scholarly journals Reduced Mass-Weighted Proper Decomposition for Modal Analysis

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Venkata K. Yadalam ◽  
B. F. Feeny
Keyword(s):  
Modal Analysis ◽  
Mass Distribution ◽  
Mass Matrix ◽  
Linear Interpolation ◽  
Modal Identification ◽  
Distributed Parameter ◽  
Arbitrary Mass ◽  
Spring System ◽  
Mass Spring ◽  
Proper Orthogonal

A method of modal analysis by a mass-weighted proper orthogonal decomposition for multi-degree-of-freedom and distributed-parameter systems of arbitrary mass distribution is outlined. The method involves reduced-order modeling of the system mass distribution so that the discretized mass matrix dimension matches the number of sensed quantities, and hence the dimension of the response ensemble and correlation matrix. In this case, the linear interpolation of unsensed displacements is used to reduce the size of the mass matrix. The idea is applied to the modal identification of a mass-spring system and an exponential rod.

scholarly journals Reduced Mass-Weighted Proper Decomposition for Modal Analysis

2008 ◽  
Author(s):  
Venkata K. Yadalam ◽  
B. F. Feeny
Keyword(s):  
Modal Analysis ◽  
Mass Distribution ◽  
Mass Matrix ◽  
Linear Interpolation ◽  
Modal Identification ◽  
Lumped Mass ◽  
Arbitrary Mass ◽  
Spring System ◽  
Mass Spring ◽  
Proper Orthogonal

A method of modal analysis by proper orthogonal decomposition for large-order systems of arbitrary mass distribution is outlined. The method involves reduced-order modeling of the system mass distribution so that the discretized mass matrix dimension matches the number of sensed quantities, and hence the dimension of the response ensemble and correlation matrix. In this case, the linear interpolation of unsensed displacements is used to perform an effective lumped mass homogenization. The idea is applied to the modal identification of a mass-spring system and an exponential rod.

scholarly journals Scaling Mode Shapes in Output-Only Structure by a Mass-Change-Based Method

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Liangliang Yu ◽  
Hanwen Song
Keyword(s):  
Modal Analysis ◽  
Mass Distribution ◽  
Null Space ◽  
Mass Matrix ◽  
Small Mass ◽  
Mass Change ◽  
Mode Shapes ◽  
Distribution Matrix ◽  
Distribution Vector ◽  
Output Only

A mass-change-based method based on output-only data for the rescaling of mode shapes in operational modal analysis (OMA) is introduced. The mass distribution matrix, which is defined as a diagonal matrix whose diagonal elements represent the ratios among the diagonal elements of the mass matrix, is calculated using the unscaled mode shapes. Based on the theory of null space, the mass distribution vector or mass distribution matrix is obtained. A small mass with calibrated weight is added to a certain location of the structure, and then the mass distribution vector of the modified structure is estimated. The mass matrix is identified according to the difference of the mass distribution vectors between the original and modified structures. Additionally, the universal set of modes is unnecessary when calculating the mass distribution matrix, indicating that modal truncation is allowed in the proposed method. The mass-scaled mode shapes estimated in OMA according to the proposed method are compared with those obtained by experimental modal analysis. A simulation is employed to validate the feasibility of the method. Finally, the method is tested on output-only data from an experiment on a five-storey structure, and the results confirm the effectiveness of the method.

scholarly journals Obtaining Mode Shapes through the Karhunen-Loève Expansion for Distributed-Parameter Linear Systems

2002 ◽  
Vol 9 (4-5) ◽  
pp. 177-192 ◽  
Author(s):  
Claudio Wolter ◽  
Marcelo A. Trindade ◽  
Rubens Sampaio
Keyword(s):  
Linear Systems ◽  
Random Noise ◽  
Mode Shapes ◽  
Distributed Parameter ◽  
Spectral Technique ◽  
Physical Experiments ◽  
Analysis And Synthesis ◽  
Impulsive Forces ◽  
Mass Spring ◽  
Proper Orthogonal

The Karhunen-Loève expansion is a powerful spectral technique for the analysis and synthesis of dynamical systems. It consists in decomposing a spatial correlation matrix, which can be obtained through numerical or physical experiments. The decomposition produces orthogonal eigenfunctions or proper orthogonal modes, and eigenvalues that provide a measurement of how much energy is contained in each mode. The relation between KL modes and mode shapes of linear vibrating systems has already been derived and demonstrated for two and three dofs mass-spring-damper systems. The purpose of this paper is to extend this investigation to more complex distributed-parameter linear systems. A plane truss and a simply supported plate subjected to impulsive forces, commonly used in modal analysis are studied. The resulting KL modes are compared to the analytical mode shapes. Damping and random noise effects in the procedure performance are evaluated. Two methods for indirectly obtaining natural frequencies are also presented.

scholarly journals Full-Field Operational Modal Analysis of an Aircraft Composite Panel from the Dynamic Response in Multi-Impact Test

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1602
Author(s):  
Ángel Molina-Viedma ◽  
Elías López-Alba ◽  
Luis Felipe-Sesé ◽  
Francisco Díaz
Keyword(s):  
Modal Analysis ◽  
Energy Absorption ◽  
High Speed ◽  
Operational Modal Analysis ◽  
Modal Identification ◽  
Image Correlation ◽  
Composite Panel ◽  
Impact Excitation ◽  
Full Field ◽  
The Impact

Experimental characterization and validation of skin components in aircraft entails multiple evaluations (structural, aerodynamic, acoustic, etc.) and expensive campaigns. They require different rigs and equipment to perform the necessary tests. Two of the main dynamic characterizations include the energy absorption under impact forcing and the identification of modal parameters through the vibration response under any broadband excitation, which also includes impacts. This work exploits the response of a stiffened aircraft composite panel submitted to a multi-impact excitation, which is intended for impact and energy absorption analysis. Based on the high stiffness of composite materials, the study worked under the assumption that the global response to the multi-impact excitation is linear with small strains, neglecting the nonlinear behavior produced by local damage generation. Then, modal identification could be performed. The vibration after the impact was measured by high-speed 3D digital image correlation and employed for full-field operational modal analysis. Multiple modes were characterized in a wide spectrum, exploiting the advantages of the full-field noninvasive techniques. These results described a consistent modal behavior of the panel along with good indicators of mode separation given by the auto modal assurance criterion (Auto-MAC). Hence, it illustrates the possibility of performing these dynamic characterizations in a single test, offering additional information while reducing time and investment during the validation of these structures.

Dynamic Force and Torque Analysis of Spherical Four Link Mechanisms

1983 ◽  
Vol 105 (3) ◽  
pp. 492-497 ◽  
Author(s):  
A. T. Yang ◽  
Sun Zhishang
Keyword(s):  
Dynamic Analysis ◽  
Optimum Design ◽  
Mass Distribution ◽  
High Speed ◽  
Dynamic Force ◽  
Arbitrary Mass ◽  
Link Mechanism ◽  
Torque Analysis ◽  
Analytical Expressions

In this paper we present a dynamic analysis of a general spherical four-link mechanism whose links have arbitrary mass distribution. Results, which are in explicit analytical expressions in terms of inertia-induced forces and moments in links, are useful for optimum design of the mechanism under high-speed operation.

Graphene-Based Resonant Sensors for Detection of Ultra-Fine Nanoparticles: Molecular Dynamics and Nonlocal Elasticity Investigations

NANO ◽  
2015 ◽  
Vol 10 (02) ◽  
pp. 1550024 ◽  
Author(s):  
S. Kamal Jalali ◽  
M. Hassan Naei ◽  
Nicola Maria Pugno
Keyword(s):  
Molecular Dynamics ◽  
Nonlocal Elasticity ◽  
Md Simulations ◽  
Small Scale ◽  
Frequency Shifts ◽  
Resonant Sensors ◽  
Embedded Atom ◽  
Metal Metal ◽  
Spring System ◽  
Mass Spring

Application of single layered graphene sheets (SLGSs) as resonant sensors in detection of ultra-fine nanoparticles (NPs) is investigated via molecular dynamics (MD) and nonlocal elasticity approaches. To take into consideration the effect of geometric nonlinearity, nonlocality and atomic interactions between SLGSs and NPs, a nonlinear nonlocal plate model carrying an attached mass-spring system is introduced and a combination of pseudo-spectral (PS) and integral quadrature (IQ) methods is proposed to numerically determine the frequency shifts caused by the attached metal NPs. In MD simulations, interactions between carbon–carbon, metal–metal and metal–carbon atoms are described by adaptive intermolecular reactive empirical bond order (AIREBO) potential, embedded atom method (EAM), and Lennard–Jones (L–J) potential, respectively. Nonlocal small-scale parameter is calibrated by matching frequency shifts obtained by nonlocal and MD simulation approaches with same vibration amplitude. The influence of nonlinearity, nonlocality and distribution of attached NPs on frequency shifts and sensitivity of the SLGS sensors are discussed in detail.

scholarly journals Looseness localization for bolted joints using Bayesian operational modal analysis and modal strain energy

2018 ◽  
Vol 10 (11) ◽  
pp. 168781401880869 ◽  
Author(s):  
Yu-Jia Hu ◽  
Wei-Gong Guo ◽  
Cheng Jiang ◽  
Yun-Lai Zhou ◽  
Weidong Zhu
Keyword(s):  
Modal Analysis ◽  
Strain Energy ◽  
Damage Index ◽  
Operational Modal Analysis ◽  
Modal Identification ◽  
Bolted Joints ◽  
Mode Shapes ◽  
Bolted Connections ◽  
Modal Strain Energy ◽  
Beam Structures

Bayesian operational modal analysis and modal strain energy are employed for determining the damage and looseness of bolted joints in beam structures under ambient excitation. With this ambient modal identification technique, mode shapes of a damaged beam structure with loosened bolted connections are obtained based on Bayesian theory. Then, the corresponding modal strain energy can be calculated based on the mode shapes. The modal strain energy of the structure with loosened bolted connections is compared with the theoretical one without bolted joints to define a damage index. This approach uses vibration-based nondestructive testing of locations and looseness of bolted joints in beam structures with different boundary conditions by first obtaining modal parameters from ambient vibration data. The damage index is then used to identify locations and looseness of bolted joints in beam structures with single or multiple bolted joints. Furthermore, the comparison between damage indexes due to different looseness levels of bolted connections demonstrates a qualitatively proportional relationship.

scholarly journals Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

2013 ◽  
Vol 14 (5) ◽  
pp. 1228-1251 ◽  
Author(s):  
Yan Li ◽  
I-Liang Chern ◽  
Joung-Dong Kim ◽  
Xiaolin Li
Keyword(s):  
Upper Bound ◽  
Mesh Size ◽  
Front Tracking ◽  
Time Step ◽  
Mass System ◽  
Ode System ◽  
Spring System ◽  
Fabric Surface ◽  
Mass Spring ◽  
Eigen Frequency

AbstractWe use front tracking data structures and functions to model the dynamic evolution of fabric surface. We represent the fabric surface by a triangulated mesh with preset equilibrium side length. The stretching and wrinkling of the surface are modeled by the mass-spring system. The external driving force is added to the fabric motion through the “Impulse method” which computes the velocity of the point mass by superposition of momentum. The mass-spring system is a nonlinear ODE system. Added by the numerical and computational analysis, we show that the spring system has an upper bound of the eigen frequency. We analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the eigen-frequency This upper bound plays an important role in determining the numerical stability and accuracy of the ODE system. Based on this analysis, we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion. We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.

scholarly journals El conocimiento semántico en la representación de problemas de ecuaciones diferenciales como modelos matemáticos. [Semantic knowledge in the representation of problems of differential equations as mathematical models]

2018 ◽  
Vol 7 (3) ◽  
pp. 31
Author(s):  
Rosa Virginia Hernández ◽  
Luis Fernando Mariño ◽  
Mawency Vergel
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Equilibrium Point ◽  
Semantic Knowledge ◽  
External Representation ◽  
Damping Force ◽  
Mathematical Problems ◽  
Spring System ◽  
Linear Differential ◽  
Mass Spring

En este artículo se presenta la caracterización del conocimiento semántico evidenciado por un grupo de estudiantes en la representación externa a problemas de ecuaciones diferenciales lineales de segundo orden como modelos matemáticos. El trabajo fue cuantitativo de tipo exploratorio y descriptivo utilizando un cuestionario en la recolección de información. El soporte teórico que dio sentido al estudio fue el modelo de dos etapas propuesto por Mayer R. para la resolución de problemas matemáticos, el ciclo de modelación bajo la perspectiva cognitiva según Borromeo Ferri y la teoría de las representaciones de Goldin y Kaput. La investigación se centró específicamente en la fase de representación del modelo. Entre los principales hallazgos se destaca que cada participante hace su propia representación externa a conceptos como: sistema masa-resorte, peso, masa, punto de equilibrio, constante de elasticidad, punto de equilibrio, ley de Hooke, fuerza amortiguadora, fuerza externa, ley de Newton, entre otros. Se evidencian también dificultades en el tránsito del lenguaje natural al lenguaje matemático y la representación externa de cada una de los signos, símbolos o expresiones matemáticas inmersas en el problema de palabra, debido a que el resolutor tiene que construir un modelo mental de la situación real y plasmarlo en un modelo matemático. Lo anterior pone de manifiesto la importancia que tiene el conocimiento semántico en la etapa de traducción cuando se intentan resolver problemas como situaciones reales a modelar.Palabras clave: resolución de problemas, ciclos de modelación, problemas de palabra, representaciones externas, conocimiento extra matemático, modelación matemática. AbstractThis article presents the characterization of the semantic knowledge evidenced by a group of students in the external representation to problems of second order linear differential equations as mathematical models. The work was quantitative exploratory and descriptive using a questionnaire in the collection of information. The theoretical support that gave meaning to the study was the two-stage model proposed by Mayer R. for solving mathematical problems, the modeling cycle under the cognitive perspective according to Borromeo Ferri and the theory of representations of Goldin and Kaput. The research focused specifically on the representation phase of the model. Among the main findings is that each participant makes his own external representation to concepts such as: mass-spring system, weight, mass, equilibrium point, constant of elasticity, equilibrium point, Hooke's law, damping force, external force, law of Newton, among others. Difficulties are also evident in the transition from natural language to mathematical language and the external representation of each of the signs, symbols or mathematical expressions involved in the word problem, because the resolver has to construct a mental model of the real situation and translate it into a mathematical model. This demonstrates the importance of semantic knowledge in the translation stage when trying to solve problems as real situations to be modeledKeywords: problem solving, modeling cycles, word problems, external representations, extra mathematical knowledge, mathematical modeling.ResumoEste artigo apresenta a caracterização do conhecimento semântico evidenciado por um grupo de estudantes na representação externa a problemas de equações diferenciais lineares de segunda ordem como modelos matemáticos. O trabalho foi quantitativo exploratório e descritivo usando um questionário na coleta de informações. O suporte teórico que deu sentido ao estudo foi o modelo de dois estágios proposto por Mayer R. para resolver problemas matemáticos, o ciclo de modelagem sob a perspectiva cognitiva de acordo com Borromeo Ferri e a teoria das representações de Goldin e Kaput. A pesquisa focalizou especificamente a fase de representação do modelo. Entre os principais achados, cada participante faz sua própria representação externa para conceitos como: sistema de massa-mola, peso, massa, ponto de equilíbrio, constante de elasticidade, ponto de equilíbrio, lei de Hooke, força de amortecimento, força externa, lei de Newton, entre outros. As dificuldades também são evidentes na transição da linguagem natural para a linguagem matemática e a representação externa de cada um dos signos, símbolos ou expressões matemáticas envolvidas na palavra problema, porque o resolvedor tem que construir um modelo mental da situação real e traduzi-lo para um modelo matemático. Isso demonstra a importância do conhecimento semântico na fase de tradução ao tentar resolver problemas como situações reais a serem modeladas. ______________________________________________________ Palavras-chave: resolução de problemas, ciclos de modelagem, problemas de palavra, representação externa, conhecimento extra matemático, modelagem matemática

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