scholarly journals Assessment of stress state and dynamic characteristics of plane and spatial structure

2021 ◽  
Vol 2070 (1) ◽  
pp. 012156
Author(s):  
Z. Urazmukhamedova ◽  
D. Juraev ◽  
M. Mirsaidov
Keyword(s):  
Stress State ◽  
Dynamic Characteristics ◽  
Eigenvalue Problems ◽  
Variational Equation ◽  
Design Stage ◽  
Algebraic Equations ◽  
Earth Dams ◽  
Low Frequencies ◽  
Modes Of Vibration ◽  
Spatial Test

Abstract This study is devoted to the assessment of the stress state and dynamic characteristics of various structures. The actual task at the design stage is to determine the parameters of a structure. In this article, a mathematical model was developed for assessing the stress state and dynamic characteristics of plane and spatial structures based on the Lagrange variational equation using the d’Alembert principle. The variational problem for the structures considered by the finite element method leads to the solution of nonhomogeneous algebraic equations or to the solution of algebraic eigenvalue problems. To assess the adequacy of the model and the accuracy of the numerical results obtained, a plane and spatial test problem with an exact solution was solved. Using the proposed model, the eigenfrequencies and modes of oscillations of the gravitational and earth dams (296 m high) of the Nurek reservoir were investigated. At that, it was revealed that in the natural modes of vibration of earth dams, the greatest displacements under low frequencies are observed at the crest part or at the middle of the slopes.

scholarly journals Minimization of Stress State of a Hub of Friction Pair

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Vagif M. Mirsalimov ◽  
Parvana E. Akhundova
Keyword(s):  
Stress State ◽  
Friction Pair ◽  
Circumferential Stress ◽  
Design Stage ◽  
Friction Unit ◽  
Surface Model ◽  
Oil Well ◽  
Algebraic Equations ◽  
Minimax Criterion ◽  
External Contour

The function of displacements of external contour points of a friction pair hub that could provide minimization of stress state of a hub was determined on the basis of minimax criterion. The problem is to decrease stress state at that place where it is important. The rough friction surface model is used. To solve a problem of optimal design of friction unit the closed system of algebraic equations is constructed. Increase of serviceability of friction pair parts may be controlled by design-engineering methods, in particular by geometry of triboconjugation elements. Minimization of maximum circumferential stress on contact surface of friction unit is of great importance in the design stage for increasing the serviceability of friction pair. The obtained function of displacements of the hub’s external contour points provides the serviceability of friction pair elements. The calculation of friction pair for oil-well sucker-rod pumps is considered as an example.

Study on the Multi-Body Dynamic Characteristics of FPSO Soft Yoke Mooring System Based on Symplectic Algorithm

2019 ◽  
Author(s):  
Wenhua Wu ◽  
Baicheng Lyu ◽  
Ji Yao ◽  
Qianjin Yue ◽  
Zhang Yantao ◽  
...  
Keyword(s):  
Stress State ◽  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Single Point ◽  
Differential Algebraic Equations ◽  
Mooring System ◽  
Algebraic Equations ◽  
Restoring Force ◽  
Hamilton System ◽  
Multi Body

Abstract The soft yoke single-point mooring (SYMS) system is the main mooring approach for the floating production storage and offloading (FPSO) unit. As a typical multi-rigid-body system, a SYMS consists of the single-point turret, yoke, mooring legs, and mooring support. It releases the rotational degrees of freedom of an FPSO through the combined effects of multiple joint structures, so as to deliver the weather-vane effect of the FPSO. In this paper, a multi-body dynamics model of the soft yoke mooring system was established. To deal with the difficult integration in the process of solving differential-algebraic equations, a symplectic numerical integration method was proposed on the basis of the Zu Chongzhi method. The proposed solution format had simple symplectic property automatically satisfying the Hamilton system, as well as a high accuracy in solving nonlinear systems. The measured data of the FPSO’s six degrees of freedom (6DoF) under two different sea conditions were selected, and the mooring restoring force of the SYMS was calculated. The calculated results showed that the symplectic solution method could the actual stress state of the structures with more obvious dynamic characteristics. Furthermore, the displacement and stress state of the single-body structures, such as the mooring legs and yoke, and the analysis result could comprehensively evaluate the overall working state of the SYMS.

scholarly journals Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams

2005 ◽  
Vol 12 (6) ◽  
pp. 425-434 ◽  
Author(s):  
Menglin Lou ◽  
Qiuhua Duan ◽  
Genda Chen
Keyword(s):  
Perturbation Method ◽  
Dynamic Characteristics ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Solution Process ◽  
Equation Of Motion ◽  
Timoshenko Beams ◽  
Algebraic Equations ◽  
Nonlinear Algebraic Equations ◽  
Shear Distortion

Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are discussed in detail.

scholarly journals Natural Vibrations of the Reinforced Tapered Shell with Taking Into Account the Viscoelastic Properties of the Material

2021 ◽  
Vol 264 ◽  
pp. 01011
Author(s):  
Matlab Ishmamatov ◽  
Nurillo Kulmuratov ◽  
Nasriddin Ахmedov ◽  
Shaxob Хаlilov ◽  
Sherzod Ablakulov
Keyword(s):  
Conical Shell ◽  
Variational Principles ◽  
Variational Equation ◽  
Frequency Equation ◽  
Main Element ◽  
Algebraic Equations ◽  
Natural Vibrations ◽  
Natural Oscillations ◽  
Conical Shells ◽  
Truncated Conical Shell

In this paper, the integro-differential equations of natural oscillations of a viscoelastic ribbed truncated conical shell are obtained based on the Lagrange variational equation. The general research methodology is based on the variational principles of mechanics and variational methods. Geometrically nonlinear mathematical models of the deformation of ribbed conical shells are obtained, considering such factors as the discrete introduction of edges. Based on the finite element method, a method for solving and an algorithm for the equations of natural oscillations of a viscoelastic ribbed truncated conical shell with articulated and freely supported edges is developed. The problem is reduced to solving homogeneous algebraic equations with complex coefficients of large order. For a solution to exist, the main determinant of a system of algebraic equations must be zero. From this condition, we obtain a frequency equation with complex output parameters. The study of natural vibrations of viscoelastic panels of truncated conical shells is carried out, and some characteristic features are revealed. The complex roots of the frequency equation are determined by the Muller method. At each iteration of the Muller method, the Gauss method is used with the main element selection. As the number of edges increases, the real and imaginary parts of the eigenfrequencies increase, respectively.

Conditions for the planes of symmetry of an elastically supported rigid body

2009 ◽  
Vol 223 (8) ◽  
pp. 1755-1766 ◽  
Author(s):  
S J Jang ◽  
Y J Choi
Keyword(s):  
Rigid Body ◽  
Eigenvalue Problems ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Mass Matrices ◽  
Out Of Plane ◽  
Modes Of Vibration ◽  
Compliance Matrices ◽  
Special Points ◽  
Elastically Supported

Introducing the planes of symmetry into an oscillating rigid body suspended by springs simplifies the complexity of the equations of motion and decouples the modes of vibration into in-plane and out-of-plane modes. There have been some research results from the investigation into the conditions for planes of symmetry in which prior conditions for the simplification of the equations of motion are required. In this article, the conditions for the planes of symmetry that do not need prior conditions for simplification are presented. The conditions are derived from direct expansions of eigenvalue problems for stiffness and mass matrices that are expressed in terms of in-plane and out-of-plane modes and the orthogonality condition with respect to the mass matrix. Two special points, the planar couple point and the perpendicular translation point are identified, where the expressions for stiffness and compliance matrices can be greatly simplified. The simplified expressions are utilized to obtain the analytical expressions for the axes of vibration of a vibration system with planes of symmetry.

Evaluation for Static and Dynamic Characteristics of a Miniaturized Machine Tool According to Its Configuration

2006 ◽  
Author(s):  
J. H. Lee ◽  
S. H. Yang ◽  
Y. S. Kim
Keyword(s):  
Machine Tool ◽  
Dynamic Characteristics ◽  
Manufacturing System ◽  
Error Modeling ◽  
Design Stage ◽  
Volumetric Error ◽  
Actual System ◽  
Static And Dynamic Characteristics ◽  
Spindle Unit ◽  
Small Parts

Miniaturization for manufacturing system has been studied widely since the development of the smallest lathe in the world. Several prototypes are implemented, which are used to produce small parts with high precision. Accuracy and stiffness are the most important factors for design in the development of miniaturized systems. This study presents a method to evaluate static and dynamic characteristics of a miniaturized machine tool (mMT) according to its configuration before building the actual system. The proposed error estimation technique shows that volumetric error can be estimated indirectly at the design stage using error components of one axis and HTM (Homogeneous Transform Matrix), unlike the error modeling technique through direct measurement. Thus, accuracy of the system based on its configuration is analyzed at the design stage itself. The proposed analysis procedure is shown for the case of a 3 axis machine tool. In addition, dynamic characteristics of spindle unit affecting the spindle error are studied.

Mathematical model of piston-tool interaction in rock fracture by impact

2020 ◽  
pp. 94-103
Author(s):  
A. B. Zhabin ◽  
I. M. Lavit ◽  
A. V. Polyakov ◽  
Z. E. Kerimov
Keyword(s):  
Finite Difference ◽  
Boundary Value Problems ◽  
Variational Equation ◽  
Rock Fracture ◽  
Boundary Value ◽  
Calculation Error ◽  
Algebraic Equations ◽  
Time Curve ◽  
Linear Algebraic Equations ◽  
The Impact

The authors justify a computation model of a machine percussion system simulated by elastic cylindrical rods subjected to maximal axial load at minimal strain. Rock mass is assumed as a perfectly solid block. The piston and tool are described by the values of length, cross-section area, density and Young’s modulus. The model determines the force applied by the tool on the rock as function of time. It is assumed that transverse displacements and velocities of the rods are negligeable as compared with the axial displacements and velocities, while the rods are free from the action of the external forces different from the restraining forces. The variational equation expresses the principle of possible displacements. The variations are independent of time. The initial and boundary conditions are considered. The variational equation is solved using the method of straight lines, with replacement of a time differentiation operator by the finite difference operator. The problem reduces to the successive solving of boundary value problems with variable right-hand sides. The finite difference scheme is the approved implicit scheme of Crank-Nicolson. The boundary value problems are solved using the finite element method at each step of integrating. As a result, the variational equation transforms into a system of linear algebraic equations, and the reduced solution of this system yields the wanted force. The calculations are illustrated by the tool press force-time curve plotted with a step of 0.1 µs for hydropercussion machine G100 by Rammer, Finland. The relative calculation error of the impact duration and maximal force (in absolute magnitude) is not higher than 0.1%.

Study on Dynamic Characteristics of Circular Tunnel Concrete Lining

2013 ◽  
Vol 438-439 ◽  
pp. 1129-1132
Author(s):  
Ling Lu ◽  
Yang Zhao
Keyword(s):  
Dynamic Characteristics ◽  
Concrete Lining ◽  
Circular Tunnel ◽  
Modes Of Vibration ◽  
Water Conveyance ◽  
Vibration Performance

The dynamic characteristics of concrete lining of a circular tunnel was studied combined with the Dahuofang water-conveyance project. The first ten frequencies and modes of vibration were presented. The influence of some factors on the vibration performance of the concrete lining were analyzed, i.e. buried depth, lining thickness, youngs modulus of rock, and water in the tunnel. The results show that the buried depth and the youngs modulus of rock have greater influence on the vibration performance of concrete lining than the lining thickness and the water in the tunnel. Some aseismic measures are given out for the similar engineering.

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