Lancaster’s Method of Damping Identification Revisited

2002 ◽  
Vol 124 (4) ◽  
pp. 617-627 ◽  
Author(s):  
Sondipon Adhikari
Keyword(s):  
Transfer Functions ◽  
Past History ◽  
A Priori ◽  
Kernel Functions ◽  
Mode Shapes ◽  
Viscous Damping ◽  
Damping Matrix ◽  
Convolution Integrals ◽  
History Of ◽  
Damped Systems

Identification of damping is an active area of research in structural dynamics. In one of the earliest works, Lancaster [1] proposed a method to identify the viscous damping matrix from measured natural frequencies and mode shapes. His method requires the modes to be normalized in a particular way, which in turn a priori needs the very same viscous damping matrix. A method, based on the poles and residues of the measured transfer functions, has been proposed to overcome this basic difficulty associated with Lancaster’s method. This approach is then extended to a class of nonviscously damped systems where the damping forces depend on the past history of the velocities via convolution integrals over some kernel functions. Suitable numerical examples are given to illustrate the modified Lancaster’s method developed here.

Modal Analysis of Nonviscously Damped Beams

2006 ◽  
Vol 74 (5) ◽  
pp. 1026-1030 ◽  
Author(s):  
S. Adhikari ◽  
M. I. Friswell ◽  
Y. Lei
Keyword(s):  
Natural Frequencies ◽  
Past History ◽  
Kernel Functions ◽  
Mode Shapes ◽  
Damping Force ◽  
The Past ◽  
Convolution Integrals ◽  
Special Cases ◽  
History Of ◽  
Damping Model

Linear dynamics of Euler–Bernoulli beams with nonviscous nonlocal damping is considered. It is assumed that the damping force at a given point in the beam depends on the past history of velocities at different points via convolution integrals over exponentially decaying kernel functions. Conventional viscous and viscoelastic damping models can be obtained as special cases of this general damping model. The equation of motion of the beam with such a general damping model results in a linear partial integro-differential equation. Exact closed-form equations of the natural frequencies and mode shapes of the beam are derived. Numerical examples are provided to illustrate the new results.

Analysis of Asymmetric Nonviscously Damped Linear Dynamic Systems

2003 ◽  
Vol 70 (6) ◽  
pp. 885-893 ◽  
Author(s):  
S. Adhikari ◽  
N. Wagner
Keyword(s):  
State Space ◽  
Past History ◽  
Kernel Functions ◽  
Extended State ◽  
State Space Approach ◽  
Linear Dynamic Systems ◽  
Convolution Integrals ◽  
History Of ◽  
Damped Systems ◽  
Space Approach

Multiple-degree-of-freedom linear asymmetric nonviscously damped systems are considered. It is assumed that the nonviscous damping forces depend on the past history of velocities via convolution integrals over exponentially decaying kernel functions. An extended state-space approach involving a single asymmetric matrix is proposed. The nature of the eigensolutions in the extended state space has been explored. Some useful results relating the modal matrix in the extended state space and the modal matrix in the original space has been derived. Numerical examples are provided to illustrate the results.

A Reduced Second-Order Approach for Linear Viscoelastic Oscillators

2010 ◽  
Vol 77 (4) ◽  
Author(s):  
Sondipon Adhikari
Keyword(s):  
Past History ◽  
Kernel Functions ◽  
Second Order ◽  
Order System ◽  
Closed Form Expression ◽  
Internal Variables ◽  
Dynamical Response ◽  
Convolution Integrals ◽  
History Of ◽  
Second Order Systems

This paper proposes a new approach for the reduction in the model-order of linear multiple-degree-of-freedom viscoelastic systems via equivalent second-order systems. The assumed viscoelastic forces depend on the past history of motion via convolution integrals over kernel functions. Current methods to solve this type of problem normally use the state-space approach involving additional internal variables. Such approaches often increase the order of the eigenvalue problem to be solved and can become computationally expensive for large systems. Here, an approximate reduced second-order approach is proposed for this type of problems. The proposed approximation utilizes the idea of generalized proportional damping and expressions of approximate eigenvalues of the system. A closed-form expression of the equivalent second-order system has been derived. The new expression is obtained by elementary operations involving the mass, stiffness, and the kernel function matrix only. This enables one to approximately calculate the dynamical response of complex viscoelastic systems using the standard tools for conventional second-order systems. Representative numerical examples are given to verify the accuracy of the derived expressions.

Iterative Methods for Eigenvalues of Viscoelastic Systems

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Sondipon Adhikari ◽  
Blanca Pascual
Keyword(s):  
Past History ◽  
Iterative Algorithms ◽  
Kernel Functions ◽  
Degree Of Freedom ◽  
Internal Variables ◽  
State Space Approach ◽  
Convolution Integrals ◽  
Complex Eigenvalues ◽  
History Of ◽  
Space Approach

This paper proposes a new iterative approach for the calculation of eigenvalues of single and multiple degree-of-freedom viscoelastic systems. The Biot model of viscoelasticity is assumed. With this model, the viscoelastic forces depend on the past history of motion via convolution integrals over exponentially decaying kernel functions. Current methods to solve this type of problem normally use the state-space approach involving additional internal variables. Such approaches often increase the order of the eigenvalue problem to be solved and can become computationally expensive for large systems. The method proposed in this paper is aimed to address this issue. In total, five iterative algorithms for the real and complex eigenvalues of single and multiple degree-of-freedom systems have been proposed. The results are obtained in terms of explicit closed-form expressions. This enables one to approximately calculate the eigenvalues of complex viscoelastic systems using the eigenvalues of the underlying elastic systems. Representative numerical examples are given to verify the accuracy of the derived expressions.

A non-linear model for elastic hysteresis in the time domain: Implementation for multiple degrees of freedom

2021 ◽  
pp. 095440622198938
Author(s):  
MMS Dwaikat ◽  
C Spitas ◽  
V Spitas
Keyword(s):  
Time Domain ◽  
Degrees Of Freedom ◽  
Past History ◽  
A Priori ◽  
Dissipated Energy ◽  
Multiple Degrees Of Freedom ◽  
Frequency Correction ◽  
History Of ◽  
Proposed Modification ◽  
The Time Domain

A model that captures the weak frequency sensitivity of elastic hysteretic damping is proposed for the time-domain simulation of structures with multiple degrees of freedom (MDOF) under free or forced vibration. The model is based on a recently proposed modification to the conventional single degree of freedom (SDOF) viscous damping model, utilising a correction factor computed based on the local instantaneous response to adjust the damping coefficient such that the dissipated energy remains insensitive to the frequency characteristics of the motion. The model compares favourably to the well-established viscous (incl. Collar’s frequency correction), Rayleigh and Reid MDOF models, is applicable to any type of loading and, unlike other classes of damping models, such as Rayleigh, modal, Bouc-Wen, Biot, and Collar/Neumark, does not require extensive calibration, knowledge of the past history of motion, or a priori knowledge of the excitation characteristics and frequency.

scholarly journals Boosting CNN-based primary quantization matrix estimation of double JPEG images via a classification-like architecture

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Benedetta Tondi ◽  
Andrea Costanzo ◽  
Dequ Huang ◽  
Bin Li
Keyword(s):  
Deep Learning ◽  
Past History ◽  
A Priori ◽  
Superior Performance ◽  
Regression Problem ◽  
Practical Applications ◽  
Matrix Estimation ◽  
Compressed Images ◽  
History Of ◽  
The One

AbstractEstimating the primary quantization matrix of double JPEG compressed images is a problem of relevant importance in image forensics since it allows to infer important information about the past history of an image. In addition, the inconsistencies of the primary quantization matrices across different image regions can be used to localize splicing in double JPEG tampered images. Traditional model-based approaches work under specific assumptions on the relationship between the first and second compression qualities and on the alignment of the JPEG grid. Recently, a deep learning-based estimator capable to work under a wide variety of conditions has been proposed that outperforms tailored existing methods in most of the cases. The method is based on a convolutional neural network (CNN) that is trained to solve the estimation as a standard regression problem. By exploiting the integer nature of the quantization coefficients, in this paper, we propose a deep learning technique that performs the estimation by resorting to a simil-classification architecture. The CNN is trained with a loss function that takes into account both the accuracy and the mean square error (MSE) of the estimation. Results confirm the superior performance of the proposed technique, compared to the state-of-the art methods based on statistical analysis and, in particular, deep learning regression. Moreover, the capability of the method to work under general operative conditions, regarding the alignment of the second compression grid with the one of first compression and the combinations of the JPEG qualities of former and second compression, is very relevant in practical applications, where these information are unknown a priori.

Identification of Multi-Degree of Freedom Systems With Nonproportional Damping Using the Resonant Decay Method

2004 ◽  
Vol 126 (2) ◽  
pp. 298-306 ◽  
Author(s):  
Steven Naylor ◽  
Michael F. Platten ◽  
Jan R. Wright ◽  
Jonathan E. Cooper
Keyword(s):  
Measurement Noise ◽  
Mode Shapes ◽  
Damping Matrix ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Rigid Body Modes ◽  
Nonproportional Damping ◽  
Modal Mass ◽  
Damped Systems ◽  
Modal Space

This paper describes an extension of the force appropriation approach which permits the identification of the modal mass, damping and stiffness matrices of nonproportionally damped systems using multiple exciters. Appropriated excitation bursts are applied to the system at each natural frequency, followed by a regression analysis in modal space. The approach is illustrated on a simulated model of a plate with discrete dampers positioned to introduce significant damping nonproportionality. The influence of out-of-band flexible and rigid body modes, imperfect appropriation, measurement noise and impure mode shapes is considered. The method is shown to provide adequate estimates of the modal damping matrix.

scholarly journals Proposal of a Viscous Model for Nonviscously Damped Beams Based on Fractional Derivatives

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Mario Lázaro ◽  
Jose M. Molines-Cano ◽  
Ignacio Ferrer ◽  
Vicente Albero
Keyword(s):  
Fractional Derivatives ◽  
Viscoelastic Materials ◽  
One Dimensional ◽  
Damping Matrix ◽  
Convolution Integrals ◽  
Stiffness Matrices ◽  
History Of ◽  
Numerical Tools ◽  
Theoretical Results ◽  
Modal Space

Viscoelastic materials are widely used in structural dynamics for the control of the vibrations and energy dissipation. They are characterized by damping forces that depend on the history of the velocity response via hereditary functions involved in convolution integrals, leading to a frequency-dependent damping matrix. In this paper, one-dimensional beam structures with viscoelastic materials based on fractional derivatives are considered. In this work, the construction of a new equivalent viscous system with fictitious parameters but capable of reproducing the response of the viscoelastic original one with acceptable accuracy is proposed. This allows us to take advantage of the well-known available numerical tools for viscous systems and use them to find response of viscoelastic structures. The process requires the numerical computation of complex frequencies. The new fictitious viscous parameters are found to be matching the information provided by the frequency response functions. New mass, damping, and stiffness matrices are found, which in addition have the property of proportionality, so they become diagonal in the modal space. The theoretical results are contrasted with two different numerical examples.

Damping Identification for Mistuned Blisks

2010 ◽  
Author(s):  
Darren E. Holland ◽  
Bogdan I. Epureanu ◽  
Sergio Filippi
Keyword(s):  
Frequency Response ◽  
Forced Response ◽  
Measurement Noise ◽  
Mode Shapes ◽  
Viscous Damping ◽  
Complex Frequency ◽  
Structural Damping ◽  
General Methodology ◽  
Damping Matrix ◽  
Applied Forces

A novel structural damping identification method is presented. The approach is robust with respect to measurement noise and makes use of highly effective reduced-order-models (ROMs). Several different methods are currently available for damping identification. Most of these techniques can be grouped into two types based on the nature of the system information that is needed for the damping identification. The first type involves measuring damped eigenvalues and mode shapes, and does not require measurements of the system excitation. The second type involves measuring the forces applied to the system and constructing (full) frequency response functions. In contrast to existing techniques, the proposed method avoids complications involved in measuring damped modal characteristics or applied forces, while identifying structural damping only from displacement or velocity measurements. The focus of this work is identification of damping in systems with high modal density (such as cyclically symmetric systems) exemplified by blisks and bladed disks. First, a novel, general methodology for identifying (uniform) structural damping is presented. This method uses undamped tuned system mode shapes and a minimum of two measurements. Next, a more general methodology is formulated, which incorporates stiffness mistuning and uses ROMs for enhanced robustness and fast calculations. Validation of the damping identification is done by comparing the performance of the viscous damping method by Lee et al. with the proposed method. In Lee’s method, the complex frequency response function is used to determine a viscous damping matrix. This method is adjusted to identify structural damping where the damping matrix is now diagonal. For a low dimensional system and noiseless measurements, both Lee’s method and the proposed approach correctly identify the structural damping. Introducing measurement noise causes inaccuracies in the identification results obtained using Lee’s method, while the proposed method remains accurate. Next, two measurement filters are proposed to further increase the accuracy and robustness of the proposed damping identification by reducing the effect of measurement noise. The first filter applies to measurements which are approximately equal in amplitude and phase although they occur at different frequencies. The second filter removes measurements where the magnitude of the response is low. These filters are implemented for a complex validation structure: a one-piece bladed disk with stiffness mistuning. Simulated forced response measurements are generated by ANSYS and corrupted by noise. Next, measurements of the modal amplitudes and phases for the blisk are obtained through an elaborate and complex process of measurement point selection, mode selection, and data filtering similar to the one associated with mistuning identification. These filtered measurements are then shown to be accurate for use in the novel damping identification methodology.

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