Michael Bahtiarian, Noise Control Engineering, Inc.

(Originally Presented at the Insitute of Environmental Science & Technology Conference, May 2000)

Mr. Bahtiarian is currently a staff engineer at Noise Control Engineering in Billerica, Massachusetts where he is involved in the testing, designing and analysis of noise & vibration control treatments for all types of marine vessels. He is a full member of the Institute of Noise Control Engineering (INCE). Mr. Bahtiarian earned a BS in Mechanical Engineering from Pennsylvania State University and a MS in Mechanical Engineering from RPI.


This paper discusses the investigation of a intermittent, but serious vibration problem on an ocean-going vessel. Upon first examination, the problem appeared to be resonance excitation. Typical methods of testing for resonances such as modal impact or shaker tests were not possible due to the size of the test object. Initial data suggested that the ship was vibrating in a cantilevered beam mode with a frequency equal to the shaft rotation rate. A second series of tests confirmed the vibration at the noted frequency, but with a free-free beam mode shape. Structural modifications would require major additions of steel and weight to the ship. After some deliberations, the propulsion system was inspected and mechanical problems were discovered. Repair to the propulsion system was undertaken, and structural modifications were not required.

KEYWORDS: Vibration, Shipboard, Natural Frequency, Resonances.


Shipboard vibration has many forms. For diesel driven vessels, the engines induce large accelerations that travel from the foundation of the engine throughout the ship. In most compartments, this type of vibration normally manifests itself as audible noise. Most shipboard noise problems are actually reduced by controlling vibration. This paper discusses the investigation of a passing but serious ship-wide vibration on a 250 foot ocean-going vessel.

A likeness of the Offshore Supply Vessel (OSV) is shown in Figure 1. It is designed to supply offshore oil and gas platforms with supplies and also serve as a rescue vessel. The OSV’s are relatively small vessels for the open ocean they navigate. Part of their duty is to "stand-by" an oil or gas rig in the event of an emergency. This leaves the OSV in open ocean for extended periods of time and places the crew in some of the harshest conditions for maritime service. As such, degradation of crew comforts are taken seriously.

FIGURE 1: "Outboard Profile" of Typical Offshore Supply Vessel or OSV.


The author was aboard a recently delivered OSV, conducting an unrelated noise survey. The vibration was first noticed while sleeping on the vessel during an overnight passage. In conversation with the captain, the details of the vibration were further reported. The vessel had been experiencing a severe shaking whenever the vessel was fully loaded with supplies. The vibration was quite evident in the accommodations area at the forward part of the ship and not noticed in the aft machinery spaces. The author’s personal observation was that the vibration was higher the more forward in the vessel you went. It also appeared that the vibration was low in frequency.

"Resonance", would be the first thought to any sound and vibration engineer, experiencing a sleep depriving vibration. A 250 foot ship, just like any other structure will generate high vibration, when an input force is at a frequency equal to the structure’s natural frequency. Ship’s are full of resonant conditions on structures like engine foundations, bulkheads and masts. None are as rare or problematic as a "ship mode" which is the condition where the entire vessel vibrates as an unconstrained beam.

The purpose for writing this paper is to describe the extraordinary effort required, when the unconstrained beam houses complex machinery, is 250 feet long and weighs 5,000 tons. The vast size of the structure presented great difficulties in diagnosing and solving a theorized resonance problem. Typical methods of testing for resonances such as modal analysis, impact or shaker tests are practically impossible.


Since the author was already aboard the vessel, a set of measurements were taken to learn as much as possible, such as the vibration’s frequency and amplitude. Measurements were taken with an accelerometer and portable spectrum analyzer on the ship’s deck at various locations from the bow to the aft end of the accommodations area. Measurements were not taken aft of the accommodations spaces. Figure 2 is a comparison of deck vibration above the Main Deck for unloaded and fully loaded conditions.

Identification of the peaks in Figure 2 is the next step in understanding the vibration condition, and knowledge of the ship’s propulsion train is necessary. Figure 3 is a diagram of one of two of the vessel’s propulsion trains. Each system has a 4-bladed propeller, that is powered by a pair of 3,100 horsepower diesel engines. The torque from the two engines are coupled at a reduction gearbox with a 5.488:1 reduction ratio.

FIGURE 2: Vertical Vibration, Bow above the Main Deck, Fully Loaded & Unloaded Conditions.

(See Table 1 for identification of peaks)

During shipboard testing, one of the most important parameters to record is the main engine speed. During the two tests show in Figure 2, the diesel rotation speed was 900 rpm or 15 Hz. This value is divided by the reduction gearbox ratio to determine the output shaft frequency. The output shaft frequency is multiplied by the number of propeller blades to determine the blade-pass frequency.

FIGURE 3: Diagram of OSV Propulsion System one side shown. Ship has Port and Starboard Systems.

The propulsion plant’s forcing frequencies are computed as described above and summarized in Table 1. This table identifies the peaks shown in Figure 2. Looking at Figure 2 it is seen that the most significant change in vibration is at the peaks (1) and (3). The lowest frequency peak, the Propeller Shaft Rate (1), is the peak that dramatically increases when the vessel is fully loaded with cargo. The vibration decrease with loading at the 3rd harmonic of the output shaft rotation (3) will be evident by the end of the paper.


TABLE 1: Propulsion System Forcing Frequencies.







Propeller Shaft Rotation Rate (RR)



2nd Harmonic of Propeller Shaft RR



3rd Harmonic of Propeller Shaft RR



Propeller Blade Rate (4 Blades)



Propulsion Diesel RR (900 rpm)



2nd Harmonic of Propeller Blade Rate

At this point, in the process, we have defined the vibrational frequency at 2.75 Hz and confirmed the low frequency sensation. Narrowband data similar to that shown in Figure 2 were taken at various locations along the length of the accommodations area. These locations are identified by frame number, where higher frame numbers represent further aft in the ship. Data taken along the length of the vessel at the frequency of maximum vibration (2.75 Hz) was plotted as a function of frame number, Figure 4.

FIGURE 4: Vibration Amplitude at 2.75 Hz vs. Location on the Ship (higher frame numbers indicate further aft)

The source of the vibration based on the 2.75 Hertz frequency is the propeller output shaft. The most interesting fact about Figure 4, is that the shafts are located far aft in the vessel, at frames 85 to 103. There are no other mechanical equipment forward that would produce vibration at this frequency. The only way for the amplitude of the vibration to increase as you move forward in the ship would be a resonant condition, and this initial set of data suggests that the forward section of the ship is resonating in cantilevered beam mode.

So far the initial testing has confirmed that a vibration condition exists at a frequency equal to the propeller shaft once per rev. The amplitude of the vibration increases as you move more closer to the bow and further from the source. The final fact that complicates the situation is that the vibration condition is not consistent. The condition appears to change with vessel loading and the reasons for this needs to be understood.


Marine ship references by [1] & [2] state that the 2 noded hull mode for a ship of this size can range from 2 to 3 Hz. The initial conclusion was that the forward portion of the ship was vibrating as a cantilevered beam, but a 2-noded hull mode vibrates as a free-free beam. The author quickly realized that measurements aft of the accommodations were not taken, due to hazards of the open work deck area. It was quite possible that the aft portion of the vessel were vibrating as much as the bow, and thus the data could indicate a 2-noded ship mode as suggested by theory.

References [1] & [2] both provide an equation for the prediction of a vessel’s natural frequency as a function of the vessel’s moment of inertia, displacement, length between perpendiculars (frames), breadth amidships, and mean draft. Once a vessel is constructed, all of the parameters above are constant except the vessel’s displacement and draft which define the vessel’s weight and how deep it floats in the water, respectively. Cargo loading would affect both parameters!

Draft values are recorded in a ship’s log. The author requested the draft levels for the periods when the ship was empty to fully loaded. The draft readings can be used to determine the displacement. Using this information and the equation presented in reference [1], the author calculated the 2-noded natural frequency as given in Table 2.

TABLE 2: Calculated 2-Noded Natural Frequency.


Mean Draft (ft)






Empty, Bow Down




Empty, Bow Up








Fully Loaded, Design




Two conclusions are drawn from this information. Most importantly, it appeared quite reasonable for the primary hull mode to be excited by the propeller shaft once per rev at 2.75 Hz. However, the reason for the excitation was not explained by the change in natural frequency due to loading. The 0.3 Hz change in the natural frequency are too small to cause changes in resonant response. Another reason must be found.


A second series of tests were planed to further quantify the mode shape and determine why the propeller shaft was producing the input force. By the end of the second set of tests, it would be important to know if the problem was due to the input force or the ship’s natural frequency characteristic. This would then focus repair efforts at either the machinery or the structure. Whereas machinery repair could be straight forward, potential stiffening of the ship’s hull may not be feasible.

Up to this point, the only testing conducted was during the previous unrelated visit to the OSV. The next visit was dedicated to the vibration problem in question. The test agenda included: measurement of vibration at various points along the full ship’s length and key locations around the propulsion plant.

Since the input frequency was the propeller shaft rotation rate, it is important to monitor the vibration near this shaft. Measurement positions included the propulsion diesel, gearbox, shaft bearings and shaft hull penetration called the stuffing box. It would have been advantageous to perform a modal analysis of the ship, but this would not be possible. The OSV was under contract in the North Atlantic. The second set of tests were performed during the coldest period of the winter of 1999 and during a brief port visit between "stand-by" duty. Both time available on the ship and harsh winter conditions prevented conducting any type of modal testing.

The next best approach was to conduct a series of magnitude and phase measurements along the length of the ship. A two channel HP spectrum analyzer with two ICP accelerometers and 50 feet of coaxial cable was used to perform "daisy chain" magnitude and phase measurements. For example with four measurement locations A, B, C & D, amplitude and phase were first taken between points A & B. Next amplitude and phase were measured for points B & C and then C & D. In this manner the phase relationship can be determined between all the points. That is, if location A was out of phase with location B and location B is in phase with location C, we can assume that A is out of phase with C.

Unfortunately, during the second test phase, the severe vibration condition could not be re-produced. Various vessel loading conditions were tried, but a full ship’s cargo was not available during the test time. The measurements outlined above were taken anyway. Vibration measurements around the output shaft did not provide any evidence of high source vibration from the output shaft.

Figure 5 shows the compilation of the amplitude and phase data along the ship’s length. The amplitude values were taken directly from the data. The phase is represented by the positive or negative value of the amplitude. This was computed "by hand" by assigning same sign for approximate 0 degree phase and negative value for approximate 180 degree phase. Various conditions were tested and the average of this data appears to provide adequate approximation of a 2-noded ship hull mode.

FIGURE 5: Graph of Approximate Vessel Mode Shape Vibration on OSV Main Deck at 2.75 Hz.


Since the subject vibration condition did not occur during the detailed test phase, the author was left with speculation. Three elements affect the generation of the excessive vibration. They are (1) the ship's natural frequency, (2) the shaft operating speed and (3) the ship cargo loading. Fixing this problem obviously involves modifying at least one of these three elements.

Modifying the ship's natural frequency is accomplished by stiffening the hull, adding pontoons to decrease the displacement or installing a dynamic absorber (a large mass on springs). All options are a significant and very expensive undertakings. Either decreasing or increasing the shaft operating speed to avoid coincidence with the natural frequency would eliminate the vibration. On a permanent basis, it requires changing the reduction ratio of the gearbox and possibly the propeller. This is less costly than structural modifications, but still a pricey solution.

Correcting the structural or mechanical deficiency caused when the vessel is fully loaded, may provide the most economical solution. Suggestions for the next steps were provided and were to be carried out by other marine consultants. These steps included shaft alignment, inspection of the gearbox output shaft bearings, stem tube bearings and rudder bearings, and deflection computation at these bearing points for the various loading conditions.

Of all the recommendations, alignment measurements were conducted by the gearbox distributor under various cargo loading conditions. The alignment measurements showed that the clearances in the stern tube journal bearing were too small when the vessel is fully loaded. The location of inboard tanks and deck cargo is such that a bending moment is applied to the bearing and with improper clearance a high vibration at the shaft rotation rate was produced. This condition produced the input force causing the ship’s natural frequency to resonate.

This condition is consistent with the decrease in the third harmonic of the shaft rate found in Figure 3. When the shaft was unloaded, the bearing clearance caused a misalignment condition that was alleviated with load. Repairing the bearing ended the severe vibrations.


In retrospect, the natural frequency condition was the symptom not the disease, and the cure involved repairing machinery, not de-tuning the ship. Given the great cost to change the natural frequency of a ship, the restraint in suggesting such modifications were prudent. The data presented shows that vibration theory applies to structures of all sizes, including an ocean-going vessel. This ship and all its complexities still behaves structurally as a free-free beam. The important point to consider is that even though vibration theory applies, it does not mean that vibration theory will provide the solution, and other factors must be kept in mind in reaching a solution.



  1. Vorus, William S., Principles of Naval Architecture, Chapter 7 "Vibration", Published by the Society of Naval Architects and Marine Engineers, 1988.
  2. Vibration Control in Ships, Published by Veritec, Hovik Norway, 1985.

Mike Bahtiarian

Noise Control Engineering Inc.

799 Middlesex Tnpk

Billerica MA 01821


978-667-7047 (Fax)

mailto: nonoise@noise-control.com