What are the differences between lumped and consistent mass matrices?

The consistent mass matrix is fully populated whereas lumped mass matrix is diagonal. Stiffness matrix: The stiffness matrix [k] is symmetric. The total stiffness matrix will be formed by assembling all the elements together to form a structure.

What is a lumped mass?

A lumped mass is a load that can be applied to a node in a static stress, natural frequency (modal) or modal superposition analysis. A lumped mass can be used to resist the translation or rotation of a node.

What is consistent mass system?

Abstract: A technique is developed for constructing a consistent mass matrix for vibration analysis of general structural configurations. It is shown that the natural frequencies obtained by using the consistent mass matrix are upper bounds to the exact solution.

What are the two types of mass matrix?

Lumped and.

Consistent.

Mass Matrices.

Why mass matrix is diagonal?

Each mass matrix has along its block diagonal the scalar mass, the inertia relative to the fuselage center of mass, and the inertia of the linkage. Off-diagonal terms represent inertial couplings within the system. The total mass matrix of the system is a summation of the mass matrices of each rigid body.

What is lumped mass structural dynamics?

6.4. For the lumped mass model the suspension components are considered lumped together to form a single mass. The mass is connected to the vehicle body at the wheel centre by a translational joint that only allows vertical sliding motion with no change in the relative camber angle between the road wheels and the body.

What is lumped mass of vehicle?

A lumped-mass model is used to simulate the engine thermal behaviour. It is composed of a total of 57 nodes: 29 for metallic masses, 15 for engine oil, 4 for coolant inside the engine, 3 for gases, 2 for air in the under bonnet.

What is lumped mass idealization?

Lumped mass idealization is used to discretize the original beam structure with distributed mass to a weightless beam with distributed masses substituted with lumped masses at different nodal points. A numerical example obtained from literature is given to illustrate the application of the present model.

What is meant by mass matrix?

In analytical mechanics, the mass matrix is a symmetric matrix M that expresses the connection between the time derivative of the generalized coordinate vector q of a system and the kinetic energy T of that system, by the equation. where denotes the transpose of the vector .

What is a generalized mass matrix?

The mass matrix M(p) describes the generalized mass and inertia of the system as a function of the vehicle pose. Off-diagonal terms represent inertial couplings within the system. The total mass matrix of the system is a summation of the mass matrices of each rigid body.

What is consistent mass matrix?

We have considered mass of the element as uniformly distributed throughout the element. Hence, these mass matrices are called as consistent matrices. We distribute the complete mass of the element at the two nodes. The mass matrix formed in this way is called as lumped mass matrix.

What lumped mass approach?

A lumped-mass method is introduced to study the propagation of elastic waves in two-dimensional periodic systems. First, it is used to calculate the band structure of an array of Pb columns in an epoxy background. Second, the method is applied to the same array of Pb columns in a soft rubber background.

What is the difference between consistent mass matrix and lumped mass matrix?

If µ = 0 and µ = 1 this combination reduces to theconsistent and lumped mass matrix, respectively. lumped mass matrix have diagonal elements only . but consistent mass matrix have element all over the matrix . lumped mass matrix have less accuracy as compared to consistent mass matrix .

A lumped mass is a load that can be applied to a node in a static stress, natural frequency (modal) or modal superposition analysis. A lumped mass can be used to resist the translation or rotation of a node. In which µ is a free scalar parameter. This is called the LC (“lumped- consistent ”) weighted mass.

What is the LC (lumped-consistent weighted mass)?

In which µ is a free scalar parameter. This is called the LC (“lumped-consistent”) weighted mass. matrix. If µ = 0 and µ = 1 this combination reduces to theconsistent and lumped mass matrix, respectively.

What is the difference between mass and consistent mass?

On the other hand when the entire mass of system is evenly distributed over it’s length it is known as consistent mass. Also in consistent mass system “same shape functions are used for both stiffness matrix and mass matrix”.