Optimum distribution of additive damping for vibrating frames

Redistribution of an initially uniformly applied additive damping is numerically and experimentally investigated for a vibrating plane frame. It is found that an optimum redistribution can reduce amplitudes of resonant responses by up to 60% (with the cost or the weight of the damping treatment kept constant). Optimally selected non-uniform distributions of additive damping may thus be worth considering in many practical cases.     

Optimum thickness distribution of unconstrained viscoelastic damping layer treatments for plates

This paper concerns the optimum thickness distribution of unconstrained viscoelastic damping layer treatments for plates. The system loss factor is expressed in terms of the mechanical properties of the plate and damping layer and the layer/plate thickness ratio. Optimum distributions of the thickness ratio that maximize the system loss factor are obtained through sequential unconstrained minimization techniques. Results are presented for both simply-supported and edge-fixed rectangular plates with aspect ratios of 1·0 to 4·0. These results indicate that the system loss factor can be increased by as much as 100%, or more, by optimizing the thickness distribution of the damping treatment. Also revealed are the regions of the plate where added damping treatments are most effective.     

Optimum conditions for superradiant damping

The conditions are investigated under which cooperative or superradiant effects are greatest in an inhomogeneously broadened atomic system that is excited by a coherent light pulse. The coupled non-linear atomic equations of motion are solved numerically for excitation pulses of various areas. It is shown that the absolute intensity of the response decreases strongly with decreasing pulse are below π, but that the relative superradiant contribution increases with decreasing pulse area. The reasons for this are discussed, and it is suggested that excitation by a pulse in the neighborhood of π/2 may represent an optimum compromise for the observation of superradiance.     

Detection of directional energy damping in vibrating systems

The transmission efficiency, frequency and amplitude alteration have been measured by a simple technique of coupled oscillators with a frequency gradient and in a system of non-Newtonian fluid in the form of corn-flour slime. The system of coupled oscillators was found to exhibit preferential energy transfer towards the low frequency end with the reverse propagation severely damped. Energy transfer in all directions was damped in the non-Newtonian fluid in comparison with water. Also the damping in non-Newtonian fluids works only after a lower limit for input amplitude. While most of the previous studies focussed on dissipation of energy within shock-absorbing systems, we demonstrate the contribution of re-distribution of energy reaching the output end to achieve shock absorbing.      

Optimized electric networks for vibration damping of piezoactuated beams

This paper studies the multimodal vibration damping of an elastic beam equipped with multiple piezoelectric actuators connected to an electric network. Two analytical models of the electromechanical coupled structure are considered: a homogenized one, accurate when a large number of actuators is employed, is used to derive simple design criteria for the electric network; and a discrete one, able to face real situations when few actuators are employed, is adopted to test the network performance, defined as the exponential time-decay rate of the free vibrations of the controlled structure. Some electric networks are presented and compared in simulation to networks previously proposed in the literature, in order to evaluate their performances in broadband vibration control.     

On linear modeling of interface damping in vibrating structures

Dissipation of mechanical vibration energy at contact interfaces in a structure, commonly referred to as interface damping, is an important source of vibration damping in built-up structures and its modeling is the focus of the present study. The approach taken uses interface forces which are linearly dependent on the relative vibration displacements at the contact interfaces.The main objective is to demonstrate a straightforward technique for simulation of interface damping in built-up structures using FE modeling and simple, distributed, damping forces localized to interfaces where the damping occurs.As an illustration of the resulting damping the dissipated power is used for evaluation purposes. This is calculated from surface integrals over the contact interfaces and allows for explicit assessment of the effect of simulated interface forces for different cases and frequencies. The resulting loss factor at resonance is explicitly evaluated and, using linear simulations, it is demonstrated that high damping levels may arise even though the displacement differences between contacting surfaces at damped interfaces may be very small.     

Strategies for using cellular automata to locate constrained layer damping on vibrating structures

It is often hard to optimise constrained layer damping (CLD) for structures more complicated than simple beams and plates as its performance depends on its location, the shape of the applied patch, the mode shapes of the structure and the material properties. This paper considers the use of cellular automata (CA) in conjunction with finite element analysis to obtain an efficient coverage of CLD on structures. The effectiveness of several different sets of local rules governing the CA are compared against each other for a structure with known optimum coverage—namely a plate. The algorithm which attempts to replicate most closely known optimal configurations is considered the most successful. This algorithm is then used to generate an efficient CLD treatment that targets several modes of a curved composite panel. To validate the modelling approaches used, results are also presented of a comparison between theoretical and experimentally obtained modal properties of the damped curved panel.     

Dynamic analysis of slip damping in clamped layered beams with non-uniform pressure distribution at the interface

Slip damping is a mechanism exploited for dissipating noise and vibration energy in aerodynamic and machine structures. Such slip in layered structures can be simulated by applying pressure to hold the members together at the interface. However, while most analyses of the mechanism assume an environment of uniform pressure at the interface, experiments to date have confirmed that this is rarely the case. There have been recent attempts to relax the restriction of uniform interface pressure to allow for more realistic pressure profiles that are encountered in practice. However, such works have mostly been limited to static loading for which it has been established that the interfacial pressure gradient does play a dominant role in modulating the level of energy dissipation. This paper is an attempt to extend such analyses to account for cases of realistic dynamic loading that drive such structural vibration in the first instance. In particular, it is shown that under dynamic loads, frequency variation more than non-uniformity in the interface pressure can have significant effect on both the energy dissipation and the logarithmic damping decrement associated with the mechanism of slip damping in such layered structures.     

Spectral finite elements for vibrating rods and beams with random field properties

The classical stochastic Helmholtz equation grasps, through the random field of the refraction index, the spatial variability in the mass density but not the variability in elastic moduli or geometric parameters. In contradistinction to this restriction, the present analysis accounts for the spatial randomness of mass density as well as those of elastic properties and cross-sectional geometric properties of rods undergoing longitudinal vibrations and of Timoshenko beams in flexural vibrations. All the material variabilities are described here by random Fourier series with a typical (average) characteristic size of inhomogeneity d, which is either smaller, comparable to, or larger than the wavelength. The third length scale entering the problem, but kept constant, is the rod or beam length. We investigate the relative effects of random noises in all the material parameters on the spectral stiffness matrices associated with rods and beams for a very wide range of frequencies.     

An alternative to modal analysis for material stiffness and damping identification from vibrating plates

This paper presents an alternative to modal analysis to extract stiffness and damping parameters from thin vibrating plates. Full-field slope measurements are performed through a deflectometry technique on a plate vibrating at a given frequency. Images are recorded in phase and at π/2 lag from the excitation. From this information, deflection fields are computed by integration and curvature fields are obtained by differentiation. This information is then input into the principle of virtual work to extract both stiffness and damping parameters. This procedure, known as the Virtual Fields Method, is detailed in the paper and the notion of special optimized virtual fields is extended to the present problem. Validation on simulated data is performed before moving to experimental data. One of the main advantages of this technique is that it is completely insensitive to the damping coming from the boundary conditions. This is illustrated experimentally on two tests where a viscoelastic layer and rubber washers are added in the experimental set up.     

Shear and compressional damping effects of constrained layered beams

A theory is formulated for combined shear and compressional damping effects of contrained layered beam structures with complicated cross section areas. The theory is applied to some selected theoretical examples. The calculation results indicate that the loss factor values of these beams are larger over a wider frequency range than could be expected from corresponding shear damping effect only or compressional damping treatment only.     

Response and damping of a rectangular cantilever plate with vibrating beam dampers

In this work the use of beams as auxiliary mass dampers for cantilever plates is considered. Because the cantilever plate problem, which is of strong industrial interest, does not lend itself to a Lévy-type solution, the procedure developed by Ritz is used. Structural damping is incorporated into the main and auxiliary systems by treating them as having a complex elastic modulus. With appropriate selection of the parameters, the fundamental resonance of the plate is split into two new ones with considerably suppressed responses. In order to verify the analysis, an experimental investigation was carried out and the results obtained were compared with the theory developed.     

An integral equation approach to the fundamental frequency of vibrating beams

An approximation to the lowest natural frequency of vibrating beams is obtained analytically by applying eigenvalue, eigenfunction theory to the defining integral equation. The method produces successively closer values for both upper and lower bounds to the fundamental frequency. It is found that the second lower bound provides in itself a good approximation to published values and a graph is derived which provides a bound for the error in this approximation without further computation. The application of integral equations to the formulation of mechanical engineering problems is increasing and one aim of the paper is to draw attention to the possibility of obtaining analytical solutions.