Deterministic Responses for
Single Degree ofFreedom
Structures
James F. Wilson
Once the single degree of freedom dynamic model for an offshore structure is
formulated and the loading conditions are identified, the structurel response
characteristics are calculated using its équation of motion. The response characteristics are of two types: the natural frequency, and the time history of
displacement v{t) or of rotation 9(t). The frequency calculation is generally
necessary to assure the integrity of the structural design. This is because an
offshore structure in depths exceeding 70 m generally has a natural frequency
falling in the range of the expected wave frequencies, which may lead to a dangerous condition of structural résonance.
The peak displacement or rotation response is sought where several possible extreme environmental loading conditions are applied, generally one at a
time. These loads include the effects of high winds, waves, and also earthquake
excitation. Typically, the peak dynamic response for each loading is then compared to its static response, or its response if the same loading were applied
very slowly. This response ratio, dynamic to static, is called by several nanties,
including the dynamic amplification factor, the dynamic load factor, and the
impact factor. This response ratio can be applied to the expected static loads
for design purposes.
In this chapter, natural frequencies and dynamic responses of selected linear
and nonlinear structural models are evaluated. For linear Systems, the classical
response functions due to harmonie and impulse loading are derived, followed by
the response due to a general, time-dependent loading. The response analysis
for nonlinear Systems employs first order perturbation theory and numerical
methods. Example problems illustrate the calculations of the natural frequency
and the dynamic response for several types of offshore structures: a fixed-legged
structure such as a jackup rig in response to earthquake excitation at the sea
floor; and responses to a single design wave of a spread-moored ship and a SALM
buoy, bot h of which are supported by nonlinear restraints.
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Single Degree ofFreedom
Structures
James F. Wilson
Once the single degree of freedom dynamic model for an offshore structure is
formulated and the loading conditions are identified, the structurel response
characteristics are calculated using its équation of motion. The response characteristics are of two types: the natural frequency, and the time history of
displacement v{t) or of rotation 9(t). The frequency calculation is generally
necessary to assure the integrity of the structural design. This is because an
offshore structure in depths exceeding 70 m generally has a natural frequency
falling in the range of the expected wave frequencies, which may lead to a dangerous condition of structural résonance.
The peak displacement or rotation response is sought where several possible extreme environmental loading conditions are applied, generally one at a
time. These loads include the effects of high winds, waves, and also earthquake
excitation. Typically, the peak dynamic response for each loading is then compared to its static response, or its response if the same loading were applied
very slowly. This response ratio, dynamic to static, is called by several nanties,
including the dynamic amplification factor, the dynamic load factor, and the
impact factor. This response ratio can be applied to the expected static loads
for design purposes.
In this chapter, natural frequencies and dynamic responses of selected linear
and nonlinear structural models are evaluated. For linear Systems, the classical
response functions due to harmonie and impulse loading are derived, followed by
the response due to a general, time-dependent loading. The response analysis
for nonlinear Systems employs first order perturbation theory and numerical
methods. Example problems illustrate the calculations of the natural frequency
and the dynamic response for several types of offshore structures: a fixed-legged
structure such as a jackup rig in response to earthquake excitation at the sea
floor; and responses to a single design wave of a spread-moored ship and a SALM
buoy, bot h of which are supported by nonlinear restraints.
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