Prediction and measurement of modal damping factors for viscoelasticspace structures

Abstract

The procedure outlined in this paper extends the finite element method to viscoelastic space structures; predictions of mode shapes, frequencies, and damping factors can be made based on a new modeling approach that uses specific measured material data. Briefly, the procedure is as follows: 1) the modulus function of the material is measured from free-decay tests of a uniform cantilever beam of the subject material, and 2) these material data are then inserted into the new damped-structure modeling technique. These two steps are illustrated and validated using a strawman space structure fabricated entirely from a single epoxy material. Predicted damping characteristics based on material data and the new modeling technique are compared with modal data obtained for the test structure. Using commercially available software, the modal test data are processed to obtain mode shapes, frequencies, and damping factors. A comparison between predicted eigenvalues and experimentally determined modal frequencies and damping factors indicates that the proposed new technique is a valuable tool in structural analysis.

Smoothing, Interpolating, and Modeling Complex Modulus Data for Viscoelastic Damping Materials, Including a New Approach to Temperature Shift Functions

“…( )Csmall ; /2 ≈ πβ η tan max (23) is of interest and the expression for the exponent (24) in terms of the other parameters in E21 is useful. Another useful relationship is that maximum loss factor occurs at a reduced radian frequency of…”

“…Note that Equation 53 may be placed in GHM form [23,24]; consider two terms, without loss of generality, from Equation 53:…”

Numerical Formulation in Finite Elements of Damping in Composites Materials Using First-Order Shear Deformation Theory

“…After, Lagrange's equations are used, considering the nodal displacements and rotations as generalized coordinates, to obtain the following elementary mass and stiffness matrices, respectively: In equations (7)(8)(9)   C represent, respectively, the orthotropic bending and shear elastic matrices of the kth layer, which are constructed according to the Classical Laminate Theory (CLT) as follows: From the elementary matrices computed for each element of the finite element mesh, the global equations of motion are constructed, accounting for the node connectivity, using standard finite element assembling procedures (Huebner et al, 1982). After assembling, the global equations of motion in the time domain can be written as follows: …”

“…Moreover, the levels of noise and vibration they are subjected passengers of vehiclesis an importante aspectin evaluating the quality of products, and there for impact with respectto their market competitiveness. Among the various techniques for vibration control which have been devised, the socalled passive techniques have been incorporated in many industrial systems as they present a number of advantages as compared to active strategies such as cost effectiveness, broadband operational effectiveness and inherent stability (Nayak et al (2005); Rikards et al 1995;McTavish et al, 1992). For the purposes of this paper, the First-order Shear Deformation Theory -FSDT is retained and the viscoelastic damping is represented by the complex modulus approach associated with the concept of shift factor and reduced frequency according to the frequency-temperature superposition principle (Lima et al, 2009) The mathematical modeling has been implemented by using the commercial available software MATLAB®.…”

Stochastic Modeling of Surface Viscoelastic Treatments Combined with Model Condensation Procedures

“…In the context of passive control of mechanical vibrations, much effort has been devoted to the development of finite element models capable of accounting for the typical dependence of the viscoelastic behavior with respect to frequency and temperature [1][2][3][4][5]. A natural extension of the deterministic modeling capability is to account for the uncertainties in the design variables aiming at evaluating the influence of the variability on the model predictions [6][7][8][9].…”