Vibro-acoustical analysis and design of a multiple-layer constrained viscoelastic damping structure

The goal of this research is to provide a framework for vibro-acoustical analysis and design of a multiple-layer constrained damping structure. The existing research on damping and viscoelastic damping mechanism is limited to the following four mainstream approaches: modeling techniques of damping treatments/materials; control through the electrical-mechanical effect using the piezoelectric layer; optimization by adjusting the parameters of the structure to meet the design requirements; and identification of the damping material’s properties through the response of the structure. This research proposes a systematic design methodology for the multiple-layer constrained damping beam giving consideration to vibro-acoustics. A modeling technique to study the vibro-acoustics of multiple-layered viscoelastic laminated beams using the Biot damping model is presented using a hybrid numerical model. The boundary element method (BEM) is used to model the acoustical cavity whereas the Finite Element Method (FEM) is the basis for vibration analysis of the multiple-layered beam structure. Through the proposed procedure, the analysis can easily be extended to other complex geometry with arbitrary boundary conditions. The nonlinear behavior of viscoelastic damping materials is represented by the Biot damping model taking into account the effects of frequency, temperature and different damping materials for individual layers. A curve-fitting procedure used to obtain the Biot constants for different damping materials for each temperature is explained. The results from structural vibration analysis for selected beams agree with published closed-form results and results for the radiated noise for a sample beam structure obtained using a commercial BEM software is compared with the acoustical results of the same beam with using the Biot damping model. The extension of the Biot damping model is demonstrated to study MDOF (Multiple Degrees of Freedom) dynamics equations of a discrete system in order to introduce different types of viscoelastic damping materials. The mechanical properties of viscoelastic damping materials such as shear modulus and loss factor change with respect to different ambient temperatures and frequencies. The application of multiple-layer treatment increases the damping characteristic of the structure significantly and thus helps to attenuate the vibration and noise for a broad range of frequency and temperature. The main contributions of this dissertation include the following three major tasks: 1) Study of the viscoelastic damping mechanism and the dynamics equation of a multilayer damped system incorporating the Biot damping model. 2) Building the Finite Element Method (FEM) model of the multiple-layer constrained viscoelastic damping beam and conducting the vibration analysis. 3) Extending the vibration problem to the Boundary Element Method (BEM) based acoustical problem and comparing the results with commercial simulation software

Vibration control of beams and plates with hybrid active-passive constrained layer damping treatments

The concept of hybrid active-passive constrained layer damping treatments, which consists of viscoelastic materials, piezoelectric materials and elastic constraining materials, was proposed in the 1990s in order to ameliorate problems of instability in traditional active control systems in the higher frequency range. In this paper, the performances of four types of hybrid active-passive constrained layer damping treatments are investigated for beam and plate applications. These types are Active Constrained Layer Damping (ACLD), Active-Passive Constrained Layer Damping (APCLD), Active Control/Passive Constrained Layer Damping (AC/PCLD) and Active Control/Passive Stand-Off Layer Damping (AC/PSOLD). The performances of each treatment are compared through simulation with numerical models using the Finite Element Method. Finally, control performances of all configurations for curved plates are discussed with measured Frequency Response Functions of each case

Finite element modeling of viscoelastic core sandwich panels

Thin layers of viscoelastic materials are often used in the core of sandwich plates orin surface constrained damping treatments as an effective way to reduce dynamic responseof light structures. However the usual approach to model these structures, using a layeredscheme of plate and brick finite elements, demands a cumbersome spatial modelling task.In this work a layerwise-based facet-shell finite element model is proposed which is ableto describe accurately the stiffness, damping and mass of the composite plate. Some fi-nite element remedies are applied in the finite element formulation in order to improve itsmembrane formulation, avoid shear locking and introduce the drilling degrees of freedom.Experimental results obtained on several sandwich plates with viscoelastic layers are usedto validate the applicability of the proposed model for the simulation of sandwich plateswith a single or multiple viscoelastic cores

Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme

A Newmark-diffusive scheme is presented for the time-domain solution of dynamic systems containing fractional derivatives. This scheme combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for example after finite element discretization), with a diffusive representation based on the transformation of the fractional operator into a diagonal system of linear differential equations, which can be seen as internal memory variables. The focus is given on the algorithm implementation into a finite element framework, the strategies for choosing diffusive parameters, and applications to beam structures with a fractional Zener model

Complex Eigenvalue Analysis for Structures with Viscoelastic Behavior

This document deals with a method for eigenvalue extraction for the analysis of structures with viscoelastic materials. A generalized Maxwell model is used to model linear viscoelasticity. Such kind of model necessitates a state-space formulation to perform eigenvalue analysis with standard solvers. This formulation is very close to ADF formulation. The use of several materials on the same structure and during the same analysis may lead to a large number of internal states. This article purpose is to identify simultaneously all the viscoelastic materials and to constrain them to have the same time-constants. As it is usually possible, the size of the state-space problem is therefore widely reduced. Moreover, an accurate method for reducing mass and stiffness operators is proposed; The enhancement of the modal basis allows to obtain good results with large reduction. As the length of the paper is limited, only theoretical development are presented in the present paper while numerical results will be presented in the conference.Comment: ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2011), Washington : France (2011

Visco-hyperelastic model with damage for simulating cyclic thermoplastic elastomers behavior applied to an industrial component

In this work a nonlinear phenomenological visco-hyperelastic model including damage consideration is developed to simulate the behavior of Santoprene 101-73 material. This type of elastomeric material is widely used in the automotive and aeronautic sectors, as it has multiple advantages. However, there are still challenges in properly analyzing the mechanical phenomena that these materials exhibit. To simulate this kind of material a lot of theories have been exposed, but none of them have been endorsed unanimously. In this paper, a new model is presented based on the literature, and on experimental data. The test samples were extracted from an air intake duct component of an automotive engine. Inelastic phenomena such as hyperelasticity, viscoelasticity and damage are considered singularly in this model, thus modifying and improving some relevant models found in the literature. Optimization algorithms were used to find out the model parameter values that lead to the best fit of the experimental curves from the tests. An adequate fitting was obtained for the experimental results of a cyclic uniaxial loading of Santoprene 101-73

Exact 3D solution for static and damped harmonic response of simply supported general laminates

The state-space method is adapted to obtain three dimensional exact solutions for the static and damped dynamic behaviors of simply supported general laminates. The state-space method is written in a general form that permits to handle both cross-ply and antisymmetric angle-ply laminates. This general form also permits to obtain exact solutions for general laminates, albeit with some constraints. For the general case and for the static behavior, either an additive term is added to the load to simulate simply supported boundary conditions, or the plate bends in a particular way. For the dynamic behavior, the general case leads to pairs of natural frequencies for each order, with associated mode shapes. Finite element simulations have been performed to validate most of the results presented in this study. As the boundary conditions needed for the general case are not so straightforward, a specific discussion has been added. It is shown that these boundary conditions also work for the two aforementioned laminate classes. The damped harmonic response of a non symmetrical isotropic sandwich is studied for different frequencies around the fundamental frequency. The static and undamped dynamic behaviors of the [-15/15], [0/30/0] and [-10/0/40] laminates are studied for various length-to-thickness ratios

Integrating damping and non-linearities in a vibration design process

Classical vibration design uses modes and transfer functions generated with the superposition principle to allow the verification of design objectives. If redesign is needed, one optimizes mass and stiffness in order to modify the transfer until the specification is met. Integrating damping and non-linearities in the optimization of detailed industrial models is however still considered a major difficulty, even though the physical mechanisms are well known. Approaches to handle viscoelastic damping and time domain modal damping are thus discussed. Distributed non-linearities, such as contact and friction, are becoming accessible to transient simulation, but lead to responses where modes are no longer defined. It is however illustrated that operational deflection shapes, associated with a singular value decomposition of the response, give similar information. Finally, a fundamental aspect of non-linear vibration simulation is the volume of output and the associated numerical cost. Model reduction is a key ingredient of practical approaches and a perspective on related issues is given