v2.01.320 SDLD320 - Transient response of a free system of 3 masses and 2 springs under harmonic excitation

Summary:

We consider the transient analysis of a discrete linear mass/spring system with three completely free degrees of freedom. This system has non-proportional damping. Sinusoidal excitation is applied to one end of the system.

In this problem, we test, through a discrete model, the calculation of the transient response of a system whose rigid modes are not fixed. We are only interested in the transitional regime. To do this, the solution will be sought through integration on a complete modal basis.

The results obtained (displacement, speed and acceleration) are compared to an average of results from industrial codes and an improved \(\beta\) -Newmark numerical integration method.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
  • 1.4. Initial conditions
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark results
  • 2.3. Uncertainty about the solution
  • 2.4. Bibliographical references
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
  • 3.4. notes
• 4. Summary of results