Constrained Layer Damping Patches Research Articles

A nonlinear vibration model of fiber metal laminated thin plate treated with constrained layer damping patches

This paper explores the nonlinear vibration characteristics of fiber metal laminated thin plate(FMLTP) treated with constrained layer damping(CLD) patches. Additionally, based on the Jones-Nelson nonlinear material theory and the von Kármán geometric nonlinear theory, a theoretical model for FMLTP with CLD patches is established, considering material nonlinearity. Using the energy method, an energy equation is formulated and the nonlinear natural frequencies and vibration responses of the studied structure are iteratively determined through the Newton-Raphson method under various excitation amplitudes. Additionally, the modal damping ratios are calculated utilizing the complex modulus method. To validate the effectiveness of the model, a corresponding testing system is constructed, and tests are conducted on a 5-layer TA2/TC500 FMLTP treated with two pieces of CLD patches. The test results show excellent agreement with the theoretical results. Finally, the influences of different CLD patches treatment methods on the vibration characteristics of the FMLTP are discussed.

Constrained layer damping for mitigating vibration of a rotating disk-drum coupled structure

Rotating disk-drum coupled structures are commonly employed in large rotating machines. They are prone to have vibration issues caused by their decreasing thickness to meet lightweight demands. Constrained layer damping (CLD) is a widely used technique to reduce vibrations, but no studies have yet investigated its application on rotating coupled structures. In this paper, a universal model is proposed and experiments are conducted to investigate the influence of CLD on a rotating cylindrical shell ended by an annular disk. This approach considers the rotating effects, and formulates the equations of motion using the Rayleigh-Ritz method with the help of the Sanders shell theory and Mindlin plate theory. Different sets of artificial springs are applied to model the coupling and boundary conditions. The proposed approach is validated by comparing the numerical results with those obtained from modal and rotor experiments. Then the modal parameters and vibration responses are evaluated for different rotational speeds, and the influences of the location and thickness ratio of the CLD patch and the coupling stiffness on the dynamic characteristics of the system are discussed.

Viscoelastic damping design – A novel approach for shape optimization of Constrained Layer Damping treatments at different ambient temperatures

Passive damping plays an important role in the vibration mitigation of aeronautic structures. In contrast to active systems, passive damping systems do not require any energy supply. Thus, their readiness is independent, which reduces the failure probability compared to active systems. Constrained Layer Damping (CLD) has become an established treatment for damping bending vibrations. Unlike other passive systems such as shock-mounts, CLD can be compactly integrated into an existing structure as an add-on solution. However, the design scope is limited by mass constraints and the optimal design for maximum damping must be found by optimization. For this purpose, a novel optimization approach is presented. The layer widths of the core and face layers of a CLD structure are treated as design parameters. Compared to the strategy of placing CLD patches on vibration antinodes, the proposed approach provides up to 52 % higher damping. The optimal design of a generic beam structure is determined considering different modes, viscoelastic material stiffnesses and ambient temperatures. Furthermore, the simulated damping is experimentally verified for a shape-optimized beam. The analyses show that the optimal design depends significantly on the viscoelastic material stiffness and is therefore temperature dependent. As a consequence, a generalized design guideline for CLD treatments cannot be derived.

Nonlinear vibration analysis of fiber reinforced composite cylindrical shells with partial constrained layer damping treatment

This research proposes a novel analytical model capable of accurately predicting the strain-dependent characteristics of fiber reinforced composite shells (FRCSs) with partial constrained layer damping (CLD) treatment by considering the nonlinearities of fiber reinforced composite and viscoelastic materials simultaneously. The nonlinear material properties are represented based on Jones-Nelson nonlinear theory, energy-based strain energy method, and complex modulus method. Then, the governing equations of motion for FRCSs are developed via Ritz method, and the identification procedure of nonlinear fitting parameters is also presented. By taking a T300 carbon fiber/epoxy resin cylindrical shell with partial CLD patches as an example, a series of experiments are carried out to validate the proposed modeling approach. Finally, the effects of material properties on nonlinear vibration behaviors of FRCSs covered with partial CLD patches are evaluated. Comparisons show that the proposed nonlinear model is more accuracy than that without considering strain dependence, where the maximum errors between the proposed model and measured data for natural frequencies, damping ratios and resonant response are 6.9%, 11.3%, and 11.2%, respectively.

Passive vibration control of plate using nodal patterns of mode shape

Passive constrained layer damping (PCLD) is nowadays a general method for reducing vibrations. Constrained layer damping (CLD) is a very good technology in terms of reducing vibration energy. This paper deals with optimal damping of first three modes of a thin square cantilever plate by constrained viscoelastic layers which are positioned according to the nodal patterns of the mode. In essence, the CLD patches are cut according to the nodal patterns and then applied on to the bare plate. Thus, this approach uses prior information of the deformation patterns of the plate. The ABAQUS finite element analysis software was used to create viscoelastically damped plate models subjected to forced vibration. The direct steady-state dynamic analysis was used to obtain the frequency response functions from which the resonance frequencies of the models were derived. Vibration control using nodal pattern CLD patches is a better way to apply CLD treatment to a plate. This is because the mode shapes give good predictions of where the maximum strains are in the plate as well as the design and size of the damping patches required. It is believed that the methodology proposed in this research work is capable of providing good results.

Multiobjective optimization for vibration reduction in composite plate structures using constrained layer damping

This paper presents a multiobjective optimization approach to minimize weight and maximize modal damping in laminated composite panels with Constrained Layer Damping (CLD) treatments. The design variables are the number and position of the CLD patch treatments on the surface of the laminated plate. The Direct MultiSearch (DMS) solver for multiobjective optimization problems is used in this work. DMS is a solver which does not use any derivatives of the objective functions. A previously developed finite element model for sandwich plates with viscoelastic core and anisotropic laminated face layers is adapted to model the plate with the CLD treatments. Applications for L-shaped and T-shaped plates are presented and both trade-off Pareto optimal fronts and the respective treatment configurations are obtained and the results are analyzed and discussed.

Multiobjective optimization of constrained layer damping treatments in composite plate structures

ABSTRACTThe optimal design of laminated composite panels with constrained layer damping (CLD) treatments is addressed in this article. The objectives are simultaneously to minimize weight and maximize modal damping. The design variables are the number and position of CLD patch treatments on the surface of the laminated plate. The problem is solved using Direct MultiSearch solver, which does not use any derivatives of the objective functions. A finite element model for sandwich plates with viscoelastic core and laminated face layers is used. Trade-off Pareto optimal fronts and the respective treatment configurations are obtained and the results are analyzed and discussed.

Application of level set method to optimal vibration control of plate structures

Vibration control plays a crucial role in many structures, especially in the lightweight ones. One of the most commonly practiced method to suppress the undesirable vibration of structures is to attach patches of the constrained layer damping (CLD) onto the surface of the structure. In order to consider the weight efficiency of a structure, the best shapes and locations of the CLD patches should be determined to achieve the optimum vibration suppression with minimum usage of the CLD patches. This paper proposes a novel topology optimization technique that can determine the best shape and location of the applied CLD patches, simultaneously. Passive vibration control is formulated in the context of the level set method, which is a numerical technique to track shapes and locations concurrently. The optimal damping set could be found in a structure, in its fundamental vibration mode, such that the maximum modal loss factor of the system is achieved. Two different plate structures will be considered and the damping patches will be optimally located on them. At the same time, the best shapes of the damping patches will be determined too. In one example, the numerical results will be compared with those obtained from the experimental tests to validate the accuracy of the proposed method. This comparison reveals the effectiveness of the level set approach in finding the optimum shape and location of the CLD patches.

Evolution of Constrained Layer Damping Using a Modified Cellular Automata Algorithm

In order to improve the treatment efficiency of the constrained layer damping (CLD), it is meaningful to have a study on its layout optimization. This paper based on current research of Cellular Automata (CA) algorithm for CLD optimization, points out that the current application of CA algorithm is less efficient, considering that adding or deleting a single CLD patch almost does no change to the entire structure, then makes a simplification and modification of CA algorithm. With the aim at improving the structural modal loss factor, this paper uses the current CA algorithm and its modified algorithm to optimize a partial CLD plate. The results have shown that the modified CA algorithm for CLD optimization can not only substantially increase computing efficiency, but to some extent, improve the optimization effectiveness.

Evolution of constrained layer damping using a cellular automaton algorithm

Constrained layer damping (CLD) is a highly effective passive vibration control strategy if optimized adequately. Factors controlling CLD performance are well documented for the flexural modes of beams but not for more complicated mode shapes or structures. The current paper introduces an approach that is suitable for locating CLD on any type of structure. It follows the cellular automaton (CA) principle and relies on the use of finite element models to describe the vibration properties of the structure. The ability of the algorithm to reach the best solution is demonstrated by applying it to the bending and torsion modes of a plate. Configurations that give the most weight-efficient coverage for each type of mode are first obtained by adapting the existing ‘optimum length’ principle used for treated beams. Next, a CA algorithm is developed, which grows CLD patches one at a time on the surface of the plate according to a simple set of rules. The effectiveness of the algorithm is then assessed by comparing the generated configurations with the known optimum ones.

A comparative study on optimization of constrained layer damping treatment for structural vibration control

This paper presents a comparison of optimization algorithms for constrained layer damping (CLD) patches’ layout with an objective to minimize the maximum vibration response of the odd modes, which constitutes the dominant acoustic radiation, of a simply supported beam excited by a harmonic transverse force. An analytical model developed for relating the displacement response of the beam with bonded CLD patches and their layout is adopted to formulate the optimization problem. Four different nonlinear optimization methods/algorithms, sub-problem approximation method, the first-order method, sequential quadratic programming (SQP) and genetic algorithm (GA), are then, respectively, used to optimize the CLD patches’ locations and lengths with the aim of minimum displacement amplitude at the middle beam. The efficiency of each considered optimization method is evaluated and also compared in terms of obtained optimal beam displacement and the added weight owing to damping treatment. The results show that GA is most efficient in obtaining the best optimum for this optimization problem in spite of highest computation efforts required to improve its stability.

Minimization of sound radiation from baffled beams through optimization of partial constrained layer damping treatment

An optimization study is presented with aim to minimize the sound power radiated by a simply supported, baffled beam with constrained layer damping (CLD) treatment. The governing equation of motion for the calculation of time-harmonic response of a partially CLD covered beam is derived first on the basis of energy approach. Assumed-modes method is used to solve the equation with obtained frequency response functions at different beam locations, which are further used for the calculation of its radiated sound power into half free-space by using Rayleigh’s integral. The optimization problem is then formulated to minimize the sound power radiated by the beam over a frequency range of interest covering multiple resonant modes. A genetic algorithm-based penalty function method is employed to search for the optimum of location/length of the CLD patch and the shear modulus of viscoelastic layer. Optimal results show that for a simply supported beam with a transverse force applied at its central location, it is not necessary to fully cover the structure using CLD patch in order to achieve the largest reduction in the sound power radiated by the beam over a frequency range. With inclusion of the amount of damping material to be minimized, the optimal CLD coverage length is only one-fourth of the base beam’s. Moreover, the optima of three design variables, the CLD coverage length, location on the beam and the shear modulus of viscoelastic layer, are highly relevant to each other.

Discontinuous constrained layer damping treatments applied to a vibrating free‐free beam.

The vibration response to application of discontinuous constrained layer damping (CLD) patches to varied portions of a free‐free beam was studied. Since neither closed‐form solutions nor finite element methods can be readily implemented for CLD analysis with partial coverage of a structure under broadband excitation [C. T. Sun and Y. P. Lu, Vibration Damping of Structural Elements (Prentice‐Hall, Englewood Cliffs, NJ, 1995), pp. 318–362], an empirical approach was taken. The test object was a 26.5‐ × 1‐ × 1/8‐in. steel beam, and was subjected to a chirp. The aim was to quantify the relative effectiveness of varied lengths and positions of CLD patches in reducing the response of the first five resonant modes of the beam. Assessment of the potential for strain energy dissipation was made based on the net displacement of the beam (appropriately phased mode summation), with relative phase of the summed modes specific to the input force signal. Attempts were made to correlate the effect of CLD on each mode to the time‐averaged percentage of strain energy for that mode under the treatment patch, coupled with the percentage of the beam’s strain energy under the patch. [Work supported by NSF.]