Function Of Lateral Displacement Research Articles

Study on the Lateral Dynamic Impedance of Pile Groups in Transversely Isotropic Soil Using Novak’s Plane Model

In order to consider the effect of anisotropy of soil around the pile on the lateral vibration of pile groups, the soil around the pile is regarded as a transversely isotropic medium, and a lateral dynamic interaction model of pile-pile in transversely isotropic soil is established. According to Novak’s plane assumption and wave propagation theory, the lateral vibration of transversely isotropic soil layer is solved by introducing potential function and using mathematical and physical means, and the attenuation function of lateral displacement of free field is given. The Dobry and Dazetas simplified solution of attenuation function is different from that of solution of plane model. The pile-pile horizontal dynamic interaction factor in transversely isotropic soil is obtained by using the initial parameter method and Krylov function. The horizontal dynamic impedance of pile groups is obtained by using the pile-pile superposition principle. The change rule of the lateral displacement attenuation function of transversely isotropic soil with frequency is related to the direction and frequency. The ratio G h v of the shear modulus in the lateral plane to the shear modulus in the vertical plane and the pile spacing S / d have a great impact on the lateral vibration of pile groups, and when the pile spacing is large, the curves of attenuation function varying with frequency fluctuate greatly. The ratio of elastic modulus of pile to vertical plane shear modulus of soil E p / G v has an effect on the lateral stiffness of pile groups, which is related to frequency, while the effect on dynamic damping is not affected by frequency. The difference of mechanical properties on different surfaces of soil around the pile has a great influence on the lateral vibration of pile groups in transversely isotropic soil, and the influence of the anisotropy on the attenuation function of the lateral displacement and the dynamic impedance cannot be ignored.

Wind-resistant structural optimization of irregular tall building using CFD and improved genetic algorithm for sustainable and cost-effective design

Tall buildings with irregular shapes and considerable heights are gaining popularity in creating the vertical cities around the world. They also considered one of the major energy consumers with little regards to sustainability. Tall building is wind-sensitive structure and shape plays major role in determining wind loads, which usually govern the design of its lateral resisting system. Thus, evaluating wind loads properly and designing an optimal lateral system accordingly are the main challenges attributed to the design process of irregular tall building. This paper presents a computational procedure for the optimal design of wind-resistant irregular tall building to minimize the total weight of structure within design requirements in single digital environment. That is achieved firstly by creating a digital system of computational fluid dynamic (CFD) analysis that is coupled with pressure-load translation (PLT) algorithm to evaluate the wind motions on irregular tall buildings and generate the design wind loads accordingly. Genetic Algorithm (GA) with enhance design constrains function of lateral displacements, inter-story drifts and top acceleration is then developed to perform structural optimization. A numerical example using 70-story twisting reinforced concrete building is implemented to verify the feasibility of the developed computational procedures. Steady and incompressible flow applied at (0°) angle of attack was implemented in the CFD model to simulate the wind flow on the studied building. Genetic algorithm with improved design constraints of static and dynamic design requirements was developed to optimize the structure effectively and efficiently. The numerical example demonstrates its effectiveness by achieving 35.71% reduction of concrete volume from the original lateral structural system design. This is also translated into a sustainability value by lessening the embedded carbon dioxide by 4,400 tons.

Analytical Approximate Solution for Large Post-Buckling Behavior of a Fixed-Pinned Beam Subjected to Terminal Force with Shear Force Effect

Based on Euler–Bernoulli beam theory, this paper investigates large post-buckling deformation of a slender elastic beam with fixed-pinned end. Owing to the asymmetric boundary conditions, it is difficult to establish analytic solution. Based on the Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with both sinusoidal nonlinearity and cosinusoidal nonlinearity can be reduced to a polynomial equation, and the geometry condition with sinusoidal nonlinearity can also be simplified to be a cubic polynomial integral equation. The admissible lateral displacement function to satisfy the fixed-pinned boundary conditions is derived in an elegant way. The analytical approximations are obtained with the harmonic balance method. Two approximate formulae for axial load and lateral load are established for small as well as large angle of rotation at the pinned end. These approximate solutions show excellent agreement with those of the shooting method for a large range of the rotation angle at the pinned end. Moreover, due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large post-buckling response of fixed-pinned beams.

Rational design protocols for size-based particle sorting microdevices using symmetry-induced cyclical dynamics.

In this paper, we describe the unification and extension of multiple kinematic theories on the advection of colloidal particles through periodic obstacle lattices of arbitrary geometry and infinitesimally small obstacle size. We focus specifically on the particle displacement lateral to the flow direction (termed "deterministic lateral displacement") and the particle-obstacle interaction frequency, and develop methods for describing these as a function of particle size and lattice parameters for arbitrary lattice geometries. We then demonstrate design algorithms for microfluidic devices consisting of chained obstacle lattices of this type that approximate any lateral displacement function of size to arbitrary accuracy with respect to multiple optimization metrics, prove their validity mathematically, and compare the generated results favorably to designs in the literature with respect to metrics such as accuracy, device size, and complexity.

任意弹性边界的多段梁自由振动研究

The vibration characteristics of continuous multi-segment beams were studied. Other than classical boundary conditions (such as simple supports), the elastic constraints were considered to analyze the free vibration characteristics of multi-segment beams. Firstly, according to the spectro-geometric method, 4 auxiliary functions were added on the basis of the traditional Fourier series to construct the lateral displacement function for each segment of the beam. Secondly, new expressions of the Lagrangian functions for the beam structure were obtained by substitution of the supposed spectro-geometric form into the Lagrangian functions. The free vibration problem was transformed into the standard matrix eigenvalue form from the Hamiltonian principle, and the natural frequencies and modes of the beam under arbitrary boundary conditions were obtained. For 4 numerical examples, the natural frequencies and modes of the continuous multi-segment beams were calculated under different boundary conditions of variant spring stiffness values. Comparison of the results between existing literatures and this work shows correctness, standardization and efficiency of the proposed method.

A new shuttle-shaped buckling-restrained brace. Theoretical study on buckling behavior and load resistance

This paper proposes a new type of buckling-restrained braces (BRBs), namely shuttle-shaped buckling-restrained braces (SS-BRBs). The proposed SS-BRB is composed of a circular steel tube as the inner core, and a shuttle-shaped thin-walled steel tube as the external restraining member. The space between them is filled by a steel-plate isolation system. The shuttle-shaped restraining member of the SS-BRB significantly improves load-carrying efficiency and saves material in its strength design. Moreover, the SS-BRB is more aesthetically appealing and can be utilized as an exposed BRB in long-span or spatial structures. In terms of the concept of restraining ratio of a BRB, no design method of an SS-BRB is available currently because it concerns the solution of the elastic buckling load of an SS-BRB. Therefore, the elastic buckling load of a pin-ended SS-BRB is initially studied by adopting the equilibrium method and is further verified through finite element (FE) method. The lateral displacement function of an SS-BRB, and the longitudinal stress at the extreme fiber of the external restraining member are derived by considering an initial geometric imperfection that is consistent with the first order overall buckling shape of the SS-BRB. A correction factor considering shear deformation has been incorporated for a more accurate prediction. The lower limit of the restraining ratio for a load-bearing type of SS-BRBs is further obtained based on yielding of the extreme fiber of the restraining member. Furthermore, the proposed formula has incorporated a strain hardening factor for the SS-BRB that experiences strain hardening of the core after its initial yielding. The proposed formulas have been validated through FE numerical analysis. The findings in this paper provide fundamentals to develop the design method for an energy-dissipation type of SS-BRBs.

Roll System and Stock’s Multi-parameter Coupling Dynamic Modeling Based on the Shape Control of Steel Strip

The existence of rolling deformation area in the rolling mill system is the main characteristic which distinguishes the other machinery. In order to analyze the dynamic property of roll system’s flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simultaneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through introducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the coupled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural deformation movement’s mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment of dynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.

Optimization of Rail Profiles to Improve Vehicle Running Stability in Switch Panel of High-Speed Railway Turnouts

A method for optimizing rail profiles to improve vehicle running stability in switch panel of high-speed railway turnouts is proposed in this paper. The stock rail profiles are optimized to decrease the rolling radii difference (RRD). Such characteristics are defined through given rail profiles, and the target rolling radii difference is defined as a function of lateral displacements of wheel set. The improved sequential quadratic programming (SQP) method is used to generate a sequence of improving profiles leading to the optimum one. The wheel-rail contact geometry and train-turnout dynamic interaction of the optimized profiles and those of nominal profiles are calculated for comparison. Without lateral displacement of wheel set, the maximum RRD in relation to a nominal profile will be kept within 0.5 mm–1 mm, while that in relation to an optimized profile will be kept within 0.3 mm–0.5 mm. For the facing and trailing move of vehicle passing the switch panel in the through route, the lateral wheel-rail contact force is decreased by 34.0% and 29.9%, respectively, the lateral acceleration of car body is decreased by 41.9% and 40.7%, respectively, and the optimized profile will not greatly influence the vertical wheel-rail contact force. The proposed method works efficiently and the results prove to be quite reasonable.

Predicting dynamic response of large amplitude free vibrations of cantilever tapered beams on a nonlinear elastic foundation

The purpose of this paper is to investigate the nonlinear vibration behavior of single and double tapered cantilever beams on the nonlinear foundation and present an alternative analytical method to solve the issue. Unlike other literatures, the admissible lateral displacement function satisfying the geometric boundary conditions of a single or double tapered cantilever beam is derived by using Rayleigh-Ritz method. Analytical approximate solutions in closed and explicit form are obtained by combining the Lagrange method with the Galerkin and Newton linearization method. Compared with the exact (numeric) results, the accuracy of these approximate solutions is presented. The effects of different parameters such as vibration amplitude, and foundation stiff parameters on nonlinear frequencies and displacement response of the tapered beams are easily analyzed, with the brief expressions of the present analytical approximate solutions.

A practical method for calculating eigenfrequencies of a cantilever microbeam with the attached tip mass

This paper is concerned with the free vibration of cantilever microbeams with attached tip mass in a systematical manner. Small size effects on the vibrations of the microbeam are taken into consideration by introducing a scale parameter. A Fourier sine series is used to represent the lateral displacement function. Stokes’ transformation is applied in the present formulation and corresponding derivatives are presented explicitly. The present formulations can be readily reduced to those for others classical elasticity models by setting corresponding small scale parameter to zero. Several parametric studies are performed to validate the present solutions and the effects of various important physical parameters (scale parameter, tip mass) are investigated.

Nonlinear vibration analysis of a type of tapered cantilever beams by using an analytical approximate method

In this paper, an alternative analytical method is presented to evaluate the nonlinear vibration behavior of single and double tapered cantilever beams. The admissible lateral displacement function satisfying the geometric boundary conditions of a single or double tapered cantilever beam is derived by using Rayleigh-Ritz method. Based on the Lagrange method and the Newton Harmonic Balance (NHB) method, analytical approximate solutions in closed and explicit form are obtained. These approximate solutions show excellent agreement with those of numeric method for small as well as large amplitude. Moreover, due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large amplitude vibration response of tapered beams.

Magnetic attraction forces between permanent magnet group arrays in a mobile magnetic clamp for pocket machining

A mobile magnetic clamp was recently tested for pocket milling on a fuselage panel. The magnetic clamps need to provide sufficient support force against the milling thrust force and sufficient drag force to overcome the frictional force. Triangular arrays of cylindrical permanent magnets are used. Axial magnetic attraction forces between magnet groups are calculated based on recently published formula at various axial heights and lateral displacements. A model is here proposed to estimate lateral magnetic attraction forces as a function of lateral displacement between two cylindrical permanent magnets. Experiments conducted using a dynamometer table to validate the measured axial and lateral magnetic forces strongly support the analytically predicted magnetic forces.

Buckling Analysis of a Rotationally Restrained Single Walled Carbon Nanotube

This paper presents an analytical formulation of nonlocal elasticity theory for the buckling analysis of simply supported carbon nanotubes with rotational springs at both ends. The lateral displacement function is represented by a Fourier sine series expansion. Stoke's transformation is applied to construct the coe cient matrix of the corresponding systems of linear equations. This matrix gives more exibility in boundary conditions. The accuracy of proposed method is validated for three well-known boundary conditions available in the literature. A very good agreement has been obtained. The present method permits to have more e cient stability matrix for calculating the buckling loads of carbon nanotubes with any desired boundary conditions.

A compact analytical method for vibration analysis of single-walled carbon nanotubes with restrained boundary conditions

In the present study, free vibration of single-walled carbon nanotubes (SWCNTs) with restrained boundary conditions is studied using nonlocal elasticity theory. To give generality to the present problem, the SWCNT is assumed to be elastically restrained by means of rotational and translational springs at the ends. The lateral displacement function is considered to be in the form of a Fourier sine series. The first, second and higher order derivatives of the Fourier sine series are legitimized using Stoke's transformation. The main advantage of this transformation is its capability of dealing with various boundary conditions to determine the vibration frequencies. Numerical results are given for different nonlocality parameters, different length of SWCNTs and different boundary conditions. The present formulation can be used for the dynamic analyses of SWCNTs with generally restrained boundary conditions.

Transient analysis of nonlinear Euler–Bernoulli micro-beam with thermoelastic damping, via nonlinear normal modes

In this paper an Euler–Bernoulli model has been used for vibration analysis of micro-beams with large transverse deflection. Thermoelastic damping is considered to be the dominant damping mechanism and introduced as imaginary stiffness into the equation of motion by evaluating temperature profile as a function of lateral displacement. The obtained equation of motion is analyzed in the case of pure single mode motion by two methods; nonlinear normal mode theory and the Galerkin procedure. In contrast with the Galerkin procedure, nonlinear normal mode analysis introduces a nonconventional nonlinear damping term in modal oscillator which results in strong damping in case of large amplitude vibrations. Evaluated modal oscillators are solved using harmonic balance method and tackling damping terms introduced as an imaginary stiffness is discussed. It has been shown also that nonlinear modal analysis of micro-beam with thermoelastic damping predicts parameters such as inverse quality factor, and frequency shift, to have an extrema point at certain amplitude during transient response due to the mentioned nonlinear damping term; and the effect of system׳s characteristics on this critical amplitude has also been discussed.

Post-buckling analysis of composite beams: A simple intuitive formulation

Post-buckling analysis of composite beams with axially immovable ends is investigated using an Intuitive formulation. Intuitive formulation uses two parameters namely critical buckling load and axial stretching force developed in the post-buckled domain of composite beam. Geometric nonlinearity of von-Karman type is taken into consideration which accounts for membrane stretching action of the beam. Axial stretching force developed in post-buckled domain of composite beam is evaluated by using an axial governing equation and is expressed either in terms of lateral displacement function as an integrated value, or as a function of both axial and lateral displacement functions at any discrete location of the beam. The available expressions of critical buckling load and derived expressions of axial stretching force developed in the beam are used for obtaining an approximate closed-form expressions for the post-buckling loads of various beam boundary conditions. Numerical accuracy of the proposed analytical closed-form expressions obtained from the intuitive formulation are compared to the available finite element solutions for symmetric and asymmetric lay-up schemes of laminated composite beam. Effect of central amplitude ratio and lay-up orientation on post-buckling load variation is briefly discussed for various beam boundary conditions considered in this study.

A simplified analysis method for the lateral deformation of braced excavations

Pile-anchor retaining structure is widely used in foundation pit engineering and side slope engineering in many countries. In contrast to strut, pile-anchor retaining structure has its typical features and advantages. It does not occupy the internal space of the foundation pit, and the project cost is much lower. Accurate prediction of the lateral displacement of the retaining structure is very important in the design stage. A simplified analysis method and several calculation assumptions of the lateral deformation of pile-anchor retaining structures are set up according to the engineering features. The expression function of lateral displacement versus depth is solved by means of a fitted function and the quasi-elastic summation method. The parameters are obtained through the stiffness equation of the anchors and the principle of minimum potential energy. The analytical evaluation of the lateral deformation curve is then completed, whose applicability is proved through practical engineering.

Analytical Solution of Sidewise Buckling of Two-Hinged Circular Arch under Concentrated Force

By the setting torsional and lateral displacement function of sidewise buckling of two-hinged circular arch under concentrated force, the single-arch structure's bending, torsional deformation and external force potential can be constructed. An analytical solution for the lateral critical buckling load of two-hinged arch is first deduced by using the energy method; the results are also compared and analyzed by the finite element method. The results show that the analytical solution of single arch’s lateral critical buckling load is in good agreement with the finite element numerical solution, and the validity of the formula is proven.

Buckling of piles in cohesive soil supporting jointless bridges

Soil-structure and especially soil-pile interaction is one of the main sources of complication in the analysis of jointless bridges. Because of the complexity of the problem, calculation of the critical buckling load of embedded piles has always been a concern to the designers since piles are relatively slender elements. In the current design method, for simplification it is assumed that soil reaction is a linear function of the lateral displacement. In this paper, a new approach is proposed which utilizes the energy method and incorporates p-y curves to estimate the critical axial load of piles embedded in cohesive soil. Pile head displacement is also incorporated into capacity calculation. In this method, the soil reaction is a nonlinear function of lateral displacement and can efficiently model the soil-structure interaction. The method is validated with experimental data for solving the governing differential equation along with calculation of buckling load. Results of parametric study reveal that buckling loads estimated by equivalent cantilever method are highly above the corresponding loads estimated by the energy method at relatively small pile head movement. Furthermore, for this condition it is shown that fully embedded piles will fail before reaching the estimated buckling load because of yielding; consequently, buckling analysis does not govern the design of piles fully embedded in cohesive soil. However for partially embedded piles, the buckling load may govern.

Analytical Evaluation of Lateral Displacement of Cemented Soil Retaining Wall for Excavation

A fitting function of lateral displacement of cemented soil retaining wall was proposed according to several measured data of excavations. On this basis, the retaining wall was treated as a homogeneous elastic vertical beam, whose toe and heel were restricted by a spring constraint but still could be moved and rotated. An analytical formula of the lateral displacement of the retaining wall was deduced with the principle of minimum potential energy with consideration of all the external forces. Compared with some other measured data, the average relative error of the formula was less than 10%, which preliminary indicated the formula’s practical value.