Modal response of free spanning pipelines based on dimensional analysis

• The governing differential equation for a free spanning pipeline is solved.
• A dimensional analysis is carried out for the free span problem.
• Closed analytical formulae are derived for eigenfrequencies and modal stresses.
• The novel formulae account for axial forces in the calculation of modal stresses.
• The accuracy is improved compared to expressions widely used in pipeline design.

The paper examines the problem of an axially loaded pipeline resting on semi-infinite elastic supports on either side of a free span. A dimensional analysis of the problem is carried out, and it is demonstrated that the eigenfrequencies and associated maximum modal stresses of the pipe may be uniquely represented as functions of only two non-dimensional parameters. Explicit analytical formulae for the modal response quantities are derived, with improved accuracy and applicability range as compared to approximate expressions that are widely used in the pipeline industry today.