The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The ...The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The field of displacements is for- mulated using the classical broken line hypothesis and the proposed nonlinear hypothesis that generalizes the classical one. Using both hypotheses, the strains are determined as well as the stresses of each layer. The kinetic energy, the elastic strain energy, and the work of load are also determined. The system of equations of motion is derived using Hamilton＇s principle. Finally, the system of three equations is reduced to one equation of motion, in particular, the Mathieu equation. The Bubnov-Galerkin method is used to solve the system of equations of motion, and the Runge-Kutta method is used to solve the second-order differential equation. Numerical calculations are done for the chosen family of beams. The critical loads, unstable regions, angular frequencies of the beam, and the static and dynamic equilibrium paths are calculated analytically and verified numerically. The results of this study are presented in the forms of figures and tables.展开更多
In this paper modelling of the translational motion of transportation rail-guided cart with rope suspended payload is considered. The linearly moving cart,driven by a travel mechanism,is modelled as a discrete six deg...In this paper modelling of the translational motion of transportation rail-guided cart with rope suspended payload is considered. The linearly moving cart,driven by a travel mechanism,is modelled as a discrete six degrees of freedom (DOF) dynamic system. The hoisting mechanism for lowering and lifting the payload is considered and is included in the dynamic model as one DOF system. Differential equations of motion of the cart elements are derived using Lagrangian dynamics and are solved for a set of real-life constant parameters of the cart. A two-sided interaction was observed between the swinging payload and the travel mechanism. Results for kinematical and force parameters of the system are obtained. A verification of the proposed model was conducted.展开更多
In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary l...In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only two unknowns which are independent of the numbers of elements divided. The present analysis can also be extended to the study of the vibration of such beams with viscous and hysteretic damping and other kinds of beams and other structural elements with arbitrary nonhomogeneity and arbitrary variable thickness.展开更多
In this paper, a computation method has been developed so as to compare the finite element method (FEM) with the test results directly. The structure is divided into the 'master' and 'slave' degrees of...In this paper, a computation method has been developed so as to compare the finite element method (FEM) with the test results directly. The structure is divided into the 'master' and 'slave' degrees of freedom. The simplified model can be obtained with modal reduction. Then the design sensitivity analysis of the eigenvalues and eigenvectors has been carried out using the modal frequency and modal shape of the test. A two-story frame structure and a jacket model structure have been calculated. Meanwhile, the modified coefficient, the FEM computational and experimental values have been given. It has been shown that the FEM model modified using the test modal value is efficient.展开更多
This paper presents a new finite element method for solving static and dynamic problems in laying operation of pipelines. The effect of the viscoelastic soil behavior is considered by using the Pasternak foundation mo...This paper presents a new finite element method for solving static and dynamic problems in laying operation of pipelines. The effect of the viscoelastic soil behavior is considered by using the Pasternak foundation model. Some examples are also presented.展开更多
基金Project supported by the Ministry of Science and Higher Education of Poland(Nos.04/43/DSPB/0085and 02/21/DSPB/3464)
文摘The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The field of displacements is for- mulated using the classical broken line hypothesis and the proposed nonlinear hypothesis that generalizes the classical one. Using both hypotheses, the strains are determined as well as the stresses of each layer. The kinetic energy, the elastic strain energy, and the work of load are also determined. The system of equations of motion is derived using Hamilton＇s principle. Finally, the system of three equations is reduced to one equation of motion, in particular, the Mathieu equation. The Bubnov-Galerkin method is used to solve the system of equations of motion, and the Runge-Kutta method is used to solve the second-order differential equation. Numerical calculations are done for the chosen family of beams. The critical loads, unstable regions, angular frequencies of the beam, and the static and dynamic equilibrium paths are calculated analytically and verified numerically. The results of this study are presented in the forms of figures and tables.
文摘In this paper modelling of the translational motion of transportation rail-guided cart with rope suspended payload is considered. The linearly moving cart,driven by a travel mechanism,is modelled as a discrete six degrees of freedom (DOF) dynamic system. The hoisting mechanism for lowering and lifting the payload is considered and is included in the dynamic model as one DOF system. Differential equations of motion of the cart elements are derived using Lagrangian dynamics and are solved for a set of real-life constant parameters of the cart. A two-sided interaction was observed between the swinging payload and the travel mechanism. Results for kinematical and force parameters of the system are obtained. A verification of the proposed model was conducted.
文摘In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only two unknowns which are independent of the numbers of elements divided. The present analysis can also be extended to the study of the vibration of such beams with viscous and hysteretic damping and other kinds of beams and other structural elements with arbitrary nonhomogeneity and arbitrary variable thickness.
文摘In this paper, a computation method has been developed so as to compare the finite element method (FEM) with the test results directly. The structure is divided into the 'master' and 'slave' degrees of freedom. The simplified model can be obtained with modal reduction. Then the design sensitivity analysis of the eigenvalues and eigenvectors has been carried out using the modal frequency and modal shape of the test. A two-story frame structure and a jacket model structure have been calculated. Meanwhile, the modified coefficient, the FEM computational and experimental values have been given. It has been shown that the FEM model modified using the test modal value is efficient.
基金This project is financially supported by the National Science Foundation of China
文摘This paper presents a new finite element method for solving static and dynamic problems in laying operation of pipelines. The effect of the viscoelastic soil behavior is considered by using the Pasternak foundation model. Some examples are also presented.
