INTERNATIONAL JOURNAL OF DESIGN AND MANUFACTURING TECHNOLOGY (IJDMT) FREE VIBRATION ANALYSIS OF PASSENGER BOAT

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1 INTERNATIONAL JOURNAL OF DESIGN AND MANUFACTURING TECHNOLOGY (IJDMT) Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14) ISSN (Print) ISSN (Online) Volume 5, Issue 3, September - December (2014), pp IAEME: Journal Impact Factor (2014): (Calculated by GISI) IJDMT I A E M E FREE VIBRATION ANALYSIS OF PASSENGER BOAT MUHAMMED SHAHID ALI 1, Dr.C.G NANDAKUMAR 2 1 Department of Mechanical Engineering, MES College of Engineering and Technology, Cochin, India, 2 Department of Ship Technology, Cochin University of Science and Technology, Cochin, India, ABSTRACT Vibration is the oscillatory motion of a structure which is influenced by various excitation forces on it. Vibration of a passenger boat may cause passenger discomfort, structural damage etc. If the frequency of excitation coincides with any of the system natural frequency, resonance occurs. So the estimation of vibration is important in any passenger vessel. In this paper, the natural frequency of a passenger boat SWTD 75 is determined using a finite element beam model. The comparison has been carried out with classical methods. Suitable boundary conditions have been selected for approximating wave and still water conditions. Free vibration analysis of boat has been carried out in various load conditions. This may be helpful to determine the condition in which system vibrates unsafely. ANSYS, finite element software is used for analysis. Keywords: Elastic Foundation Beam Model of Passenger Boat, FE Analysis of Passenger Boat, Passenger Boat Vibration, Resonance In Boat, SWTD INTRODUCTION A passenger boat is a watercraft whose primary function is to carry passengers to their required destination. The analyses of vibration of passenger boats are important for the sake of passenger comfort. Natural frequency depends on the total mass and stiffness of the system as well as the distribution of this. When the exciting frequency coincides with any one of the system (boat) natural frequencies, the resonance occurs, and badly affects the passenger comfort. The oscillating forces may originate from within the boat itself such as reciprocating engine inside the boat or the external forces like those generated by propeller, wave or wind. The natural frequency of the boat depends on the density of the hull material and hence the natural frequencies of a boat may differ depending on the density of the material such as Wood, Steel, Aluminum or FRP. The parallel body of a passenger boat is generally 75% or in other words the transverse section of a passenger boat generally remain prismatic for 75% of the total length and has a converging profile to the aft. For structural analysis, floating vessels are idealized as one dimensional (longitudinal) beams floating in water. Floating vessels are considered to be either in sagging, hogging or in still water condition. When in waves the entire vessel is poised over the two wave crest, it is called sagging and when the vessel is poised over one wave crest, it is called hogging condition. The sagging condition can be considered as simply supported at the ends and the hogging as a cantilever. For the analysis of boat in still water condition boat is considered as beam on elastic foundation. The major issue encountered while analyzing a boat structure are the non prismatic hull form, uneven distribution of load along the longitudinal and transverse direction. This paper addresses the issues and attempts to estimate the vibration characteristics of passenger boat by finite element method. 1

2 2. DYNAMIC ANALYSIS Vibration may occur on the boat due to external forces. As far as the external forces are concerned, there are two types which have to be considered, firstly due to propeller, and secondly those due to environment of the boat i.e river. The periodic force on the boat hull due to the rotation of propeller can be calculated [1], as in (1): Where N is revolution per unit time of the propeller in rpm and n b is the number of blades in the propeller. (1) Encounter frequency of the boat due to steady wave [1] is given by(2): (2) Where V is the speed of boat and v is speed of wave in m/s and l is the wave length. Natural frequency ω of a multi point loaded beam can be determined by the Dunkerly s equation [2] and can be written as in (3): (3) are the natural frequency of the beam due to individual point loads and can be determined by considering the beam which is eccentrically loaded and ω s is the natural frequency of the beam due to its self weight. The natural frequency of beam with several masses can also be calculated using Rayleigh s method [3]. Rayleigh s equation can be written as in (4): = (4) W j is the mass on the beam at j th position and u j is the deflection of the beam at the same position. Natural frequency of a beam on elastic foundation can be found out by the formula [3], as in (5): = ; i=1, 2, 3... (5) Where λ i is the dimensionless parameter which is a function of boundary conditions applied to the beam, L is the length of the beam in m, E is the modulus of elasticity of the material of the beam in N/m 2,m is the mass per unit length of the beam and E f is the foundation modulus and can be calculated by finding the ratio between foundation spring stiffness and separation of the springs. That is: 3. FINITE ELEMENT ANALYSIS OF PASSENGER BOAT Floating vessels have dominant longitudinal dimensions compared to that of cross section. So most often one dimensional model with adequate flexural characteristics is adopted for finite element analysis of ships and boats. 3.1 Description of Software ANSYS, Inc. is a finite element engineering simulation software (computer-aided engineering, or CAE) that offers engineering simulation solution a design process requires. Companies in a wide variety of industries use ANSYS software. It allows engineers to construct computer models of structures, machine components, or systems; apply 2 (6)

3 operating loads and other design criteria; and study physical responses such as stress levels, temperature distributions, pressure etc. It permits an evaluation of a design without having to build and destroy multiple prototypes in testing. In the present study software version ANSYS12 has been used. 3.2 Description of Element [4] BEAM188 finite element available in the ANSYS finite element library which has been derived based on Timoshenko beam theory, has been used. This element accommodates first order shear deformations and transverse shear strain is assumed as constant through the cross section. Fig. 1 Beam 188 Geometry The geometry of BEAM 188 element is shown Fig. 1. This two noded beam element has six degrees of freedom at each node which includes translations in the x, y, and z directions and rotations about the x, y, and z directions. 3.3 Description of Structure A passenger boat SWTD 75 to carry 75 persons is considered as the structure for the present investigation. The dimensions and other data of the boat are listed in Table 1. The schematic of the boat is shown in Fig. 2. Table 1 Dimensional details of SWTD75 Sl. No Boat details Dimensions 1 Overall boat length 18m 2 Breadth moulded 4m 3 Depth moulded 1.4m 4 Draught 0.65m 5 Steel weight 17405kg 6 Full load displacement 22530kg Fig. 2 Description of SWTD 75 3

4 3.4 Input and Output details For static analysis and modal analysis of the boat, the input data used are listed as in Table 2. Moment of inertia of the boat has been determined in two sections one is at mid ship section (I 1 ) and other at 1m from the bow end (I 2 ). Table2. Input Details Sl. No. Parameters Notation value 1 Modulus of elasticity E 206GPa 2 Poisson s Ratio ν Maximum Engine Speed N e 1500rpm 4 Number of blades n 3 5 Gear Ratio 3:1 6 Speed of the boat V 5.1 m/s 7 Moment of Inertia of beam at midship section[5]. I m 4 8 Moment of Inertia of beam at 1m from bow. I m 4 The output contains nodal displacements included in the overall nodal solution, stress output, membrane and bending stress, principal stress, thermal strains etc. 4. Generation of Finite Element Model of Passenger Boat The simple model that has been used repeatedly over years to demonstrate certain fundamental aspects of ship or boat vibration is the continuous beam model of the hull. Here the boat hull is represented by a uniform onedimensional beam. 4.1 Simply Supported beam model of boat Simply supported beam model corresponds to the boat condition in wave crests at the bow and aft. Simply supported condition is given to both ends. i.e. UX, UY, UZ, ROTX, ROTY constraints are arrested in one end and UY only is constrained in the other end. The finite element beam model of the boat is shown in Fig. 3. Fig. 3 Simply Supported Beam Model of the Boat Moment of inertia of the boat structure has been determined for midship section and 1m from from bow and the same has been assigned for the beam in the respective positions in order to compensate for the non prismatic nature of the boat. The density of the beam has been calculated from the steel weight of the boat. 4.2 Beam on Elastic Foundation model Elastic foundation beam model is corresponds to the still water condition of the boat. The beam is supported by an elastic foundation, of stiffness k f per unit length, representing the buoyancy spring of water (Water specific weight times section beam) [6]. Hence the buoyant force is calculated at every meter length of the boat and the value has been given to the model as spring stiffness. Schematic of the elastic foundation model for fully loaded condition is depicted as shown in Fig. 4. Free vibration analysis is conducted using this model. 4

5 5. LOAD CASES FOR FREE VIBRATION ANALYSIS Fig. 4 Elastic Foundation Beam Model of the Boat Various load combinations on the boat for which the free vibration characteristics on still water condition and wave conditions are described subsequently. The passenger boat has been divided into six sections A to F as shown in Fig Light ship condition is assumed for this condition. Only structural masses are considered In this case passengers are seated at starboard side near aft and port side near bow. Loads considered in sections B and E The passengers are present at the port side only. That is, loading in sections A, C, E. This case represents the heeling condition on the beam All passengers present in the seat, steel weight and live load distributed along longitudinal direction as shown in Fig.5 Fig.5 Loads and weights in the boat The masses distributed on the boat for each load cases are as tabulated in Table 3. Table 3 Mass Distributions in Various s s Description of load Case Mass in kg Load case1 Light ship condition Load case2 Passengers are seated in starboard side near bow and port side near aft Load case3 Heeling condition Load case4 Fully loaded condition

6 6. RESULTS AND DISCUSSIONS The results of the free vibration analyses conducted for simply supported and elastic foundation beam models are shown in the following tables. The lowest natural frequency of the boat for load case 4 has been shown along with the natural frequency values evaluated from classical method using equations are shown in Table 4. Table 4 Natural Frequencies of the Boat for fully loaded Condition Simply Supported beam model Elastic Foundation Beam model Dunkerly s Raleigh s FEM FEM Classical Method method Method 22Hz 17.5 Hz 23.5 Hz 28.4 Hz 27.5 Hz The first mode of vibration from the free vibration analysis of the simply supported and elastic foundation beam models corresponding to load case 4 are as shown in Fig.6 and Fig.7 respectively. Fig.6 First Mode Shape of Simply Supported Beam Model Fig.7 First Mode Shape of Elastic Foundation Beam Model The first three natural frequencies for the four load cases 1-4 in Hz are shown in Table 5. Table 5 Natural Frequencies for the Four s Simply Supported beam model Elastic Foundation Beam model Since elastic foundation model and simply supported model of beam is approximated to boat on still water condition and on wave condition respectively. Both the results show little deviation from each other. Also natural frequency of elastic foundation model is little greater than that of simply supported model. The major excitation frequencies on the boat structure due to external causes are listed as shown in Table 6. 6

7 Table 6 External Excitation Frequencies on the Boat Sl.No Cause of excitation Frequency in Hz 1 Maximum Engine Speed 25 2 Propeller rotation corresponding to maximum engine speed 25 3 Steadily applied wave force Since natural frequency increases with decrease in total mass of the boat. Comparing above two tables, it can be informed that, there may be a chance of resonance in light ship condition with maximum engine speed or propeller rotation. Various resonance conditions also can be determined subsequently. 7. CONCLUSION Natural frequencies of the passenger boat SWTD 75 have been determined using beam model in various load conditions. A comparative study has been conducted of the same with classical method and finite element method. The chances of occurring the resonance have been discussed. REFERENCES [1]. W. Muckle, Naval Architecture of marine engineers (Butterworth&Co.Publishers Ltd, London, 1927). [2]. V. P Singh, Mechanical Vibrations (Dhanpatrai Publishing Company,NewDelhi, 2008) [3]. S Timoshenko, D. H. Young, and W. Weaver, Vibration Problem in Engineering,(Fourth Edition, John Wiley& Sons, New York,1974). [4]. Element Reference, ANSYS 12.1 Documentation preview, ANSYS, Inc., Canonsburg, PA [5]. E. C Tupper, Introduction to Naval Architecture(Fourth Edition, Elsevier India Pvt.Ltd, NewDelhi.2004). [6]. F. M Lewis, Principles of Naval Architecture Vol II. (The society of Naval Architecture and marine engineers, 1988). [7]. F. M Lewis, and P. Comstock, Principle of Naval Architecture(Fourth Edition,The society of Naval Architecture and marine engineers). [8]. J. C Daidola, Natural Vibration of beams in a fluid with application to ships and other marine structures, TranSNAME, 92, 1984, [9]. F. M Lewis, Propeller Vibration. TranSNAME, 43, 1935, [10]. F.M Lewis, and A. J. Tachmindji, Propeller forces exciting hull vibration, TranSNAME,62,1954, [11]. G. Aertssen, and R. D. Lembre, Calculation and measurement of the vertical and horizontal vibration frequencies of large ore carriers, North east coast institute of engineer,86, 1969, [12]. G. Andersson and K. Norrand, A method of vertical vibration with several nodes and some other aspects of ship vibration, TransRINA,111, 1969, [13]. H. M. Mottsmith, Vibration equation for a structure, Journal of Ship Research, 14, 1970, [14]. J. E Greenspon, Theoretical developments in the vibration of hulls, Journal of Ship Research, 6, 1963, [15]. L. A. Baier and J. Ormondroyd, Vibration at the stern of single screw vessels, TranSNAME, 48, 1952, [16]. M. N Norwood and R. S Dow, Dynamic Analysis of Ship Structures, Ships and offshore Structures, 8, 2013, [17]. R. E. D Bishop, R. Eatock, and K. L. Jackson, On the structural dynamics of ship hulls in waves, TrasRINA, 115, 1973, [18]. T. R Lin, J. Pan, O. Shea, and C. K. Mechefske, A study of vibration and vibration control of ship structures, Marine structures, 22, 2009, [19]. W. Fricke and Ing, Strength and vibration analysis of modern cargo ships using FEM. North East Coast Institute of Engineers,107, 1991, [20] R S Rajpurohit and R S Prasad, Analysis of Mechanical Structure Under Vibration Using Vibration Measuring System International Journal of Mechanical Engineering & Technology (IJMET), Volume 4, Issue 1, 2013, pp , ISSN Print: , ISSN Online: