Mohan D. Rao

Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes

In this paper, the application of passive damping technology using viscoelastic materials to control noise and vibration in vehicles and commercial airplanes is described. Special damped laminates and spray paints suitable for mass production and capable of forming with conventional techniques are now manufactured in a continuous manner using advanced processes. These are widely used in the automotive and aerospace industry in a variety of applications to reduce noise and vibration and to improve interior sound quality. Many of these recent applications are not readily available for dissemination in academe and archival literature. It is hoped that the material presented in this paper will be useful for instruction and further research in developing new and innovative applications in other industries.

Dynamic Analysis and Design of Laminated Composite Beams with Multiple Damping Layers

This paper describes the formulation of a theory for the prediction of damping and natural frequencies of laminated composite beams with multiple viscoelastic damping layers. The damping layers are constrained (or sandwiched) by anisotropic laminates. The in-plane shear strains of the damping layers and the constraining layers are included in the model. Closed-form solutions for the resonance frequencies and modal loss factors of the composite beam system under simple supports are derived using the energy and Ritz method. A parametric study has been conducted to study the variation of dynamic stiffness and modal loss factor of the system with structural parameters (e.g., the ply orientations of laminas, thickness of the damping layers and the laminates), operating temperature, and damping material properties. The design of composite beams for maximizing the damping capacity is also presented in this paper which includes the determination of operating temperature range corresponding to given structural parameters and finding optimal structural parameters corresponding to given temperature range. Finally, some experimental results are compared with theory for the cases of single and double damping layer beam systems that show good agreement between predicted and measured natural frequencies.

Dynamic analysis and damping of composite structures embedded with viscoelastic layers

Abstract In recent years, it has been found that composites co-cured with viscoelastic materials can enhance the damping capacity of a composite structural system with little reduction in stiffness and strength. Because of the anisotropy of the constraining layers, the damping mechanism of co-cured composites is quite different from that of conventional structures with metal constraining layers. This paper presents an analysis of the dynamic properties of multiple damping layer, laminated composite beams with anisotropic stiffness layers, by means of the finite element-based modal strain energy method. ANSYS 4.4A finite element software has been used for this study. The variation of resonance frequencies and modal loss factors of various beam samples with temperature is studied. Some of these results are compared with the closed-form theoretical results of an earlier published work. For obtaining optimium dynamic properties, the effects of different parameters, such as layer orientation angle and compliant layering, are studied. Also, the effect of using a combination of different damping materials in the system for obtaining stable damping properties over a wide temperature range is studied.

Vibration analysis of adhesively bonded lap joint, part I: Theory

Abstract An analytical model to study the coupled transverse and longitudinal vibration of a bonded lap joint system is described in this paper. The system consists of a pair of parallel and identical beams which are lap-jointed over a certain length by a viscoelastic material. The unjointed ends of the beams are assumed to be simply supported. The governing equations of motion for the forced vibration of the system under transverse distributed loads are derived using the energy method and Hamiltons principle. Both shear and thickness deformation in the adhesive layer is included in the analysis. The theoretical development of the model is presented in this paper. The numerical solutions of the governing equations for free vibration along with boundary and continuity conditions yield the system natural frequencies, loss factors and mode shapes. The details of the numerical solution scheme and results for free vibration are included in the accompanying paper.

Vibration analysis of adhesively bonded lap joint, part II: Numerical solution

Abstract This paper is the second of two papers dealing with dynamic modeling of a bonded lap joint system. The theoretical development of the model to study the coupled transverse and longitudinal vibration of a bonded joint system was described in Part I. The numerical solution of the equations of motion along with boundary and continuity conditions as derived in Part I yields the system resonance frequencies, modal loss factors and mode shapes. The details of the numerical solution scheme along with a discussion of results are presented in this paper.

Estimation of frequency-averaged loss factors by the power injection and the impulse response decay methods

This paper describes a comparison, both analytically and experimentally, between two widely used loss factor estimation techniques frequently used in statistical energy analysis. Analytical models of simple spring/mass/damper systems were created to compare frequency-averaged loss factor values from the single subsystem power injection method and the impulse response decay method. The parameters of the analytical models were varied to study the effects of the total number of modes, amount of damping, location of modes within frequency bands, and the width of the frequency bands on loss factor estimation. The analytical study shows that both methods give accurate loss factor values as long as the damping values remain realistic for linear systems and at least one modal resonance is present in each frequency band. These analytical results were verified experimentally by measuring the loss factors of simple steel plates, with and without damping treatments applied.

Dynamic testing of shock absorbers under non-sinusoidal conditions

Abstract This paper deals with the dynamic characterization of an automotive shock absorber, the continuation of an earlier work [1]. The objective of this ongoing research is to develop a testing and analysis methodology for obtaining dynamic properties of automotive shock absorbers for use in CAE-NVH low-to-mid-frequency chassis models. Stepped sine sweep excitation is currently used in industry to obtain shock absorber parameters along with their frequency and amplitude dependence. Sine-on-sine testing, which involves excitation using two different sine waves, has been done in this study to understand the effects of the presence of multiple sine waves on the estimated dynamic properties. In an effort to obtain all frequency dependent parameters simultaneously, different types of broadband random excitation have also been studied. Results are compared with stepped sine sweep tests. Additionally, actual road data measured on different road profiles have been used as input excitation to obtain the shock absorber parameters for broad frequency bands under realistic amplitude and frequency conditions. These results are compared with both simulated random excitation and stepped sine sweep test results.

Prediction of loss factors of curved sandwich beams

Abstract In this paper an analytical model for the coupled flexural and longitudinal vibration of a curved sandwich beam system is described. The system consists of a primary beam and a constraining beam with a viscoelastic damping material forming the core. The governing equations of motion for the forced vibration of the system are derived using the energy method and Hamiltons principle. Both shear and thickness deformation in the adhesive layer are included in the analysis. A matrix equation for solving the system resonance frequencies and loss factors is obtained by using the Rayleigh-Ritz method. A parametric study has been conducted to evaluate the effects of curvature, core thickness and adhesive shear modulus on the system resonance frequencies and loss factors. The implications of this parametric study on the damping effectiveness of the system along with some design guidelines are presented in the paper.

The effects of different input excitation on the dynamic characterization of an automotive shock absorber

This paper deals with the dynamic characterization of an automotive shock absorber, a continuation of an earlier work [1]. The objective of this on-going research is to develop a testing and analysis methodology for obtaining dynamic properties of automotive shock absorbers for use in CAE-NVH low-to-mid frequency chassis models. First, the effects of temperature and nominal length on the stiffness and damping of the shock absorber are studied and their importance in the development of a standard test method discussed. The effects of different types of input excitation on the dynamic properties of the shock absorber are then examined. Stepped sine sweep excitation is currently used in industry to obtain shock absorber parameters along with their frequency and amplitude dependence. Sine-on-sine testing, which involves excitation using two different sine waves has been done in this study to understand the effects of the presence of multiple sine waves on the estimated dynamic properties. In an effort to obtain all frequency dependent parameters simultaneously, different types of broadband random excitations have been studied. Results are compared with stepped sine sweep tests. Additionally, actual road data measured on different road profiles has been used as input excitation to obtain the shock absorber parameters for broad frequency bands under realistic amplitude and frequency conditions. These results are compared with both simulated random excitation and stepped sine sweep test results. INTRODUCTION The shock absorber is one of the most important elements in a vehicle suspension system. It is also one the most non-linear and complex elements to model. The current method of characterizing the dynamic properties of shock absorbers for CAE models involves testing at discrete frequencies, displacements, and preloads using an MTS test machine. The dynamic stiffness (K) and damping (C) are extracted by fitting a linear model of the form F(ω)=K*x(ω)+C*v(ω) to the measured input displacement (x), velocity (v), and output force (F). The excitation technique is a pure sine excitation at the desired frequency and amplitude. These harmonic excitations are then swept through all desired frequency and amplitudes. Parametric and non-parametric models also exist for the shock absorber. A non-parametric model based on a restoring force surface mapping has been developed [2,3,4]. The model considers the force to be a function of displacement and velocity. Although, this model is more applicable to a single frequency excitation, it serves as a useful tool for identifying the non-linearity’s in the system. A comprehensive physical model was developed by Lang [5], later condensed and validated by Morman [6]. Lang’s model has more than 80 parameters, is computationally complex and is not suitable for comprehensive vehicle simulation studies. Morman’s model has been shown to be useful for studying the effects of design changes for a particular shock. Reybrouck [7] has developed a physical model, which has 14 parameters, valid for frequencies up to 20 Hz, but has limited appeal for the analysis of shock absorbers for NVH applications.

Viscoelastic analysis of bonded tubular joints under torsion

Abstract In this paper, a theoretical analysis to evaluate the stress field in the adhesive layers of tubular bonded joints subjected to torsional loading is presented. The formulation is suitable to study the static behavior of the joint under general loading conditions as well as steady-state behavior under cyclic loading conditions. The adhesive material is modeled using linear viscoelasticity and numerical results for the shear stresses in the adhesives, joint compliance and joint loss factor are presented for various cases that provide some insights and guidelines in the design of the joint.