Structural Analysis Expert Needed

I'm seeking assistance with a structural analysis

Key Areas of Analysis:

Perform detailed analysis of beams under various loading conditions (point loads, distributed loads).
Derive and calculate deflection curves, bending moments, and shear force distributions for beams with different support conditions (e.g., simply supported, fixed, cantilever).
Identify maximum and minimum moments in beams and determine their precise locations.
Buckling Analysis:

Calculate critical buckling loads for columns and beams subjected to axial loads using Euler's formula and other methods.
Analyze the stability of columns and beams to predict buckling under specified loading conditions.
Provide step-by-step solutions for deriving buckling loads and stability conditions.
Vibration Analysis:

Analyze the natural frequencies and mode shapes of structural elements such as beams and rods.
Solve vibration problems for systems modeled as single-degree-of-freedom (SDOF) and multiple-degree-of-freedom (MDOF) systems.
Derive equations for time responses of vibrating systems and analyze both steady-state and transient behaviors.
Evaluate the effects of damping and resonance on system stability and response.
Dynamic System Analysis:

Conduct analysis of dynamic systems involving masses, springs, and dampers subjected to time-varying loads.
Derive governing differential equations for dynamic systems and solve for displacement functions and system responses.
Assess system stability and response under various loading conditions, including harmonic forces.
Application of Differential Equations:

Utilize ordinary and partial differential equations to solve structural problems related to deflections, vibrations, and buckling.
Apply analytical methods, such as Fourier series, to solve complex structural dynamics problems.