The Out-of-Plane Stability Analysis of Crane Jib with Two Symmetric Drawbars

2013 ◽  
Vol 446-447 ◽  
pp. 469-473
Author(s):  
Nian Li Lu ◽  
Ce Chen ◽  
Shi Ming Liu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Boundary Conditions ◽  
Characteristic Equation ◽  
Critical Condition ◽  
Design Rules ◽  
Special Cases ◽  
Out Of Plane

The out-of-plane stability of the crane jib with two symmetric drawbars is studied. Differential equation with two non-conservative forces caused by the two symmetric drawbars is established in critical condition. According to the boundary conditions and proper parameter processing, the out-of-plane characteristic equation is obtained for the crane jib. Comparison with the ANSYS results verified the correctness of the method. And special cases are given to show the consistency of the method used in this paper and that with one drawbar given by the Chinese Design Rules for crane (GB3811-2008). The contribution of the angle between two symmetric drawbars to the out-of-plane stability of the crane jib is also discussed. The results show that, the crane jib with two symmetric drawbars has higher out-of-plane stability than that with one drawbar, and the increase of the angle between the two symmetric drawbars will lead to the significant increase of the out-of-plane stability of the crane jib.

Out-of-Plane Stability Analysis for Crane Jib with Single Cable Considering Lateral Flexibility of the Cable Fixed Joint

2014 ◽  
Vol 685 ◽  
pp. 240-244 ◽  
Author(s):  
Peng Lan ◽  
Teng Fei Wang ◽  
Nian Li Lu
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Characteristic Equation ◽  
Lateral Stiffness ◽  
Stiffness Coefficient ◽  
The Finite Element Method ◽  
Lateral Direction ◽  
Out Of Plane ◽  
Lateral Constraint ◽  
The Stability

The out-of-plane stability of crane jib is studied considering the lateral flexibility of the fixed joint. The analytical expression of the out-of-plane buckling characteristic equation for the crane jib with single cable is obtained by establishing the bending deflection differential equation of jib under the instability critical state with the method of differential equation. The equilibrium equation of the fixed point in the lateral direction is introduced to solve the differential equation besides the boundary conditions. The analytical results obtained agree very well with the finite element method (FEM) results. To consider the lateral flexibility of the cable fixed joint, a dimensionless stiffness coefficient measuring the lateral constraint was introduced to derive the out-of-plane buckling characteristic equation. The degeneration forms of the characteristic equation under the limit cases of zero lateral stiffness, infinite lateral stiffness are further discussed. And the influence of the lateral stiffness of fixed joint on the stability of jib is investigated. It is shown that the increase of the lateral stiffness will significantly improve the buckling load of the crane jib especially when the lateral stiffness is very small.

Out-of-Plane Stability Analysis of Crane Jib with Auxiliary Bracing

2014 ◽  
Vol 1078 ◽  
pp. 201-205
Author(s):  
Teng Fei Wang ◽  
Peng Lan ◽  
Nian Li Lu
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Finite Element ◽  
Characteristic Equation ◽  
Order Effect ◽  
The Finite Element Method ◽  
Analysis Model ◽  
Lateral Direction ◽  
Out Of Plane ◽  
Deformation Compatibility

The analysis model is built to investigate the out-of-plane stability of crane jib with auxiliary bracing. Considering the second-order effect, the analytical expression of the out-of-plane buckling characteristic equation for the crane jib with auxiliary bracing is obtained by establishing the bending deflection differential equation of jib under the instability critical state with the method of differential equation. The equilibrium equation of the cable converging point in the lateral direction is introduced to solve the differential equation besides the boundary conditions and deformation compatibility equations. With the characteristic equation, the critical compression or the critical lifting load can be easily obtained. The characteristic equation is analytically expressed and the analytical results obtained agree very well with the finite element method (FEM) results. The validity of the characteristic equation is verified.

Vibration Analysis of Doubly Curved Shallow Shells With Elastic Edge Restraints

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Shiliang Jiang ◽  
Tiejun Yang ◽  
W. L. Li ◽  
Jingtao Du
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Wide Spectrum ◽  
Current Method ◽  
Entire Solution ◽  
Shallow Shells ◽  
Special Cases ◽  
Out Of Plane ◽  
Expansion Coefficients ◽  
Doubly Curved

An analytical method is derived for the vibration analysis of doubly curved shallow shells with arbitrary elastic supports alone its edges, a class of problems which are rarely attempted in the literature. Under this framework, all the classical homogeneous boundary conditions for both in-plane and out-of-plane displacements can be universally treated as the special cases when the stiffness for each of restraining springs is equal to either zero or infinity. Regardless of the boundary conditions, the displacement functions are invariably expanded as an improved trigonometric series which converges uniformly and polynomially over the entire solution domain. All the unknown expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh–Ritz technique. Unlike most of the existing solution techniques, the current method offers a unified solution to a wide spectrum of shell problems involving, such as different boundary conditions, varying material and geometric properties with no need of modifying or adapting the solution schemes and implementing procedures. A numerical example is presented to demonstrate the accuracy and reliability of the current method.

Critical Speeds of Rotating Shaft Subjected to Axial Loading and Tangential Torsion

1967 ◽  
Vol 89 (2) ◽  
pp. 259-264 ◽  
Author(s):  
N. Willems ◽  
S. M. Holzer
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Classical Theory ◽  
Axial Load ◽  
Galerkin Approximation ◽  
Axial Loading ◽  
Complex Form ◽  
Rotating Shaft ◽  
Special Cases ◽  
Predicted Values

In this study the classical theory of the bending and twisting of thin rods is utilized and applied to the case of a rotating shaft subjected to axial loading and tangential torsion. The differential equation of small bending oscillations in its complex form is solved by using a three-term Galerkin approximation satisfying the boundary conditions term by term. Convergence of the solution is indicated by comparing the two-term and three-term approximations. The special cases of a stationary shaft subjected to axial load or twist are discussed briefly. Experimental results closely agree with the theoretically predicted values.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 979
Author(s):  
Sandeep Kumar ◽  
Rajesh K. Pandey ◽  
H. M. Srivastava ◽  
G. N. Singh
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Collocation Method ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Special Cases ◽  
Collocation Approach ◽  
Linear And Nonlinear ◽  
Simulation Results ◽  
Theoretical Results

In this paper, we present a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation (GFIDE). The presented approach is based on the collocation method using Jacobi poly-fractonomials. The GFIDE is defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases. The convergence and error analysis of the proposed method are also established. Linear and nonlinear cases of the considered GFIDEs are numerically solved and simulation results are presented to validate the theoretical results.

scholarly journals Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Maozhu Zhang ◽  
Kun Li ◽  
Hongxiang Song
Keyword(s):  
Boundary Conditions ◽  
Operator Theory ◽  
Resolvent Convergence ◽  
Spectral Inclusion ◽  
Regular Approximation ◽  
Special Cases ◽  
Abstract Operator ◽  
Norm Resolvent Convergence ◽  
Sturm Liouville ◽  
Spectral Exactness

AbstractIn this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed. Via the abstract operator theory, the strongly resolvent convergence and norm resolvent convergence of a sequence of operators are obtained and it follows that the spectral inclusion of spectrum holds. Moreover, spectral exactness of spectrum holds for two special cases.

Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation

2008 ◽  
Vol 15 (3) ◽  
pp. 531-539
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Large Time Behavior ◽  
Dirichlet Boundary Conditions ◽  
Time Behavior ◽  
Integro Differential Equation ◽  
Homogeneous Data

Abstract Large time behavior of solutions to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. The rate of convergence is given, too. Dirichlet boundary conditions with homogeneous data are considered.

scholarly journals Impurity induced scale-free localization

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Boundary Conditions ◽  
Skin Effect ◽  
Reciprocal Lattice ◽  
Periodic Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Translational Invariance ◽  
Scale Free ◽  
Special Cases ◽  
Simulation Results

AbstractNon-Hermitian systems have been shown to have a dramatic sensitivity to their boundary conditions. In particular, the non-Hermitian skin effect induces collective boundary localization upon turning off boundary coupling, a feature very distinct from that under periodic boundary conditions. Here we develop a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with periodic/open boundary conditions and even their interpolations being special cases across a whole range of boundary impurity strengths. We uncover steady states with scale-free localization along or even against the direction of non-reciprocity in various impurity strength regimes. Also present are Bloch-like states that survive albeit broken translational invariance. We further explore the co-existence of non-Hermitian skin effect and scale-free localization, where even qualitative aspects of the system’s spectrum can be extremely sensitive to impurity strength. Specific circuit setups are also proposed for experimentally detecting the scale-free accumulation, with simulation results confirming our main findings.

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