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.

Frequency and Loss Factors of Sandwich Beams under Various Boundary Conditions

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.

Damping in composite materials: Properties and models

Shunted piezoelectric patches are periodically placed along rods to control the longitudinal wave propagation in these rods. The resulting periodic structure is capable of filtering the propagation of waves over specified frequency bands called stop bands. The location and width of the stop bands can be tuned, using the shunting capabilities of the piezoelectric materials, in response to external excitations and to compensate for any structural uncertainty. A mathematical model is developed to predict the response of a rod with periodic shunted piezoelectric patches and to identify its stop band characteristics. The model accounts for the aperiodicity, introduced by proper tuning of the shunted electrical impedance distribution along the rod. Disorder in the periodicity typically extends the stop bands into adjacent propagation zones and, more importantly, produces the localization of the vibration energy near the excitation source. The conditions for achieving localized vibration are established and the localization factors are evaluated for different levels of disorder on the shunting parameters. The numerical predictions demonstrate the effectiveness and potentials of the proposed treatment that requires no control energy and combines the damping characteristics of shunted piezoelectric films, the attenuation potentials of periodic structures, and the localization capabilities of aperiodic structures. The theoretical investigations presented in this paper provide the guidelines for designing tunable periodic structures with high control flexibility where propagating waves can be attenuated and localized.

https://iopscience.iop.org/article/10.1088/0964-1726/10/5/314/pdf

Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches

Š. Markuš

Papers

Loss factors and resonant frequencies of encastré damped sandwich beams

Coupled flexural-longitudinal wave motion in a periodic beam☆

Damping properties of layered cylindrical shells, vibrating in axially symmetric modes

A new approximate method of finding the loss factors of a sandwich cantilever

On eigenvalue boundary problems of transversely vibrating sandwich beams