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The design of lifting blade shapes is a key engineering application, especially in domains such as those of marine propellers, hydrofoils, and tidal energy converters. In particular, the excitation frequency must be different from that of the structure to avoid resonance. The natural frequency in the cases where the fluid–structure interaction (FSI) is considerably different if considering the coupling added mass (AM) of the water. In this study, vibration experiments were performed using a real propeller in air and water. The modal parameters, natural frequencies, and mode shapes were determined. Validations were performed using 3D solid and acoustic elements in a direct coupling finite element format. The modal results and AM ratios were in agreement with the experimental results. Convenient application and high efficiency are basic requirements for an engineering application. Therefore, an empirical formula was established for the first-order FSI natural frequency to enable rapid estimation, thereby satisfying this requirement.

An approximate, universal approach called the geometry parameter method is developed to estimate the stress intensity factor (SIF) and notch SIF (NSIF) according to linear elastic fracture mechanics (LEFM). NSIF solutions for sharp V-notches include correction coefficients for edge and central notches. The obtained results agree well with results for a double and central V-notched rectangular plate. Furthermore, explicit closed-form solutions are obtained using the proposed method for small crack ahead from a V-notch, and a reliable finite element model is described to calculate crack SIFs in V-notches under mixed loadings. The proposed method is robust and convenient for engineering applications. • An universal geometry method is proposed for stress intensity estimations. •Explicit approximate solutions of λ 1 and F 11 are developed and validated. •NSIF results are verified for 2D DENT and extended to calculate central V-notched plate. •Explicit closed-form solutions are obtained for a small crack ahead from V-notch apex. •Reliable FEM meshed calculation is performed and verified for crack SIF. [ABSTRACT FROM AUTHOR]

• A universal closed-form NSIF and SIF formula with high accuracy and applicability. • NSIF results verified for a V-notched rectangular strip under tension and bending. • Numerical results verified for a crack at the apex of a V-notched half plane. • Reliable FE mesh model for various crack propagation applications. • Numerical data conversion between the finite and half planes. This paper investigates finite width un-cracked and cracked notched plates. It extends existing empirical formulae for finite width cracked plates without notches to allow the Notch Stress Intensity Factors (NSIFs) in un-cracked notched plates and Stress Intensity Factors (SIFs) in cracked notched plates to be estimated. This is useful for quickly estimating SIFs or NSIFs, checking more detailed, e.g. finite element, calculation and providing insights that may help the quick estimation of SIF values in more complex locations. Matching results have demonstrated the reliability, and the main advantage of the approximation is its robustness and convenience for engineering applications. [ABSTRACT FROM AUTHOR]