Finite element prediction of damping in structures with. Nasa contractor report 363 5 improved finite element methodology for integrated thermal structural analysis pramote dechaumphai and earl a. Figure 520 mesh of damping matrix found using iterative method of identification with. Since the craigbampton method will require the use of boundary and interior points, it is convenient to partition these matrices into fixed, interfaced or supported boundary nodes, r. This paper presents an efficient finite element method fem for computing the modal damping of laminated composites using the general purpose finite element software.
Thus, extract the sparsity pattern of the damping matrix constructed at an arbitrary point in time but that has its timedependent coefficients active. The identification is done by performing finite element fe model updating using normal frequency response functions frfs. Programming the transient explicit finite element analysis with matlab andrei dragos mircea sirbu1, laszlo farkas2 modern research in automotive crashworthiness relies extensively on explicit finite element analysis. This is normally done by identifying the modal properties of a structure from test data, and then comparing them with the modal properties of the finite element model. Linear finite element methods the nite element methods provide spaces vnof functions that are piecewise smooth and \simple, and locally supported basis function of these spaces to achieve good approximations of the solution u2v, an e cient assembly of the system matrix with desirable properties e.
In using the finite element method for modeling of beam vibrations, the question arises. The field is the domain of interest and most often represents a. In numerical analysis, generally, the damping matrix c cannot be constructed from elementdamping matrices, such as the mass and stiffness matrices of the element assemblage. The identification is done by performing finite element fe model updating. Improved finite element methodology for integrated thermal structural analysis.
You need to create a damping matrix sparsity pattern that is valid throughout the entire integration time. In this topic, we will demonstrate the finite element method fem as a typical powerful approach which can handle vibration analysis. Pilkey abstract the characterization of damping is important in making accurate predictions of both the. P engineering college visakhapatnam, india, 530003. The applied forces are contained in the matrix fa the resulting undamped equation of motion for the free unconstrained. Unlike local damping models the internal force of the nonlocal model is. Structural element stiffness, mass, and damping matrices. Accurate modeling of damping is essential for prediction of vibration response of a structure. The inherent damping matrix is usually defined by two general approaches. Theory, implementation, and practice november 9, 2010 springer. Stiffness matrix, complex stiffness matrix, mass matrix.
Pappa nasa langley research center hampton, virginia summary structural materials in the form of graphite epoxy composites with embedded rubber layers are being used to reduce vibrations in rocket motor tubes. A gradient based finite element model updating algorithm implementing inverse eigensensitivity method has been presented through a series of. Alternately, a procedure is based on knowledge of the mass and stiffness matrices and the eigendata. Finitestrain approximations and their associated errors. Nelson and mcvaugh 3, and nelson 4 applied the theory of timoshenkos beam to build matrix of systems in order to analyze the rotor moments, rotational inertia, axial load, and shear deformation. It extends the classical finite element method by enriching the solution space for solutions to differential equations with discontinuous functions. Basic concepts the finite element method fem, or finite element analysis fea, is based on the idea of building a complicated object with simple blocks, or, dividing a complicated object into small and manageable pieces. Also the vibrational characteristics of composite sandwich shaft disc system are compared for better damping capabilities. The finite element method is used to obtain the mass and stiffness matrices for each system, and the damping matrix is fitted to a measured variation of the damping modal damping factors with. Model updating is becoming a common method to improve the correlation between finite element models and measured data. Finite element programmingwolfram language documentation.
Computation of a damping matrix for finite element model updating. Daryl logan, a first course in finite element method, thomson, india edition. Algorithm of drm with kinetic damping for finite element. The finite element method, as implemented in ndsolve, has been optimized for speed. An assembly of elementlevel equations is subsequently solved, in order to establish the response of the complete domain to a particular set of boundary conditions. Finite element vibration analysis and modal testing of graphite epoxy tubes and correlation between the data b. Fe finite element fem finite element model mac modal assurance criterion cmp correlated mode pair comac coordinate modal assurance criterion frac frequency response assurance criterion symbols magnitude 2 p2 euclidean norm. Modal analysis of damped rotor using finite element method p.
Finite element methods pdf notes fem pdf notes smartzworld. Vibration and damping analysis of orthotropic sandwich. Introduction to the finite element method fem lecture 1 the. The finite element method fem, or finite element analysis fea, is a computational technique used to obtain approximate solutions of boundary value problems in engineering. This chapter describes the use of the finite element method for solving timeharmonic acoustic problems. The direct stiffness method and the stiffness matrix. Thornton old dominion university research foundation. Computation of a damping matrix for finite element model updating deborah f.
Finite element vibration analysis of damped structures. Dynamic analysis of a spindlebearing system based on. Nasa contractor report 3 63 5 improved finite element methodology for integrated thermal structural analysis pramote dechaumphai and earl a. A new algorithm which estimates the mass, stiffness, and damping matrices of a structure from frequency response function frf measurements is also presented. Finite element damping matrix elasticity matrix modulus of. Modeling of damping in the finite element method institute. Finiteelement vibration analysis and modal testing of. Damped vibration analysis using finite element method with approximated modal damping for automotive double walls with a porous material journal of sound and vibration, vol. An efficient finite element method for computing modal. Finite element analysis of solids fluids i fall analysis solution. Finite element analysis fea, damping, modal analysis. This is a very brief introduction to some of the concepts involved in. The procedures for damping identification presented herein are based on prior knowledge of the finite element or analytical mass matrices and measured.
Finite element technique is employed to evaluate the natural frequency and damping loss factor for various combinations. Computation of a damping matrix for finite element model. The updated results have shown that the proposed damped element model updating method can be used to derive accurate models for nonviscous and nonproportional damped systems. For numerical simulations of the dynamical behavior of structures the finite element method fem has established itself as a powerful tool. The field is the domain of interest and most often represents a physical structure.
Pe281 finite element method course notes summarized by tara laforce stanford, ca 23rd may 2006 1 derivation of the method in order to derive the fundamental concepts of fem we will start by looking. All aspects of the damping identification procedure are investigated. In order to deal with the divergence and instability due to the illposedness of the nonlinear finite element fe model of strainsoftening structure in implicit static analysis, the dynamic relaxation method drm was used with kinetic damping to solve the static increments in the incremental solution procedure so that the problem becomes wellposed. The finite element method introduction finite element methods are now widely used to solve structural. An assembly of element level equations is subsequently solved, in order to establish the response of the complete domain to a particular set of boundary conditions. The extended finite element method xfem is a numerical technique based on the generalized finite element method gfem and the partition of unity method pum. Pilkey dissertation submitted to the faculty of the virginia polytechnic institute and state university. These matrix estimates are compared to the matrices of an analytical model of the same structure, and the differences are noted. Computation of a damping matrix for finite element model updating by deborah f. Abstractin this paper, the smoothe d finite element method sfem is proposed for 2d elastic problems by incorporation of the cellwise strain smoothing operation into the conventional finite elements. Vibration analysis by finite element method request pdf. Solution of finite element equilibrium equations in dynamic analysis modeling of a structural vibration problem 1 identify the frequencies con tained in the loading, using a fourier analysis if necessary. The method is based on an extended elasticviscoelastic correspondence principle, which accounts for the frequency dependence of viscoelastic complex stiffness matrices. Introduction to the finite element method fem lecture 1.
Identification of nonproportional viscous damping matrix. Modal analysis of damped rotor using finite element method. The direct updating of damping and stiffness matrices citeseerx. Damping measurement in composite materials using combined. This paper attempts to study the influence of internal material damping on the modal behaviour of a rotor shaft system. Finiteelement vibration analysis and modal testing of graphite epoxy tubes and correlation between the data. A gradient based finite element model updating algorithm implementing inverse eigensensitivity method has been presented through a series of numerically simulated cantilever beams. Crash analysts require deep understanding of finite element method and explicit time integration routines. Damping estimation in thin walled structures using finite. The procedures for damping identification presented herein are based on prior knowledge of the finite element or analytical mass matrices and measured eigendata. Modal testing has traditionally been used to confirm the validity of finite element models of structures.
Various thin walled structures are taken and the damping values are calculated. In this topic, we will demonstrate the finite element method fem as a typical powerful approach which can handle vibration. By using this matrix, you can solve a model with rayleigh damping. Structural dynamics department of civil and environmental engineering duke university henri p. Improved finite element methodology for integrated thermal. Damping matrix identification by finite element model updating. It extends the classical finite element method by enriching the solution space for solutions to differential equations with. Nonlocal finite element analysis of damped beams article pdf available in international journal of solids and structures 4422. Taylor, the finite element method, vols 1 and 2, butterworth heinemann, 2000 klausjurgen bathe, finite element procedures part 12, prentice hall, 1995. The finite element methods notes pdf fem notes pdf book starts with the topics covering introduction to finite element method, element shapes, finite element analysis pea, fea beam elements, fea two dimessional problem, lagrangian serenalipity elements, isoparametric formulation, numerical integration, etc. Figure 54 plot of damping matrix found using the iterative method with 40 dof and. Identification of nonproportional viscous damping matrix of beams.
Displacement interpolation matrix strain inside the element m. Damping matrix identification by finite element model. Even though the mass and the stiffness distribution of a structure can be modeled within the fem quite precisely, there is still a lack of suitable damping models. The objective of this work is to find a robust, practical procedure to identify damping matrices. The effectiveness of the proposed damped finite element updating method is demonstrated by numerical examples and by actual laboratory experiments. If c is diagonal as well, the method still works in the same way. The mass matrix m is nonzero when the model is timedependent. In numerical analysis, generally, the damping matrix c cannot be constructed from element damping matrices, such as the mass and stiffness matrices of the element assemblage. To initialize the finite element method data, which is needed in subsequent discretization steps, initializepdemethoddata is used.
Boundary value problems are also called field problems. Index terms finite element method fem, gauss quadrature, isoparametric element, smoothed finite element method sfem, strain smoothing. In the notation of 4s the incremental finite element equations that govern the response of the finite element system in static analysis are where k tangent stiffness matrix corresponding to the configuration of the system at time t. Pdf nonlocal finite element analysis of damped beams. Currently, the only discretization method available in this framework is the finite element method. Mass, stiffness, and damping matrix technical papers. Roy1 1department of mechanical engineering national institute of technology, rourkela769008, orissa, india abstract. This paper presents a study of damping matrix identification method using experimental data. Introduction to finite element analysis fea or finite.
Some practical procedures for the solution klaus jiirgen. Besides the loss of energy in the material itself especially the join patches contribute to the energy dissipation. Note that k only appears in the righthand side of the equation. The use of the finite element method for acoustics was initiated by 2. Mass, stiffness, and damping matrix estimates from structural measurements. Gavin fall 2018 1 preliminaries this document describes the formulation of sti. The method can accurately predict the nonproportional damping matrix even if the measured eigenvectors are polluted with random noise. Vibrating mechanical systems assembled from metallic components dissipate energy due to damping. Altering the method to deliver a diagonal lumped geometric stiffness matrix simplifies the process of solving the eigenvalue problem and results in computational savings. Finite element analysis of solids fluids i fall analysis. May 17, 2012 damped vibration analysis using finite element method with approximated modal damping for automotive double walls with a porous material journal of sound and vibration, vol. Identification of nonproportional viscous damping matrix of.
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