Composite Material and Structure

Analyzes rotor stability, plots natural frequencies against rotational speed.The formula is given by: Where: Ω is the rotational speed of the structure (in radians per second), ωn​ is the natural frequency of the composite structure (in radians per second).

Describes mass distribution and dynamic response in structural analysis.The formula is given by: Where: M is the mass matrix, a is the acceleration vector, f is the force vector.

Describes stiffness properties, force-displacement relationship, crucial in structural analysis.The formula is given by: Where: K is the stiffness matrix, u is the displacement vector, f is the force vector.

Describes structure’s response to harmonic excitation across frequencies.The formula is given by: Where: H(ω) is the Frequency Response Function, X(ω) is the complex amplitude of the response at frequency ω, F(ω) is the complex amplitude of the input excitation at frequency ω.

Rayleigh damping is a Linear model combining mass and stiffness matrices.The formula is given by: Where: C is the damping matrix, α and β are the Rayleigh damping coefficients, M is the mass matrix, K is the stiffness matrix.

Dynamic analysis studies system behavior under varying loads over time.The formula is given by: Where: F is the force acting on the system, m is the mass of the system, and a is the acceleration of the system.

Identifies, assesses, prioritizes potential failure modes and effects.The formula is given by: Where: Severity: Refers to the potential impact or seriousness of the failure mode on system performance. Occurrence: Indicates the likelihood or frequency of the failure mode occurring. Detection: Represents the effectiveness of existing detection methods in identifying the failure mode before it causes harm.

Endurance limit is a Maximum cyclic stress without fatigue failure.The formula is given by: Where: σe​ is the endurance limit (or fatigue limit), kf​ is a factor depending on the material and the type of loading condition, σu​ is the ultimate tensile strength of the material.

Crack propagates if stress exceeds critical value for material toughness.The formula is given by: Where: σ is the applied stress, a is the crack length, Kc​ is the fracture toughness of the material.

Predicts crack behavior using stress intensity, critical stress, and toughness.The formula is given by: Where: K is the stress intensity factor, σ is the applied stress, a is the crack length.