SERVICES » NAVAL
Our experience in the Naval field concerns in the shock analysis of the double resiliently mounted Diesel Generator Set addressed to the Frigates Class for the Italian/French Navy, undergoing a dynamic excitation consisting in accelerations enforced to the ship foundation, with values assigned as a time history consistent with the Technical Specification HS311AQ01M.
Following the example of the shock analysis are reported from the Isotta Fraschini Engine.
Residual accelerations and displacements of the main bodies (Engine, Generator and Subbase) are concerned in order to model correctly all the connections between the engine and the seismic mass.
The survey is a non-linear transient analysis of the aforementioned quantities, with the Large Mass Method.
Enforced motion specifies the displacement, velocity, and/or acceleration at a set of grid points for frequency and transient response.
Enforced motion is used when base motion is specified instead of, or in conjunction with, applied loads. A common application is an earthquake excitation applied to a building; in this case there are no applied loads, instead the base of the building undergoes an enforced displacement or acceleration time history.
If a very large mass m0, which is several orders of magnitude larger than the mass of the entire structure (106 times is the recommended factor), is connected to a degree-of-freedom and a dynamic load p is applied to the same degree-of-freedom, then the acceleration ü of this degree-of-freedom, to a close approximation, is given by p/m0. In other words, the load that produces a desired acceleration ü can be approximated with m0ü and the accuracy of this approximation increases as m0 is made larger in comparison to the mass of the structure, the only limit for the size of m0 being numeric overflow in the computer.
The Large Mass Method is implemented in direct transient and frequency response analysis by placing large masses m0 on all enforced degrees-of-freedom and supplying applied dynamic loads equal to m0u, m0ù or m0ü depending on whether the enforced motion is a displacement, velocity or acceleration.
For the time history, the base pulse rectangular acceleration has been applied to the structure.
The input signal for the analysis in the frequency domain has been obtained as the Fast Fourier Transform of the relative signal in the time domain.
The choice of the Df used in the frequency domain involves considerations on the other variables (total number of samples N, time step Dt and period T) used for the frequency and time domain discretization. Df has been chosen in order to guarantee a good resolution in both the (with respect to the range of interest) domains, once the number of samples had been fixed as the maximum allowed by the software (Excel) used for the pre and post-processing.
The equation:
leads to a time step Dt equal to 0.0006s and a total period T of 2.46 seconds.
The use of this time step allows to characterize the shock inputs in an acceptable way (see Fig. 2 ): it is important to point out that the signal has been intentionally transformed from discontinuous to continuous in order to reduce the presence of undesired oscillations in the input FFT; in any way, this operation has left its area (which can be directly related to its energy) substantially unchanged.
The use of a period greater than the theoretical one of the input (0.0174s) means that the vector containing the sampling of the input will be filled with null values: this will smooth the FFT behavior.
The subbase was modelled with beam elements, featuring the shape shown in the picture below. A few non-structural masses have been added to this model in order to obtain the same inertial data of the actual structure.
In the following figure is shows the Genset Locator for the results recovery points:
The sixteen resilients of the Lower Stage connect the DGS to the ship. In the model, they have been represented by a viscous-elastic element linked to a metallic ring able to undergo plastic deformation to fully absorb the impact energy.
The theoretical behavior of the structure follows closely the physical one. Indeed, the CGAP element remains open until a vertical displacement of 14 mm is obtained and, in the meantime, the stiffness of the mount is driven by the CELAS element.
Then, when the displacement reaches the limit value, the CGAP element closes and its stiffness value rises up to “infinity”, hence transferring the load to the shock-absorber element.
It should be remarked that the model simulates the behavior of the actual system both along the vertical axis and in the horizontal plane as well, in order to allow an appropriate dynamic answer in all the spatial directions.
Infact, pairs of CELAS+CGAP elements were used along both the transversal and longitudinal directions (either positive or negative) to simulate the restricted excursion of the rubber inside the mount when subjected to horizontal loads.
the load capability of the shock-absorber ring is plotted. This curve has been converted in a stress/strain curve, which in turn has been associated to the material properties of the shell elements of the shock-absorber ring model.
The above model of the shock-absorber was “tested” analytically in order to match the theoretical behavior with the actual behavior seen experimentally.
The displacements of the most representative DGS points are plotted
This trend is shown for the case of vertical shock.
The residual accelerations on the main DGS bodies are given in the Attachment J.
In each plot the accelerations of all the nodes belonging to the set identified in the previous paragraphs have been reported. The acceleration of the node to which the Large Mass is connected is shown as well, so to make it possible to check the results accuracy.
As requested, the Vertical component of the acceleration has been plotted in correspondence of each of the three Shock loads considered; besides, for the Shock loads given in input in Longitudinal and Transversal direction respectively the Longitudinal and the Transversal accelerations have been shown.
As expected, the maximum acceleration is relieved along the Vertical axis, in correspondence of the frequencies showing a high modal fraction participation along the T3 direction. The peak value is of 397.55g for node 13 at 4.07Hz. The amplitude of the Shock Signal FFT at 4.070Hz is 38.06g, this means that in this point the system has an amplification factor of 10.45.
