closed-form solutions of the critical load and buckled configuration of the pile are obtained analytically, and the natural frequencies of the pre- and post-buckling pile are examined. Finally, the effect of elastic foundation parameter on the critical load of the pile is discussed, and the effect of axial load on the natural frequencies of the pile is also explored. Numerical results show that the effect of elastic foundation parameter plays a dominant role on the critical load and buckled configuration of the pile, and the shear parameter affects the critical load directly. The axial load effect on the dynamic characteristics of the pre-buckling pile is significant, meanwhile, it may contribute very small to the post-buckling pile when the axial load exceeds some specific values.

scholarly journals Free Vibrations of an Elastically Restrained Euler Beam Resting on a Movable Winkler Foundation

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Qiang Zhou ◽  
Tong Wang
Keyword(s):  
Elastic Foundation ◽  
Free Vibrations ◽  
Wave Number ◽  
Mode Shapes ◽  
Traditional Theory ◽  
Winkler Foundation ◽  
Euler Beam ◽  
Elastically Restrained ◽  
Elastic Restraints ◽  
Natural Characteristics

The traditional theory of beam on elastic foundation implies a hypothesis that the elastic foundation is static with respect to the inertia reference frame, so it may not be applicable when the foundation is movable. A general model is presented for the free vibration of a Euler beam supported on a movable Winkler foundation and with ends elastically restrained by two vertical and two rotational springs. Frequency equations and corresponding mode shapes are analytically derived and numerically solved to study the effects of the movable Winkler foundation as well as elastic restraints on beam’s natural characteristics. Results indicate that if one of the beam ends is not vertically fixed, the effect of the foundation’s movability cannot be neglected and is mainly on the first two modes. As the foundation stiffness increases, the first wave number, sometimes together with the second one, firstly decreases to zero at the critical foundation stiffness and then increases after this point.

Dynamic Response Analysis of Xi'an Bell Tower Timber Structure under the Metro-Vibration Loading of Line 2 and 6

2013 ◽  
Vol 353-356 ◽  
pp. 1732-1738
Author(s):  
Zhao Bo Meng ◽  
Teng Fei Zhao ◽  
Jie Jin ◽  
Xi Feng Li
Keyword(s):  
Technical Specification ◽  
Interaction Model ◽  
Time History ◽  
Element Model ◽  
Response Analysis ◽  
Winkler Foundation ◽  
Analysis Model ◽  
Bell Tower ◽  
Dimensional Finite Element ◽  
The Impact

The effects of metro line 2 and line 6 on Xi'an Bell Tower was studied by numerical analysis in this paper. At first, according to the theory of Euler-Bernoulli beam in Winkler foundation, the analysis model of train-track-foundation system was established, and then, time-history curve of metro-induced loading acts on tunnel structure is obtained by using Matlab produce platform. Secondly, two-dimensional finite element model of the structure-soil-tunnel interaction model was established using ANSYS. Finally, the impact of metro line 2 and 6 and ground transportation on Xi’an Bell Tower was evaluated according to the Technical specification for protection of historic buildings against man-made vibration. The construction of Metro Line 2 and Line 6 will affect the safety of Xi'an Bell Tower.

scholarly journals Vibrations of Circular Plates with Elastically Restrained Edge against Translation and Resting on Elastic Foundation

2016 ◽  
Vol 13 (2) ◽  
pp. 187
Author(s):  
L.B. Rao ◽  
C.K. Rao
Keyword(s):  
Elastic Foundation ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Vibration Characteristics ◽  
Graphical Form ◽  
Winkler Foundation ◽  
Stiffness Ratio ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Elastically Restrained

The present paper deals with exact solutions for the free vibration characteristics of thin circular plates elastically restrained against translation and resting on Winkler-type elastic foundation based on the classical plate theory. Parametric investigations are carried out for estimating the influence of edge restraint against translation and stiffness of the elastic foundation on the natural frequencies of circular plates. The elastic edge restraint against translation and the presence of elastic foundation has been found to have a profound influence on vibration characteristics of the circular plate undergoing free transverse vibrations. Computations are carried out for natural frequencies of vibrations for varying values of translational stiffness ratio and stiffness parameter of Winkler-type foundation. Results are presented for twelve modes of vibration both in tabular and graphical form for use in design. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational edge restraint and the foundation stiffness ratio of the Winkler foundation on the natural frequencies of uniform isotropic circular plates. 

scholarly journals Transfer matrix formulation for dynamic response of Timoshenko beams resting on two-parameter elastic foundation subjected to moving load

2021 ◽  
Vol 4 (2) ◽  
pp. 99-110
Author(s):  
Baran Bozyigit
Keyword(s):  
Dynamic Response ◽  
Shear Layer ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Moving Load ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Winkler Foundation ◽  
Foundation Model ◽  
Two Parameter

In this study, the dynamic response of beams resting on two-parameter elastic foundation subjected to moving load is investigated by using the transfer matrix method (TMM). The Timoshenko beam theory (TBT) which considers shear deformation and rotational inertia is used to model the beam. The two-parameter elastic foundation model is selected as Pasternak foundation that takes into account a shear layer at the end of linear springs of Winkler foundation. The TMM which uses the relation between analytically obtained state vectors of each end of the beam is applied to solve the free vibration problem. After performing the free vibration analysis, the mathematical model is simplified into an equivalent single degree of freedom (SDOF) system by using the exact mode shapes to obtain dynamic responses. The generalized displacement is calculated for each mode by using the Runge-Kutta algorithm. A numerical case study is presented for a simply-supported Timoshenko beam on the Pasternak foundation subjected to a concentrated load. The natural frequencies obtained from finite element method (FEM) results of SAP2000 are presented with the results of TMM for comparison purposes using the Winkler foundation. The effects of shear layer on the natural frequencies of the model are revealed. The mode shapes are plotted. The proposed approach for calculating dynamic responses is validated by using the results of FEM for Winkler foundation model. Then, the effects of Winkler springs and shear layer of the foundation model on the dynamic responses are presented in figures. The effects of modal damping are discussed. Finally, the critical velocities for the model are calculated for various elastic foundation scenarios and the effects of elastic foundation parameters on the dynamic response of beam model subjected to moving load with high velocity are observed.

scholarly journals Vibrations of Circular Plates Resting on Elastic Foundation with Elastically Restrained Edge Against Translation

2018 ◽  
Vol 13 (1) ◽  
pp. 14
Author(s):  
L.B. Rao ◽  
C.K. Rao
Keyword(s):  
Elastic Foundation ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Vibration Characteristics ◽  
Graphical Form ◽  
Winkler Foundation ◽  
Stiffness Ratio ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Elastically Restrained

The present paper deals with exact solutions for the free vibration characteristics of thin circular plates resting on Winkler-type elastic foundation based on the classical plate theory elastically restrained against translation. Parametric investigations are carried out for estimating the influence of edge restraint against translation and stiffness of the elastic foundation on the natural frequencies of circular plates. The elastic edge restraint against translation and the presence of elastic foundation has been found to have a profound influence on vibration characteristics of the circular plate undergoing free transverse vibrations. Computations are carried out for natural frequencies of vibrations for varying values of translational stiffness ratio and stiffness parameter of Winkler-type foundation. Results are presented for twelve modes of vibration both in tabular and graphical form for use in the design. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational edge restraint and the foundation stiffness ratio of the Winkler foundation on the natural frequencies of uniform isotropic circular plates.  

Natural Frequencies of Railway Slab on Winkler Foundation

2014 ◽  
Vol 617 ◽  
pp. 50-53
Author(s):  
Daniela Kuchárová
Keyword(s):  
Elastic Foundation ◽  
Dynamic Characteristics ◽  
Dynamic Systems ◽  
Natural Frequencies ◽  
Numerical Solutions ◽  
Variable Stiffness ◽  
Winkler Foundation ◽  
Structural Dynamic ◽  
Natural Modes ◽  
Adequate Accuracy

Natural frequencies and natural modes represent the basic dynamic characteristics of all dynamic systems. They define the dynamic individuality of dynamic system. It is useful to know approximate relations giving the results with adequate accuracy. The analysis of plates in contact with elastic foundation is the part of structural dynamic which demands hard numerical solutions. The submitted paper presents approximate relations enabling to carry out the assessment of natural frequencies of the slabs on elastic foundation at variable stiffness with satisfactory accuracy.

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