Constrained Substructure Approach to Optimal Strain Energy Analysis

The chief tool for design of viscoelastic-based damping treatments over the past 20 years has been the modal strain energy (MSE) approach. This approach to damping design traditionally has involved a practitioner to vary placement and stiffness of add-on elements using experience and trial and error so as to maximize the add-on element share of system MSE in modes of interest. In this paper we develop a new technique for maximizing strain energy as a function of stiffness for add-on structural elements modeled as rank r perturbations to the original stiffness matrix. The technique is based on a constrained substructure approach allowing us to parameterize strain energy in terms of the eigenvalues of the perturbed structure. An optimality condition is derived that relates the input-output response at the attachment location of the add-on elements to the maximum achievable strain energy. A realizability condition is also derived which indicates whether or not the optimal solution is achievable with passive structural elements. This method has applications in the design of structural treatments for controlling sound and vibration and promises an efficient means of determining the limits of performance of passive structural treatments. An advantage of our approach over existing methods is that the maximum achievable strain energy fraction in the add-on elements is directly computable with the realizability condition then indicating whether the optimal solution is achievable.

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Some Pitfalls of Simplified Modeling for Viscoelastic Sandwich Beams

Journal of Vibration and Acoustics ◽

10.1115/1.1287030 ◽

2000 ◽

Vol 122 (4) ◽

pp. 434-439 ◽

Cited By ~ 11

Author(s):

Eric M. Austin ◽

Daniel J. Inman

Keyword(s):

Strain Energy ◽

Large Range ◽

Sandwich Beams ◽

Constrained Layer Damping ◽

Modal Strain Energy ◽

Skew Distributions ◽

Transverse Vibrations ◽

Simplified Modeling ◽

Damping Treatments

It is commonplace in academia to base models of constrained-layer damping treatments on the assumption that the facesheets displace identically during transverse vibrations. This assumption is valid for a large range of problems, particularly for problems common in the era when damping was achieved by applying foil-backed treatments to thin panels. The authors show using a very simple example that oversimplified modeling can skew distributions of modal strain energy, a common indicator of damping. [S0739-3717(00)00204-X]

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PARTIAL CONSTRAINED VISCOELASTIC DAMPING TREATMENT OF STRUCTURES: A MODAL STRAIN ENERGY APPROACH

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455406002003 ◽

2006 ◽

Vol 06 (03) ◽

pp. 397-411 ◽

Cited By ~ 15

Author(s):

R. A. S. MOREIRA ◽

J. DIAS RODRIGUES

Keyword(s):

Strain Energy ◽

Effective Means ◽

Thin Plates ◽

Viscoelastic Layer ◽

Modal Strain Energy ◽

Structural Modifications ◽

Target Mode ◽

Modal Damping ◽

The Cost ◽

Damping Treatments

The constrained viscoelastic layer damping treatment is an effective means for the passive vibration control of plate and beam-kind structures. In order to reduce the treatment cost, while minimizing structural modifications, particularly the increase in mass, constrained viscoelastic treatments can be successfully applied in a partial and localized manner. The effectiveness of these treatments depends on their extension and relative location with respect to the target mode shape, which is not usually expeditiously established. In order to minimize the cost of the numerical optimization of the partial treatments, an efficient numerical methodology based on the ratio between the modal strain energy of the treated area and that of the structure is hereby proposed. This method is used in the analysis of the location and extension effects of partial constrained viscoelastic treatments on the modal damping of thin plates. The numerical results are verified through an experimental study on specimens with partial constrained viscoelastic layer damping treatments.

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Optimisation of damping treatments based on big bang–big crunch and modal strain energy methods

Journal of Sound and Vibration ◽

10.1016/j.jsv.2013.10.023 ◽

2014 ◽

Vol 333 (5) ◽

pp. 1319-1330 ◽

Cited By ~ 10

Author(s):

Hasan Koruk ◽

Kenan Y. Sanliturk

Keyword(s):

Strain Energy ◽

Big Bang ◽

Energy Methods ◽

Modal Strain Energy ◽

Big Crunch ◽

Damping Treatments

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Dimensionless Analysis of Segmented Constrained Layer Damping Treatments with Modal Strain Energy Method

Shock and Vibration ◽

10.1155/2016/8969062 ◽

2016 ◽

Vol 2016 ◽

pp. 1-16 ◽

Cited By ~ 2

Author(s):

Shitao Tian ◽

Zhenbang Xu ◽

Qingwen Wu ◽

Chao Qin

Keyword(s):

Shear Strain ◽

Strain Field ◽

Strain Energy ◽

Design Parameters ◽

Viscoelastic Layer ◽

Constrained Layer Damping ◽

Modal Strain Energy ◽

Modal Strain Energy Method ◽

Damping Treatments ◽

Strain Energy Method

Constrained layer damping treatments promise to be an effective method to control vibration in flexible structures. Cutting both the constraining layer and the viscoelastic layer, which leads to segmentation, increases the damping efficiency. However, this approach is not always effective. A parametric study was carried out using modal strain energy method to explore interaction between segmentation and design parameters, including geometry parameters and material properties. A finite element model capable of handling treatments with extremely thin viscoelastic layer was developed based on interlaminar continuous shear stress theories. Using the developed method, influence of placing cuts and change in design parameters on the shear strain field inside the viscoelastic layer was analyzed, since most design parameters act on the damping efficiency through their influence on the shear strain field. Furthermore, optimal cut arrangements were obtained by adopting a genetic algorithm. Subject to a weight limitation, symmetric and asymmetric configurations were compared. It was shown that symmetric configurations always presented higher damping. Segmentation was found to be suitable for treatments with relatively thin viscoelastic layer. Provided that optimal viscoelastic layer thickness was selected, placing cuts would only be applicable to treatments with low shear strain level inside the viscoelastic layer.

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Topology Optimization of Free Damping Treatments on Plates Using Level Set Method

Shock and Vibration ◽

10.1155/2020/5084167 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17

Author(s):

Jian Pang ◽

Weiguang Zheng ◽

Liang Yang ◽

Yuping Wan ◽

Qibai Huang ◽

...

Keyword(s):

Finite Element ◽

Level Set Method ◽

Level Set ◽

Composite Plate ◽

Strain Energy ◽

Base Plate ◽

Experimental Results ◽

Modal Strain Energy ◽

Level Set Function ◽

Damping Treatments

Application of level set method to optimize the topology of free damping treatments on plates is investigated. The objective function is defined as a combination of several desired modal loss factors solved by the finite element-modal strain energy method. The finite element model for the composite plate is described as combining the level set function. A clamped rectangle composite plate is numerically and experimentally analyzed. The optimized results for a single modal show that the proposed method has the possibility of nucleation of new holes inside the material domain, and the final design is insensitive to initial designs. The damping treatments are guided towards the areas with high modal strain energy. For the multimodal case, the optimized result matches the normalized modal strain energy of the base plate, which would provide a simple implementation way for industrial application. Experimental results show good agreements with the proposed method. The experimental results are in good agreement with the optimization results. It is very promising to see that the optimized result for each modal has almost the same damping effect as that of the full coverage case, and the result for multimodal gets moderate damping at each modal.

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CONTEXTUAL SUBTEXT INFORMATION OF A FOREIGN LANGUAGE TEXT: HERMENEUTIC APPROACH

Naukovy Visnyk of South Ukrainian National Pedagogical University named after K D Ushynsky Linguistic Sciences ◽

10.24195/2616-5317-2020-30-5 ◽

2020 ◽

Vol 2020 (30) ◽

pp. 75-87

Author(s):

Lidiya Derbenyova

Keyword(s):

Foreign Language ◽

Optimal Solution ◽

Decision Making Process ◽

Trial And Error ◽

Transmission Of Information ◽

Hermeneutic Approach ◽

Trial And Error Method ◽

Problems Of Translation ◽

Error Method ◽

Language Text

The article focuses on the problems of translation in the field of hermeneutics, understood as a methodology in the activity of an interpreter, the doctrine of the interpretation of texts, as a component of the transmission of information in a communicative aspect. The relevance of the study is caused by the special attention of modern linguistics to the under-researched issues of hermeneutics related to the problems of transmission of foreign language text semantics in translation. The process of translation in the aspect of hermeneutics is regarded as the optimum search and decision-making process, which corresponds to a specific set of functional criteria of translation, which can take many divergent forms. The translator carries out a number of specific translation activities: the choice of linguistic means and means of expression in the translation language, replacement and compensation of nonequivalent units. The search for the optimal solution itself is carried out using the “trial and error” method. The translator always acts as an interpreter. Within the boundaries of a individual utterance, it must be mentally reconstructed as conceptual situations, the mentally linguistic actions of the author, which are verbalized in this text.

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Brains as Engines of Association

10.1093/oso/9780190880163.001.0001 ◽

2019 ◽

Cited By ~ 1

Author(s):

Dale Purves

Keyword(s):

Neural Systems ◽

Neural Function ◽

Trial And Error ◽

Nervous Systems ◽

The Past ◽

Sensing Systems ◽

Lifetime Experience ◽

Survival And Reproduction ◽

Pros And Cons ◽

And Behavior

Brains as Engines of Association seeks an operating principle of the human brain and is divided into four parts. The first part (“What Nervous Systems Do for Animals”) is intended to set the stage for understanding the emergence of neural systems as promoting what all organisms must accomplish: survival and reproduction. The second part (“Neural Systems as Engines of Association”) lays out the general argument that biological sensing systems face a daunting problem: they cannot measure the parameters of the world in the way physical instruments can. As a result, nervous systems must make and update associations (synaptic connections) on the basis of empirical success or failure over both evolutionary and individual time. The third part (“Evidence that Neural Systems Operate Empirically”) reviews evidence accumulated over the past 20 years that supports this interpretation in vision and audition, the sensory systems that have been most studied from this or any other perspective. Finally, the fourth part (“Alternative Concepts of Neural Function”) considers the pros and cons of other interpretations of how brains operate. The overarching theme is that the nervous systems of humans and every other animal operate on the basis associations between stimuli and behavior made by trial and error over species and lifetime experience.

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