Next 1. Introduction 1. Introduction (cont'd) 1. Introduction (cont'd) 1. Introduction (cont'd) 1. Introduction (cont'd) 1. Introduction (cont'd) 1. Introduction (cont'd) 1. Introduction (cont'd) 2. Rayleigh-Ritz procedure 2. Rayleigh-Ritz procedure (cont'd) 2. Rayleigh-Ritz procedure (cont'd) 2. Rayleigh-Ritz procedure (cont'd) 2. Rayleigh-Ritz procedure (cont'd) 2. Rayleigh-Ritz procedure (cont'd) 2. Rayleigh-Ritz procedure (cont'd) 2. Rayleigh-Ritz procedure (cont'd) 2. Rayleigh-Ritz procedure (cont'd) 3. A simple element analysis 3. A simple element analysis (cont'd) 3. A simple element analysis (cont'd) 3. A simple element analysis (cont'd) 3. A simple element analysis (cont'd) 3. A simple element analysis (cont'd) 24 of 47 3. A simple element analysis (cont'd) 3. A simple element analysis (cont'd) 3. A simple element analysis (cont'd) 4. Higher-order elements 4. Higher-order elements (cont'd) 5. Assembly of system equation 5. Assembly of system equation (cont'd) 5. Assembly of system equation (cont'd) 5. Assembly of system equation (cont'd) 5. Assembly of system equation (cont'd) 6.1 Static problem 6.2 Undamped dynamic problem 6.2 Undamped dynamic problem (cont'd) 6.2 Undamped dynamic problem (cont'd) 6.2 Undamped dynamic problem (cont'd) 6.3.1 Modal analysis 6.3.1 Modal analysis (cont'd) 6.3.2 Time-domain analysis 6.3.2 Time-domain analysis (cont'd) 6.3.2 Time-domain analysis (cont'd) 6.3.2 Time-domain analysis (cont'd) 6.3.2 Time-domain analysis (cont'd) 6.3.3 Complex-valued analysis

3. A simple element analysis (cont'd)

Following the Rayleigh-Ritz procedure, we substitute for \(w\) using equation 5 in equation 4, carry out the double integrations, and differentiate with respect to each of the \(c_i\) in turn. Setting the derivatives equal to zero then results in a set of algebraic equations for the \(c_i\):
\(\mathbf{A} \mathbf{c} = \mathbf{B} \mathbf{g}\)
(Eqn. 8)
where the components of \(\mathbf{g}\) represent the nodal values of the pressure field \(g\).

The components of the matrices \(\mathbf{A}\) and \(\mathbf{B}\) are functions of \(\lambda\) (which depends on the frequency, tension and area density) and of the vertex coördinates of the triangular element.

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R. Funnell
Last modified: 2018-11-07 12:52:06

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