Three-layered Sandwich Beam Research Articles

Application of decision support system on sandwich beams, verified by experiments

Experiments were made using the Brüel-Kjaer measuring devices in order to determine the static and dynamic behaviour of three-layered sandwich beams with outer layers of box-section. The good agreement between the measured values and the results of static and dynamic analysis gives the possibility to work out an economic design of such structures using an interactive Decision Support System (DSS). The DSS computer code contains six various single-criterion and seven multicriteria optimization methods. The economic design was realized considering four objective functions and fourteen nonlinear inequality constraints.

Determination of constants of a visco-elastic model of a binding agent.

A method for determining the constants of a three-element visco-elastic model of a binding agent is shown The frequency equation of a three-layer sandwich beam with a visco-elastic binding agent core is derived under the boundary condition of both ends free, and the damped free vibration frequency and time constant are measured experimentally, and these values are substituted into the frequency equation, resulting in the function of visco-elastic constants. Then, regarding the absolute value of the frequency equation as the estimation function to become zero, and considering visco-elastic constants as control variables, the visco-elastic constants of four kinds of binding agents are determined by the Rosenbrock nonlinear programming method. Then, the step impulsive response of a two-layer simple supported beam which is bound by those binding agents is analyzed by using three-layer beam theory, showing the fairly large damping effect of a binding agent.

Optimal sandwich beam design for maximum viscoelastic damping

Three-layer sandwich beams, made of two elastic outer layers and a viscoelastic layer sandwiched between them, are considered as damping structural elements. A sixth-order equation of motion with complex coefficients of a sandwich beam in free vibrations is reviewed and solved numerically for a large variety of boundary conditions. The solution is used later as part of an optimal design program. An equality constrained minimization algorithm is modified and used to obtain optimal design of damping sandwhich beams subjected to inequality design constraints. The use of the program is demonstrated by solving two design problems

Non-linear vibration analysis of multilayer beams by incremental finite elements, Part II: Damping and forced vibrations

The inclusion of simple damping of viscous type in the incremental variational equation governing the non-linear motions of multilayer beams is described. Various problems of forced non-linear response of three-layer sandwich beams are studied. Plots of the response curves reveal some complicated and interesting variation of the amplitudes of different harmonic terms, especially in the case of an unsymmetrically layered beam in which a quadratic type of non-linearity is observed.

Static Analysis of Three-Layered Sandwich Cantilever Beams

A detailed static deflection and stress analysis of three-layered sandwich cantilever beams, subjected to both uniform as well as concentrated loads, is presented here. Three types of boundary conditions dealing with the mechanism of clamping at one edge and generation of “free” edge condition at the other end are investigated. Various graphs are presented showing the effects of geometric and shear parameters on deflections and stresses. They illustrate how the mechanism of “clamping” at one edge and generation of “free” edge condition can be utilized to increase the stiffness of sandwich beams.

A comparison of some equations for the flexural vibration of damped sandwich beams

This paper compares the theories of flexural vibration of damped, three-layer sandwich beams as presented by Yan and Dowell, and by DiTaranto and Mead and Markus. Depending on the assumptions made about the internal shear stress distribution, the differential equation of transverse flexural displacement is either of fourth or sixth order. The inclusion of the effects of face-plate shear deformation and longitudinal inertia in the analysis yields a sixth order differential equation if the beam section is symmetric, and an eighth order equation if the section is unsymmetric. Flexural wave speeds and loss factors computed from the theories are presented and compared. The DiTaranto and Mead and Markus equations yield reliable values provided the flexural wavelength is greater than about four face-plate thicknesses. The Yan and Dowell equations yield reliable values only at much greater wavelengths or when the central layer in the sandwich is very thick.

An integral equation analysis of the harmonic response of three-layer beams

The integral equations of harmonic motion have been derived and solved for three-layer sandwich beams with a constrained linear viscoelastic core. The method of solution required first the construction of the Green's vector for a beam in analytical form. Following this, the integral equations were derived and readily approximated by matrix equations which were finally solved numerically. In addition to this analysis, the corresponding eigenvalue problem has been solved so that the modal frequencies and the beam loss factor could be calculated directly. The integral equation analysis offers a fast and efficient alternative to the traditional methods based on the solution of the differential equations of motion. The method has been verified by comparison with experimental results for three-layer cantilevers and simply supported beams.

Vibration Analysis of a Flexible System Mounted on a Viscoelastic Sandwich Beam

Vibration analysis of a simple flexible system mounted arbitrarily on a three-layer sandwich beam having a viscoelastic core and elastic faces is presented in this paper. The flexible system consists of a mass on rubber spring and is excited harmonically. The expressions for displacement response of mass and transmissibility provided by the whole system are obtained. The displacement response and transmissibility are studied for different geometrical and physical parameters of the sandwich beam. Some of the theoretical results are verified experimentally.

More on finite element modeling of damped composite systems

Finite element procedures are developed and verified for layered beams and rings having either continuously or discontinuously constrained viscoelastic damping layers. The two configurations considered are (1) a three-layered sandwich beam or ring (closed curved beam) consisting of two thin elastic layers with a viscoelastic core in between, and (2) a damped composite made of a thin-walled elastic structure having a finite number of mass segments or elastic segments adhered to it by a viscoelastic material. Viscoelastic material dependence on frequency and temperature is accounted for. Numerical predictions of transverse driving point impedances agree very well with available experimental data.

The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions

The sixth-order differential equation of motion is derived in terms of the transverse displacement, w, for a three-layer sandwich beam with a viscoelastic core. Mathematical expressions in terms of w are found for a variety of beam boundary conditions. The solution of the differential equation by the method of Di Taranto is shown to yield a special class of complex, forced modes of vibration which are completely uncoupled. These complex modes can only exist when the beam is externally excited by specific “damped normal loadings” which are also complex and which are proportional to the local transverse inertia loading on the beam. Use of these modes in the analysis of the forced vibration problem leads to a simple series form of solution. The orthogonality of these complex modes is briefly discussed and proved.