Analytical sensitivity analysis of frequencies and modes for composite laminated structures

• An analytical sensitivity analysis method for composite laminated structures.
• First derivatives of structural stiffness, mass matrices are derived using FEM.
• Sensitivity of discrete model converges to real solution while mesh becomes denser.

This paper describes an analytical method to calculate the sensitivity of the frequencies and modes with respect to fibre volume fractions and orientations, for the large-scale composite laminated structures with complex boundaries. Structural stiffness, mass matrices and their first derivatives with respect to fibre volume fractions and orientations are derived based on classical laminated plate theory and nonconforming rectangular element theory. The analytical sensitivity of the frequencies and modes with respect to fibre volume fractions and orientations is formulated based on vibration theory. Finally, the sensitivity analysis of the dynamic characteristics of T-shape and square composite laminated plates is demonstrated using the proposed analytical method. The accuracy and efficiency of the proposed method are also discussed. The proposed method can be employed to analyze the sensitivity of the frequencies and modes for the composite laminated structures.