142
SINGLE DEGREE OF FREEDOM STRUCTURES
Here, 0! and 02 are any two consecutive peak ampitudes during free vibration.
5.19 Carry out the necessary intégrations in équations (5.108) and (5.110)
to verify the expressions given for the buoy wave loading pi (t) and its location
z.
5.20 Starting with équation (5.111), calculate an expression for the quasistatic response 0st of this buoy, or the value of 0 for
1. For the quasi-static
load, use the amplitude of the wave loading given by the right side of this
équation. Delete ail terms involving 0 and 0, and delete ail terms containing
0 with powers greater than one. Then solve the resuit for 0 = 0st- Use the
numerical values of Table 5.3 to calculate 6st, and compare your resuit with
that obtained from Figure 5.14 for a small value of u (w = 0.05 for instance). If
these two results do not coincide, explain possible reasons for the discrepancy.
REFERENCES
Clough, R. W., and Penzien, J., Dynamics of Structures, second ed., McGraw-Hill,
New York, 1993.
Cunningham, W. J., Introduction to Nonlinear Analysis, McGraw-Hill, New York,
1964.
Den Hartog, J. P., Mechamcal Vibrations, third ed., McGraw-Hill, New York, 1947.
Forsythe, G. E., Malcolm, M. A., and Moler, C. B., Computer Methods for Mathematical Computation, Prentice-Hall, Englewood Cliffs, NJ, 1977.
Gould, P. L., and Abu-Sitta, S. H., Dynamic Response of Structures to Wind and
Earthquake Loading, Wiley, New York, 1980.
a
.
Mathematica , version 4, Wolfram Media, Inc., Champaign, IL, 1999.
Nataraja, R., and Kirk, C. L., Dynamic Response of a Gravity Platform under Random Wave Forces, OTC-2904, Proceedings of the Offshore Technology Conférence, 1977.
O Brien, J. T., and Muga, B. J., Sea Tests on a Spread-Moored Landing Craft,
/ roceedings of the Eighth Conférence on Coastal Engineering, Lisbon, Portugal,
1964.
Paz, M., Structural Dynamics: Theory and Computation, Van Nostrand Reinhold,
New York, 1980.
Rosenbach, J. B., Whitman, E. A., Meserve, B. E., and Whitman, P. M., College
Algebra, fourth ed., Ginn, Lexington, MA, 1958.
Stoker, J. J., Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience.
New York, 1963.
SINGLE DEGREE OF FREEDOM STRUCTURES
Here, 0! and 02 are any two consecutive peak ampitudes during free vibration.
5.19 Carry out the necessary intégrations in équations (5.108) and (5.110)
to verify the expressions given for the buoy wave loading pi (t) and its location
z.
5.20 Starting with équation (5.111), calculate an expression for the quasistatic response 0st of this buoy, or the value of 0 for
1. For the quasi-static
load, use the amplitude of the wave loading given by the right side of this
équation. Delete ail terms involving 0 and 0, and delete ail terms containing
0 with powers greater than one. Then solve the resuit for 0 = 0st- Use the
numerical values of Table 5.3 to calculate 6st, and compare your resuit with
that obtained from Figure 5.14 for a small value of u (w = 0.05 for instance). If
these two results do not coincide, explain possible reasons for the discrepancy.
REFERENCES
Clough, R. W., and Penzien, J., Dynamics of Structures, second ed., McGraw-Hill,
New York, 1993.
Cunningham, W. J., Introduction to Nonlinear Analysis, McGraw-Hill, New York,
1964.
Den Hartog, J. P., Mechamcal Vibrations, third ed., McGraw-Hill, New York, 1947.
Forsythe, G. E., Malcolm, M. A., and Moler, C. B., Computer Methods for Mathematical Computation, Prentice-Hall, Englewood Cliffs, NJ, 1977.
Gould, P. L., and Abu-Sitta, S. H., Dynamic Response of Structures to Wind and
Earthquake Loading, Wiley, New York, 1980.
a
.
Mathematica , version 4, Wolfram Media, Inc., Champaign, IL, 1999.
Nataraja, R., and Kirk, C. L., Dynamic Response of a Gravity Platform under Random Wave Forces, OTC-2904, Proceedings of the Offshore Technology Conférence, 1977.
O Brien, J. T., and Muga, B. J., Sea Tests on a Spread-Moored Landing Craft,
/ roceedings of the Eighth Conférence on Coastal Engineering, Lisbon, Portugal,
1964.
Paz, M., Structural Dynamics: Theory and Computation, Van Nostrand Reinhold,
New York, 1980.
Rosenbach, J. B., Whitman, E. A., Meserve, B. E., and Whitman, P. M., College
Algebra, fourth ed., Ginn, Lexington, MA, 1958.
Stoker, J. J., Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience.
New York, 1963.