The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions
TL;DR: In this article, the transverse displacement of a three-layer sandwich beam with a viscoelastic core is derived in terms of the transversal displacement, w, for a 3D beam.
About: This article is published in Journal of Sound and Vibration.The article was published on 1969-09-01. It has received 785 citations till now. The article focuses on the topics: Boundary value problem & Beam (structure).
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TL;DR: In this article, the authors used fractional calculus to model the viscoelastic behavior of a damping layer in a simply supported beam and analyzed the beam by using both a continuum formulation and a finite element formulation to predict the transient response to a step loading.
Abstract: Fractional calculus is used to model the viscoelastic behavior of a damping layer in a simply supported beam. The beam is analyzed by using both a continuum formulation and a finite element formulation to predict the transient response to a step loading. The construction of the finite element equations of motion and the resulting nontraditional orthogonality conditions for the damped mode shapes are presented. Also presented are the modified forms of matrix iteration required to calculate eigenvalues and mode shapes for the damped structure. The continuum formulation, also incorporating the fractional calculus model, is used to verify the finite element approach. The location of the poles (damping and frequency) are found to be in satisfactory agreement, as are the modal amplitudes for the first several modes.
592 citations
TL;DR: In this article, a complete set of equations of motion and boundary conditions governing the vibration of sandwich beams are derived by using the energy approach, and they are solved exactly for important boundary conditions.
Abstract: A complete set of equations of motion and boundary conditions governing the vibration of sandwich beams are derived by using the energy approach. They are solved exactly for important boundary conditions. The computational difficulties that were encountered in previous attempts at the exact solution of these equations have been overcome by careful programming. These exact results are presented in the form of design graphs and formulae, and their usage is illustrated by examples.
326 citations
TL;DR: In this article, a review of the available literature on damping in composite materials is presented, where a chronological review of test methods for damping estimation is presented in order to describe the time-line of theoretical knowledge development in this field.
Abstract: The present review aims at gathering the available literature on damping in composite materials. A chronological review of test methods for damping estimation is presented in order to describe the time-line of the theoretical knowledge development in this field. In the last years many new material configurations have emerged that deserve investigation, such as nano-composites, hybrid laminates and sandwich materials. Damping models specifically meant for non-homogeneous materials are reported to provide a background for understanding this problem. Although not widely exploited yet, fibre reinforced polymers has the potential to be tailored for damping by acting on constituents, geometry and boundary conditions. Nano-composites, for instance, are shown to possess a high potential for damping purposes. New hybrid and sandwich-type structures are emerging as noise and vibration control solutions in lightweight applications. The effort devoted to mathematical and numerical model in view of Finite Element integration of damping properties is also addressed. Finally, the conclusions summarise the ideas of the authors on needed steps to advance the state-of-the-art in each of the described topic.
240 citations
TL;DR: A comprehensive review of the various research methods and theory calculation models that are employed in engineering to study the static and dynamic vibration characteristics of viscoelastic damping material (VDM) formed structures is presented in this article.
204 citations
TL;DR: In this article, an attempt has been made to analyze and assess the various kinematics and theories used for the modeling of sandwich composites and a unified kinematic formulation is then proposed.
196 citations
References
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TL;DR: In this article, a quantitative analysis of the damping effectiveness of a constrained layer of damping tape is presented, where the loss factor η is defined as the normalized imaginary part of the complex bending stiffness of the damped plate.
Abstract: For a number of years it has been known that flexural vibrations in a plate can be damped by the application of a layer of damping (viscoelastic) material that is in turn constrained by a backing layer or foil. A common example is the damping tape currently used in aircraft.This paper presents a quantitative analysis of the damping effectiveness of such a constrained layer. As in the work of H. Oberst the damping is characterized by the loss factor η, which is the normalized imaginary part of the complex bending stiffness of the damped plate.The calculated damping factor depends on the wavelength of bending waves in the damped plate, and on the thicknesses and elastic moduli of the plate, the damping layer, and the constraining layer. A complex shear modulus is assigned to the damping layer, where all of the energy dissipation is assumed to take place.Damping factors have been determined experimentally on laboratory test bars for a number of constrained‐damping‐layer applications for frequencies from abou...
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01 Jan 1961
TL;DR: In this paper, a method is presented for the determination of the frequency response functions of the components of deformation and stress in orthotropic sandwich plates, and the analysis takes into account the transverse shear deformation of the core and the material damping of core and facings.
Abstract: : A method is presented for the determination of the frequency response functions of the components of deformation and of stress in orthotropic sandwich plates It applies to the case of simply supported rectangular plates loaded by dynamic pressure normal to their planes A similar method is presented for orthotropic sandwich cylindrical shells The boundaries of the shell are assumed as simply supported, and the dynamic pressure is normal to the middle surface In both problems, the analysis takes into account the transverse shear deformation of the core and the material damping of core and facings The results are presented in the form of expressions suitable for numerical evaluation (Author)
8 citations