Forced Vibration Numerical Analysis of Reticulate Systems by Dynamic Finite Element Method (original) (raw)
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There are many engineering structures that can be modeled as beams, carrying one, two or multi degree-of-freedom spring-mass systems. Examples of such practical applications include components of buildings, machine tools, vehicle suspensions and rotating machinery accessories of machine structures. Because of these wide ranging applications, the vibration behavior of beams carrying discrete structural elements, such as beams carrying a two degree-of-freedom spring-mass system have received considerable attention for many years.
Vibration Analysis Of Beam Subjected To Moving Loads Using Finite Element Method
It was purposed to understand the dynamic response of beam which are subjected to moving point loads. The finite element method and numerical time integration method (Newmark method) are employed in the vibration analysis. The effect of the speed of the moving load on the dynamic magnification factor which is defined as the ratio of the maximum dynamic displacement at the corresponding node in the time history to the static displacement when the load is at the mid – point of the structure is investigated. The effect of the spring stiffness attached to the frame at the conjunction points of beam and columns are also evaluated. Computer codes written in Matlab are developed to calculate the dynamic responses. Dynamic responses of the engineering structures and critical load velocities can be found with high accuracy by using the finite element method
Applied Acoustics, 2011
A general algorithm for the free vibration analysis of stepped and tapered beam type structures with multiple elastic supports is developed in this work. The analytical formulation is based on the Ritz method and on the use of orthogonal polynomials within the framework of the first order shear deformation beam theory. To verify the validity and convergence of the general algorithm several numerical examples are analyzed. A further example concerned with the determination of the dynamical properties of a bell tower is also presented and compared with the finite element method and experimental results.
European Journal of Science and Technology, 2021
In the last few decades, many numerical methods have been developed and employed to solve for various types of linear and nonlinear equations due to challenges in the aspect of the implementation of governing equations and boundary conditions, computation time, algorithm complexity, accuracy, convergency, stability of the solution and so on. Of the numerical methods in the open literature, differential quadrature (DQM), differential transform (DTM), and finite difference (FDM) methods are expressed briefly with their algorithms and compared to each other for the modal analysis of beam and plate elements. For simplicity, shear strains effects are neglected for the chosen structural elements, and plate element is reduced to one-dimensional case up to chosen simply-supported boundary condition. Under these assumptions, computed non-dimensional natural frequencies by applying concerned methods are tabulated, and mode shapes are plotted. To understand the strength and accuracy of employed methods, numerical results in the high vibration modes are investigated, and it is seen that DTM gives faster and more accurate solutions while the results of DQM depend on chosen grid distribution and has less accurate than DTM. However, the ease of implementation and accurate results for multidimensional cases are pros properties of the DQM.
Dynamic Analysis of Mechanical Structures Using Plate Finite Element Method
IAEME PUBLICATION, 2015
The finite element method is used to solve problems by dividing the deformable body in a complicated assembling subdomain form or by constructing single elements and the approximate solutions in the form of a combination of shape functions and compact support. Our paper is mainly based on the application of this method on static and dynamic analysis of mechanical structures (beam, plate and shell). The excitation forces are based on periodic, random or impulsive ones. In our case, we present a numerical solution to describe the dynamic behavior of discrete structures which have applications of big importance in many sectors of the industry, such as the space or aerodynamic structures, mechanical constructions, robotics and civil engineering. Nowadays, this method is a powerful tool, available for reasonable costs with a reduced time of execution used for the analysis of these structures. In this work, we have developed FORTRAN language program, to calculate the displacements, reactions in nodes, the axial strengths in elements and the clean fashions of the structure. Examples of verification of our language have been made, under different loads and boundary conditions at static and dynamic cases. Good results have been obtained compared to those using "SAP 2000" and Robot 2009 software programs.
Dynamic analysis of modified structural systems
1986
A set of methods is developed to determine the changes in frequencies and mode shapes of a structure resulting from modifications of the structure. These modifications can involve an increase in the number of degrees of freedom of the system as well as changes in already existing entries in the mass and stiffness matrices of the model of the structure. Indeed, the modification may .consist entirely of a refinement of the structural model. In the procedures used, each mode and frequency is .treated separately without any. need to know the other modes and frequencies. An exception is the case of multiple or close frequencies, where the whole set of equal or close eigenvalues and their eigenvectors.must be treated together. Calculations are carried out by a perturbation analysis, which can be carried as far as desired in an automatic fashion. Repeated use of the same coefficient matrix in the perturbation scheme leads to considerable economy of computational effort. Light, tuned systems attached to a structure can be treated advantageously by the p~ocedur~ developed, as shown in examples.
Dynamics Analysis of a Truss System Modelled by the Finite Element Method in the Frequency Domain
2020
The dynamic analysis of a truss system modelled by the finite element method in the frequency domain is studied. The truss system is modelled by 22 elements and has 44 degrees of freedom. The stiffness matrix and mass matrix of the truss system are obtained by using the finite element method. Differential equations of the truss system are obtained by using the obtained stiffness and mass matrix. By applying the Laplace transformation, the displacements of each node are calculated, and the equation is arranged in the frequency domain. The obtained differential equations are solved by using MATLAB. Eigen values are calculated and represented depending on the frequencies. Thus, static displacements, dynamic displacements, static reaction forces and dynamic reaction forces for each frequency are graphically obtained. Additionally, dynamic amplification factors are calculated and simulated depending on the frequencies. Dynamic displacements increased near the eigenvalues, and the dynamic...
Finite element free and forced vibration analysis of gradient elastic beam structures
Acta Mechanica, 2018
The dynamic stiffness matrix of a gradient elastic flexural Bernoulli-Euler beam finite element is analytically constructed with the aid of the basic and governing equations of motion in the frequency domain. The simple gradient theory of elasticity is used with just one material constant (internal length) in addition to the classical moduli. The flexural element has one node at every end with three degrees of freedom per node, i.e., the displacement, the slope, and the curvature. Use of this dynamic stiffness matrix for a plane system of beams enables one by a finite element analysis to determine its dynamic response harmonically varying with time external load or the natural frequencies and modal shapes of that system. The response to transient loading is obtained with the aid of Laplace transform with respect to time. A stiffness matrix is constructed in the transformed domain, the problem is formulated and solved by the finite element method, and the time domain response is finally obtained by a time domain inversion of the transform solution. Because the exact solution of the governing equation of motion in the frequency domain is used as the displacement function, the resulting dynamic stiffness matrices and the obtained structural response or natural frequencies and modal shapes are also exact. Examples are presented to illustrate the method and demonstrate its advantages. The effects of the microstructure on the dynamic behavior of beam structures are also determined.