Vibration comfort levels are becoming increasingly important for yacht owners. In order to meet vibration targets and achieve maximum vibration reduction, it is essential to study the vessel’s structural behaviour. The perspective of Van Cappellen Consultancy is to check the vibration behaviour of the construction during the yacht’s design phase. Construction parts are modelled in finite element (FE) software and analysed.

Van Cappellen Consultancy prefers to calculate natural frequency using FEM to using simplistic formulas, as FEM facilitates the analysis of complex geometries, orthotropic materials (e.g. composites), etc. and of structural modifications, such as material thickness and the addition of stiffeners or frames. Effective assessment of such structural measures is performed using FEM.

## We perform such calculations as:

**Input mobility calculation**

The dynamic behaviour of foundations is of huge interest as regards the transfer of acoustic energy from machinery to the vessel’s structure. The idea behind this is fairly simple: “the less energy transmitted into the vessel’s structure, the less energy available for the radiation of noises into interior spaces”.

Using FEM, the input mobility of a foundation can already be calculated during the early design stage. The figure below presents an example of an FE model used to calculate input mobility of the diesel engine foundations of a 135’ aluminium yacht.

**Natural frequency calculation**

Normal mode analysis of local structures (e.g. decks, bulkhead, etc.) is executed using the FE model. The results identify natural frequencies and accompanying mode shapes. When energy is fed into a structure at a frequency that coincides with the major natural frequency, an initially small vibration can be amplified. The human body can sense low frequency vibrations in particular and experiences it as uncomfortable.

**6-DOF calculation**

The main objective of decoupling the engine (source) from its support structure (receiver) through resilient mounts is to reduce structure-borne sound transmission from machinery into the vessel’s structure. This process is known as ‘isolation’.

If machinery is installed on resilient mounts, this is called a physical mass/spring system, which is known to have six rigid body modes (natural frequencies). The calculation of these frequencies, at which this physical phenomenon is expected, is referred to as a six-degrees-of-freedom calculation (6-DOF).

At Van Cappellen Consultancy, these calculations are performed using FEM.

**Example**

A support frame used underneath generator sets involves standard factory produced frames. Although Van Cappellen Consultancy can design a complete new support frame, it is more common to modify an existing frame. Mobility, dynamic stiffness, interaction between resilient mounts and frame, as well as the location of the mounts, can be checked using FEM.

With a double resilient mounted generator set, the mass and stiffness of the sub-frame (positioned between the upper and lower mounts) will be checked together using the 12-DOF calculation.