A new analysis using averaging over an uncertain set of system initial conditions yields the conclusion that these quantities should not be viewed as interchangeable, and a new definition and calculation is proposed for state in mode participation factors. Modal participation factors are scalars that measure the interaction between the modes and the directional excitation in a given reference frame. The member-wise modal in-plane displacement participation is calculated as in [16] : (30) P k − displacement = ∫ L p k − displacement dx ∑ k = 1 n ∫ L p k − displacement dx , where p k − Modal Analysis: Mass Participation. It is defined as. The Effective mass factors associated with each mode represents the amount of system mass participating Modal participation factors are scalars that measure the interaction between the modes and the directional excitation in a given reference frame. Nov 26, 2019 · The paper studies an extension to nonlinear systems of a recently proposed approach to the definition of modal participation factors. Therefore, the first mode is . Oct 1, 2021 · The selective modal analysis (SMA) framework proposed in Pérez-Arriaga et al. 1, You must turn them "on" check the "Output" normalisation field in the "Eigen-value/frequency solver" node (the one deepest down there) and change from RMS to Mass matrix mod1_u. Meanwhile many codes, such as ASCE Jan 1, 2019 · This conversion from the twist angle to displacement produces modal participation factors that are consistent for all modes, including torsion. It has even been codified in many of the codes of record. Fbase(ω)=m ω 1+ H Uo(ω) (21) ωn ωn. Expand. The effective modal mass meff,i for mode i is mÖ 2 are known as modal participation factors. The modal mass participation ratio is widely used as the metric to determine the relative significance of modes in a modal response spectrum analysis. Larger values indicate a stronger contribution to the dynamic response. The modal participation factor *i for mode i is mÖ ii Li * i (26) The modal participation vector is thus » ¼ º « ¬ ª * 0. May 30, 2018 · Modal participation factors were introduced over a quarter century ago as a way of measuring the relative participation of modes in states, and of states in modes, for linear time-invariant systems. Modal participation can be output from a modal frequency response analysis using the PFMODE output request card. doc . 2 Variables associated with the natural modes of a model. 7157 (27) The coefficient vector L and the modal participation vector * are identical in this example because the generalized mass matrix is the identity matrix. Direction factors for a particular mode are The modal mass participation factors provide an understanding of the influence of each mode of vibration on the behavior of the building. A case study is presented to aid the reader understand under what conditions each definition of MPF applies, its physical interpretation and which definitions A. An example with 3 degrees of free-dom showing the individual modal contributions is shown in Figure 1. The Effective mass factors associated with each mode represents the amount of system mass participating Jun 10, 2009 · Modal participation factors revisited: One definition replaced by two. Factor = Transpose ( Mode Shape) * Mass. (1982) enabled accurate identification of the elements of the system structure associated with specific eigenmodes based on the so-called participation factors (PFs). For real systems there is often mass participating in the forcing function (such as the mass of ground in an earthquake) and mass participating in inertia effects (the mass of the structure itself, Meq ). The selection rule represented in this article makes it possible to reflect the contributions of each mode on the behavior of a structure. The paper considers both the linear and generalized eigenvalue problems for the calculation of the Jan 1, 2014 · It was also pointed out that when the scaled matrix [V] contains ODS’s and the un-scaled matrix [U] contains mode shapes, the columns of the scale factor matrix [W] are a measure of the participation of each mode in each ODS, more commonly known as modal participation factors. So because modeshape value are positive and negative, mass positive, it's normal to get negative modal participation factor. function [Result]=ERA (Y,fs,ncols,nrows,inputs,cut,shift,EMAC_option) Modal and mass participation factors are highly correlated. On the other hand, modes with low effective masses cannot be readily excited in this manner. As the number of eigenvalues to be calculated has to be given it is the Cumulative Effective Mass Participation Factor (CEMPF) in each direction that is used to indicate up to how many modes should the user go. For example, ASCE 7-05 (7-10 is at home, sorry), Section 12. Modes with relatively high effective masses can be readily excited by base excitation. Therefore, the first mode is Determining which modes in modal analysis to focus on can be hard. It is the modal participation factor commonly used in earthquake engineering to represent a general structural response through a summation and integration of all modal responses. The effective modal mass meff,i for mode i is mÖ 3. Since their introduction by Verghese, Pérez-Arriaga and Schweppe, participation factors have been used for analysis, order reduction and controller design in a variety of fields. The modal participation factor Γ is a comparison of these two masses. Γαi= 1 mα ϕN αM NMT M i (no sum over α We would like to show you a description here but the site won’t allow us. For example, Van Lagenhove and Brughmans [ 26 ] used the concept to identify the optimal location for sensors [ 27 ] to correlate experimental and numerical data. 0 (100%) Mar 2, 2010 · The modal participation factor matrix \(MPF\) is a \(n_m \times ndf\) matrix (where ndf = 3 in 2D and 6 in 3D), where each row contains the modal participation factors for each DOF. The modal participation factors are available as global variables, and these can for example be displayed in a table using a Global Evaluation node under Derived Values in the Results branch. View in full-text Context 2 Determining which modes in modal analysis to focus on can be hard. Example file is provided for the identification of 2DOF system subject to impulse excitation with added uncertainty (gaussian white noise) to the response. After an eigenfrequency step has been used to find the eigenvalues of a model, ABAQUS/Standard automatically calculates the participation factor, the effective mass, and the composite modal damping for each mode so that these variables are available for use in Apr 16, 2015 · A modal influence factor defined by modal participation factors for each mode is presented for the selection of the best solution from among Pareto solutions. Then in the Derived Values use a "global Jul 15, 2019 · Eigensystem realization algorithm with modal indicators including consistent mode indicator and modal participation factor. In this paper, we will propose the concept of modal participation factor for the numerical instability in the dual BEM for exterior acoustics. You may notice that (if both modes are normalized to 1. Nov 27, 2021 · The modal parameter clusters shown in Figs. ) • In doing modal analysis, we should include most of the significant modes, meaning that we should extract a sufficient number of modes to evaluate. Additionally, the cumulative mass participation factor of the first three modes is approximately 90 %, which is consistent with findings by Pejovic et al. i, is a variable that indicates how strongly motion in the global x -, y - or z -direction or rotation about one of these axes (indicated by i, i = 1, 2, …, 6) is represented in the eigenvector of that mode. 11, 12, and 13 can be grouped together based on the closeness of the modal frequencies and damping along with the similarity in the associated modal participation vectors or associated state vector form of the modal participation vectors (see Sect. The term "ratio" is less meaningful than the term factor May 23, 2011 · Hi. 6 Reduction of a Redundant Interface to a Single Point 4. 1 states that, Answer: The fixed-mass participation ratio may be calculated as follows: Export the Joint Masses table to Excel by selecting Analysis Results > Joint Output > Joint Masses. This is projecting the eigenvectors onto the rigid body vectors {r} and comparing it with the eigenvectors projected onto themselves (which is 1. Direction factors therefore sum to 100. Participation factors are nondimensional scalars that measure the interaction between the modes and the state variables of a linear system. 3 Modal Participation Factors and Modal Masses for Base-Shake Analyses 3. Apr 18, 2012 · Answer: For each mode, modal direction factors identify the predominance of excitation directions. Each column of Fnr gives the participation factors for all modes for one DOF of 7 Modal Effective Mass 7. Each factor is a percentage which relates its component (translation along X or Y, or rotation about Z) to the total displacement over all diaphragms and stories. ⁢. Moreover, when a set of time or frequency domain waveforms is Mode Participation Factor (cont. Learn how mode participation factor and effective mass help identify significant modes. Oct 21, 2020 · This video lesson answers the questions: How do I determine the sufficient number of modes to extract, and how do I find the most critical natural frequencie The effective modal mass provides a method for judging the “significance” of a vibration mode. May 30, 2018 · In this paper we review different definitions of Modal Participation Factor (MPF) available in the literature and propose a simple classification and unified concept for their application with particular focus in aerospace engineering. While the definition is general, the resulting measures depend on the assumed uncertainty law governing the system initial condition, as in the linear Modal participation factors are scalars that measure the interaction between the modes and the directional excitation in a given reference frame. Jun 10, 2009 · Modal participation factors were introduced over a quarter century ago as a way of measuring the relative participation of modes in states, and of states in modes, for linear time-invariant systems. 14. We then present the proposed approach to study the propagation of dynamic modes in power networks through participation factor analysis of complex frequency variables, which is the main contribution of this work. A matrix of all participation factors for all modes is: 1 That is, each row of Fqr is an ( , (the participation factors for one mode) . The reaction force at the base Fbase due to the enforced acceleration Uo in the frequency domain is given by: ω 2. Effective mass factors. Modal Mass Participation Factor The modal effective mass was initially derived for a single degree of freedom system subject to an enforced motion through the base. Subsequently, the concept of PFs gained widespread use in power engineering and other applications Another participation factor is also available, which may be more relevant. 4. Modal participation factors were introduced over a quarter century ago as a way of measuring the relative participation of modes in states, and of states in modes, for linear time-invariant systems The participation factor for mode α α in direction i, Γαi Γ α. , 1995, Chen et al. • If the ratio of effective mass to total mass is close to 1, it means most of The modal effective mass is a modal dynamic property of a structure associated with the modal characteristics; natural frequencies, mode shapes, generalised masses, and participation factors. Jul 12, 2009 · The definition of the modal participation factor of mode i in state j refers to a condition in which the excited system state is the j-th one, as indicated by [25]. These modes can be systems modes in a modal frequency response analysis, or component modes from CMS superelement subsystems. It is found that modal reactions at supports proportionally describe the magnitudes of the modal participation factors. 9. The modal effective mass is a measure to classify the importance of a mode shape when a structure is Aug 2, 2022 · Modal Participation Factors (MPF) have several definitions; the one defined in MSC Nastran follows the civil engineering definition you gave in your post. The Effective mass factors associated with each mode represents the amount of system mass participating Modal participation represents the complex contribution of a structure or fluid mode to a response. There are This paper proposes an approach to determine the participation of algebraic variables in power system modes. 2 are known as modal participation factors. Square the Participation Factor table and divide this value by total mass. Therefore, the first mode is A. , 1996) and discrete system (Chen et al. Mar 10, 2016 · This should give you consistent modal participation factors. Once grouped in this fashion, the modal Oct 11, 2012 · 1) For Modal Participation Factor, Negative value are normal. 1 Introduction The modal effective mass is a modal dynamic property of a structure asso­ ciated with the modal characteristics; natural frequencies, mode shapes, generalised masses, and participation factors. It follows from Property 4, that LMIF (27) is a cross-correlation between the i th and j th mode components in all system states at a lag of zero. The modal effective mass is a measure to classify the importance of a mode shape when a structure is excited by base acceleration (enforced acceleration). The frequency response of an MDOF system can be presented in the same forms as the SDOF case. The approach is based on a new interpretation of the classical participation factors, as well as on the definition of adequate output variables of the system's state-space representation. indeed the mass participation factors (for linear displacements along u,v,w only, no rotation yet) are awailable in 4. Output variables May 1, 2024 · In this section, we first recall standard small-signal stability analysis using modal participation factors in the classical sense. Apr 12, 2023 · Additionally, the modal mass participation results of a structure, and its modes can be reviewed by clicking the Mass Participation tab. 3). The participation factor results are available as predefined variables in the Definitions submenu for the component. References 10/06/00 i Craig Bampton_1. 0 if mass normalized eigenvectors are requested). Participation factors have proved their usefulness in the field of electric power systems and in other applications. Modal participation factor. 5 Application of the Craig-Bampton Method to Modal Synthesis 3. 2) For Modal Participating Mass ratio, All values should be positive and less than 1. An efficient method, called the modal reaction method, for calculating the modal participation factors for support motion problems is proposed. Oct 1, 2021 · Lyapunov modal interaction factor (LMIF) is the relative participation of the i th and j th modes in the squared L 2-norm of all the states (27) E ¯ z i j = ∑ k = 1 n E x k i j. The first bending modes of the Modal participation factor is a scalar that measures the relative contribution of a vibration mode to a system state for a linear system. [34]. Thus, the modal participation factor for support motion problems can be calculated very efficiently, saving more than 99 per cent The eigenvalues (EIGVAL), eigenfrequencies in cycles/time (EIGFREQ), generalized masses (GM), composite modal damping factors (CD), participation factors for degrees of freedom 1–6 (PF1–PF6), and modal effective masses for degrees of freedom 1–6 (EM1–EM6) are automatically written to the output database as history data. 2 of 54 Jun 23, 2009 · This paper presents a new fundamental approach to modal participation analysis of linear time-invariant systems, leading to new insights and new formulas for modal participation factors. Due to the neater formulation Sep 26, 2023 · The use of the term “modal participation factor” is also a common topic in experimental modal analysis, in which different definitions have been proposed [24,25]. 2. Oct 21, 2020 · This video lesson answers the questions: How do I determine the sufficient number of modes to extract, and how do I find the most critical natural frequencie The modal participation factor *i for mode i is mÖ ii Li * i (26) The modal participation vector is thus » ¼ º « ¬ ª * 0. If all modes in a model are used, then this method is fairly rigorous in terms of overall The modal participation factors can be easily calculated during the real eigenvalue analysis run (in Rigid Format 3, for example). ABAQUS Theory Manual. 2379 1. A definition is given for local mode-in-state participation factors for smooth nonlinear autonomous systems. 5. These terms control the influence of on the modal response. This can be judged by the ratio between the effective mas and the total mass. 4 The Load Transformation Matrix (LTM) 3. Sum all joint masses to find the total mass. 0 at roof level for example) L 1 /M 1 > L 2 /M 2 since f 11 and f 21 are of the same sign while f 12 and f 22 are of opposite signs. The participation factor identifies the amount each mode contributes to the total response at a particular point. The modal participation factor for a certain mode \(i\) and DOF \(j\) indicates how strongly the motion (or rotation) associated to that DOF is represented in the Vibrationdata 2 Á [@ +@ " This video shows how to compute the modal participation factor and the modal mass participation ratio manually using mode shapes obtained from ETABS software Mar 1, 2003 · The modal participation factor for both the continuous system (Chen et al. In the Modal Analysis user has the objective of obtaining the frequencies and shapes of each mode. Apr 1, 2015 · Therefore, the Modal Participation Factor (MPF) [87], which can be easily extracted directly in ANSYS, is fused with the natural frequencies to construct a novel objective function, serving the Oct 1, 2000 · Abstract. That is the higher the cumulative participation factor, the higher the cumulative mass participation. , 1997) were derived in structural dynamics. The mass participation factor represents the amount of mass associated with the specific frequency or mode of vibration. km oj ky la ch mv wi zq qd ez