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Types of Models for Vibration Analysis,Models are developed to assist in the design and. understanding of system dynamics,Analytical models such as finite element models. are utilized in the design process,Experimental models are also used for many. systems where modeling is not practical or models,are too difficult to develop. 22 457 Mechanical Vibrations Chapter 10 2 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Finite Element Model Considerations.

Finite element models are commonly used,What are we trying to do when generating a model. CONTINUOUS DISCRETIZED,SOLUTION SOLUTION, 22 457 Mechanical Vibrations Chapter 10 3 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Finite Element Model Considerations. Modeling Issues, continuous solutions work well with structures that are well behaved. and have no geometry that is difficult to handle,most structures don t fit this simple requirement.

except for frisbees and cymbals, real structures have significant geometry variations that are. difficult to address for the applicable theory, a discretized model is needed in order to approximate the actual. the degree of discretization is dependent on the waveform of the. deformation in the structure,finite element modeling meets this need. 22 457 Mechanical Vibrations Chapter 10 4 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Finite Element Model Considerations. Finite element modeling involves the descretization of the structure. into elements or domains that are defined by nodes which describe. the elements, A field quantity such as displacement is approximated using polynomial.

interpolation over each of the domains, The best values of the field quantity at nodes results from a. minimization of the total energy, Since there are many nodes defining many elements a set of. simultaneous equations results, Typically this set of equations is very large and a computer is used to. generate results, 22 457 Mechanical Vibrations Chapter 10 5 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Finite Element Model Considerations.

Nodes represent geometric locations in the structure. Elements boundary are defined by the nodes, The type of displacement field that exists over the domain will. determine the type of element used to characterize the. Element characteristics are determined from,Theory of Elasticity. Strength of Materials, 22 457 Mechanical Vibrations Chapter 10 6 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Analytical Topics for Structural Dynamic Modeling. Structural element formulations use the same general. assumptions about their respective behavior as their respective. structural theories such as truss beam plate or shell. Continuum element formulations such as 2D and 3D solid. elements comes from theory of elasticity,12 6L 12 6L.

6L 4L2 6L 2L2,L 12 6L 12 6L,6L 2L2 6L 4L,156 22L 54 13L. E I 22L 4L2 13L 3L2,F i L Fj 420 54 13L 156 22L,13L 3L2 22L 4L2. 22 457 Mechanical Vibrations Chapter 10 7 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Analytical Topics for Structural Dynamic Modeling. The basis of the finite v,element method is,summarized below u. subdivide the structure into small finite elements. each element is defined by a finite number of node points. assemble all elements to form the entire structure. within each element a simple solution to governing equations. is formulated the solution for each element becomes a. function of unknown nodal values, general solution for all elements results in algebraic set of.

simultaneous equations, 22 457 Mechanical Vibrations Chapter 10 8 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Finite Element Model Considerations. DEGREES OF FREEDOM, maximum 6 dof can be described at a point in space. finite element use a maximum of 6 dof, most elements use less than 6 dof to describe the element. TRUSS TORSIONAL ROD,STRUCTURAL ELEMENTS,CONTINUUM ELEMENTS.

22 457 Mechanical Vibrations Chapter 10 9 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Finite Element Model Considerations. Advantages Disadvantages,Models used for design Modeling assumptions. development Joint design difficult to model,No prototypes are Component interactions are. necessary difficult to predict,Damping generally ignored. 22 457 Mechanical Vibrations Chapter 10 10 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Finite Element Model Considerations.

A TYPICAL FINITE ELEMENT USER MAY ASK,what kind of elements should be used. how many elements should I have, where can the mesh be coarse where must it be fine. what simplifying assumptions can I make, should all of the physical structural detail be included. can I use the same static model for dynamic analysis. how can I determine if my answers are accurate,how do I know if the software is used properly. 22 457 Mechanical Vibrations Chapter 10 11 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Finite Element Model Considerations.

ALL THESE QUESTIONS CAN BE ANSWERED IF, the general structural behavior is well understood. the elements available are understood,the software operation is understood. input procedures algorithms etc,BASICALLY we need to know what we are doing. IF A ROUGH BACK OF THE ENVELOP ANALYSIS,CAN NOT BE FORMULATED THEN. MOST LIKELY THE ANALYST DOES NOT KNOW,ENOUGH ABOUT THE PROBLEM AT HAND TO.

FORMULATE A FINITE ELEMENT MODEL, 22 457 Mechanical Vibrations Chapter 10 12 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Finite Element Modeling. Using standard finite element modeling techniques the following steps. are usually followed in the generation of an analytical model. node generation,element generation,coordinate transformations. assembly process,application of boundary conditions. model condensation,solution of equations,recovery process.

expansion of reduced model results, 22 457 Mechanical Vibrations Chapter 10 13 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Finite Element Modeling. Element Definition,Shape Functions,Each element is approximated by. vector of displacements in element,N shape function for selected element Quadratic. x nodal variable,Element shape functions can range from linear.

interpolation functions to higher order polynomial Polynomial. 22 457 Mechanical Vibrations Chapter 10 14 Dr Peter Avitabile. Modal Analysis Controls Laboratory,Finite Element Modeling. Strain Displacement Relationship,The strain displacement relationship is given by. vector of strain within element,B strain displacement matrix. proportional to derivatives of N,x nodal variable, 22 457 Mechanical Vibrations Chapter 10 15 Dr Peter Avitabile. 22 457 Mechanical Vibrations Chapter 10 Finite element modeling involves the descretization of the structure into elements or domains that are defined by nodes which describe the elements A field quantity such as displacement is approximated using polynomial interpolation over each of the domains The best values of the field quantity at

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