Table of Contents
What is effective mass in vibration?
The effective mass offers a physical interpretation of a physical system with multiple modes of vibration being excited dynamically from a base, similar to testing that occurs for many systems. The concept was proposed in the early 70’s by Bamford[1] with others.
What is the modal mass concept?
], the modal mass is defined as a scaling parameter for the mode shapes, i.e., it is used to convert the original unscaled mode shape vector to the scaled (mass-normalized) mode shape vector .
How do you calculate modal mass?
The modal mass, associated with mode m, is calculated as mm=aTmMam(10) where am is the normalised mode shape vector, aTm is its transpose (row vector) and M is the system’s mass matrix. The modal stiffness is calculated as km=ω2mmm(11) where ωm is the angular frequency of the mode.
What is Generalised mass?
Generalized mass The “generalized mass” associated with mode is. where is the structure’s mass matrix and is the eigenvector for mode . The superscripts N and M refer to degrees of freedom of the finite element model.
What do mode shapes tell us?
The terms mode shape or natural vibration shape are used in structural dynamics. A mode shape describes the deformation that the component would show when vibrating at the natural frequency. Thus, natural frequencies and mode shapes indicate how the structure behaves under a dynamic load.
How do you determine the effective mass of an electron?
the effective mass is determined by the band structure E(k). It can be calculated by mij-1 = (2pi/h)2d2E/dkij2. Furthermore, it can be measured by cyclotron resonanz.
What is the sum of the effective masses of all modes?
If the effective masses of all modes are added in any particular direction, the sum should give the total mass of the model, except for mass at kinematically restrained degrees of freedom.
What is the concept of modal mass?
The concept of modal mass is addressed in the classical books of structural dynamics [ 5, 6 ], modal analysis [ 1 – 4, 10 ], and also in research papers [ 11, 12 ]. In some books of classical dynamics [ 5, 13 ], the concept of modal mass has also been named as generalized mass or effective modal mass. 1.1. The Concept of Effective Mass
What is modal mass and scaling factor?
In [ 1 – 3 ], the modal mass is defined as a scaling parameter for the mode shapes, i.e., it is used to convert the original unscaled mode shape vector to the scaled (mass-normalized) mode shape vector . The concept of scaling factor , which is related to the modal mass by is also used in the field of structural dynamics [ 4 ].
What is the ratio of effective mass to total mass used for?
Ideally, the ratio of effective mass to total mass can be useful for determining whether or not a sufficient number of modes have been extracted for the “ Mode Superposition ” for further analysis. Modal superposition is a solution technique for all linear dynamic analyses.