Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 32

The mass matrix in multidimensional space follows from Newton’s law of point masses in free space.

(1.91)

Using the complex amplitude notation of harmonic motion this leads to:

(1.92)

For every mass m_i at node i the local mass matrix is depending on the available degrees of freedom for each mass node. For a two-dimensional system with {q}i={ui,vi}T we get:

(1.93)

The local matrices must by assembled for all degrees of freedom, so the system from Figure 1.17 will have the follwing mass matrix:

(1.94)