scholarly journals Corrigendum to “Modal Mass and Length of Mode Shapes in Structural Dynamics”

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
M. Aenlle ◽  
Martin Juul ◽  
R. Brincker
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Structural Dynamics ◽  
Mode Shape ◽  
Physical Meaning ◽  
Frequency Response Function ◽  
Degrees Of Freedom ◽  
Mode Shapes ◽  
Length Measure ◽  
Modal Mass

The literature about the mass associated with a certain mode, usually denoted as the modal mass, is sparse. Moreover, the units of the modal mass depend on the technique used to normalize the mode shapes, and its magnitude depends on the number of degrees of freedom (DOFs) used to discretize the model. This has led to a situation where the meaning of the modal mass and the length of the associated mode shape is not well understood. As a result, normally, both the modal mass and the length measure have no meaning as individual quantities, but only when they are combined in the frequency response function. In this paper, the problems of defining the modal mass and mode shape length are discussed, and solutions are found to define the quantities in such a way that they have individual physical meaning and can be estimated in an objective way.

scholarly journals Modal Mass and Length of Mode Shapes in Structural Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
M. Aenlle ◽  
Martin Juul ◽  
R. Brincker
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Structural Dynamics ◽  
Mode Shape ◽  
Physical Meaning ◽  
Frequency Response Function ◽  
Degrees Of Freedom ◽  
Mode Shapes ◽  
Length Measure ◽  
Modal Mass

The literature about the mass associated with a certain mode, usually denoted as the modal mass, is sparse. Moreover, the units of the modal mass depend on the technique which is used to normalize the mode shapes, and its magnitude depends on the number of degrees of freedom (DOFs) which is used to discretize the model. This has led to a situation where the meaning of the modal mass and the length of the associated mode shape is not well understood. As a result, normally, both the modal mass and the length measure have no meaning as individual quantities but only when they are combined in the frequency response function. In this paper, the problems of defining the modal mass and mode shape length are discussed, and solutions are found to define the quantities in such a way that they have individual physical meaning and can be estimated in an objective way.

Estimation of Frequency Response Function on Rotational Degrees of Freedom of Structures

1999 ◽  
Author(s):  
Naoki Hosoya ◽  
Takuya Yoshimura
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Structural Dynamics ◽  
Frequency Response Function ◽  
Degrees Of Freedom ◽  
Estimation Procedure ◽  
Rigid Block ◽  
Measurement Point ◽  
Beam Structure ◽  
Rotational Degrees Of Freedom

Abstract In conventional vibration testing, measurement of frequency response function (FRF) has been limited to translational degrees of freedom (DOF). Rotational DOFs have not been treated in experimental analysis. However, the rotational DOF is indispensable in further analysis, such as substructure synthesis, prediction of structural dynamics modification, etc. Hence, measurement of FRFs on rotational DOF is essential for expanding applicability of experimental modal analysis. This paper proposes a new method for FRF estimation on rotational DOF of structures. The following is the estimation procedure: A rigid block is fixed on the measurement point of the structure; the block is excited by conventional impact hammer; the inner force and the response of the connection point including rotational DOFs are estimated; and lastly, the FRF including rotational DOF at the connection point of the structure is obtained. The feasibility of the method is investigated experimentally by applying it to a beam structure.

scholarly journals Frequency Response Function Measurement on Simplified Disc Brake Model

2018 ◽  
Vol 68 (3) ◽  
pp. 225-230
Author(s):  
Úradníček Juraj ◽  
Miloš Musil ◽  
Michal Bachratý
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Degrees Of Freedom ◽  
Disc Brake ◽  
Damping Properties ◽  
Function Measurement ◽  
Two Degrees Of Freedom ◽  
Frequency Response Function Measurement

AbstractThe paper describes role of non-proportional damping in flutter type instability, demonstrated on simplified disc brake model. The discrete two degrees of freedom system is considered to imply damping induced instability through a system eigenvalues evaluation. The Frequency Response Function (FRF) is further calculated from measurements on the physical disc brake model. From FRF, damping properties are estimated and discussed. Several different loading states of the pad versus disc are considered to show loading impact on FRF and thus damping of the system.

Frequency Response-Based Indirect Load Identification Using Optimum Placement of Strain Gages and Accelerometers

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Hana'a M. Alqam ◽  
Anoop K. Dhingra
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Structural Response ◽  
Mode Shapes ◽  
Load Identification ◽  
Strain Gages ◽  
Design Algorithm ◽  
Displacement Mode ◽  
Optimum Sensor

This paper presents an approach for indirect identification of dynamic loads acting on a structure through measurement of structural response at a finite number of optimally selected locations. Using the concept of frequency response function (FRF), the structure itself is considered as a load transducer. Two different types of sensors are investigated to measure the structural response. These include a use of accelerometers that leads to the identification of the displacement mode shapes. The second measurement approach involves a use of strain gages since strain measurements are directly related to imposed loads. A use of mixed strain-acceleration measurements is also considered in this work. Optimum sensor locations are determined herein using the D-optimal design algorithm that provides most precise load estimates. The concepts of indirect load identification, strain frequency response function (SFRF), displacement frequency response function (DFRF), along with the optimal locations for sensors are used in this paper. The fundamental theory for strain-based modal analysis is applied to help estimate imposed harmonic loads. The similarities and differences between acceleration-based load identification and strain-based load identification are discussed through numerical examples.

A Simple Method for Extracting Normal Modes

1993 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Response Function ◽  
Frequency Response Function ◽  
Normal Modes ◽  
Mode Shapes ◽  
Phase Information ◽  
Simple Method ◽  
Resonant Frequencies ◽  
Complex Modes

Abstract A simple method for extracting the normal modes of structures is developed. The frequency response function relation between the complex and the normal modes is derived and a technique is developed to calculate the normal modes from the identified (damped) complex modes. In this method, only the magnitude and phase information at resonant frequencies are needed for extracting the normal mode shapes. A numerical example is employed to illustrate the theory. The results indicate that this method is more robust than other methods when the frequency response measurements are contaminated with noise.

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