Stiffness matrix

Flexibility method

Engineering

Materials science

Conical surface

Boundary value problem

Convergence (economics)

Economics

Vibration

Acoustics

Classical mechanics

Mechanical engineering

Physics

Finite element method

Mathematics

Equations of motion

Normal mode

Shell (structure)

Direct stiffness method

Mathematical analysis

Geometry

Composite material

Structural engineering

Economic growth

Stiffness

Mechanics

Reduction (mathematics)

Thin-Walled Structures

An analytic dynamic stiffness method (DSM) is extended to analyze the free and forced vibration of combined conical-cylindrical shells with general boundary conditions in this paper. Flügge shell theory is utilized to formulate the motion equations of each shell component. Based on the exact general solutions of the motion equations, the dynamic stiffness matrices for each shell segment are established separately and the global dynamic stiffness matrix for the whole structure is established by assembling the dynamic stiffness matrices for each shell segment similarly as finite element method (FEM) did. Natural frequencies and forced responses of the combined shells are obtained based on the global dynamic stiffness matrix. Through comparing vibration results of DSM with ones from open literature and FEM, rapid convergence, good accuracy, and high efficiency of the DSM are demonstrated. In the numerical examples, the influences of boundary conditions, axial and circumferential mode numbers, and semi-vertex angles on the free vibration are studied. The effects of direction and location of external force and structural damping on the forced vibration are also discussed.

Vibration analysis of combined conical-cylindrical shells based on the dynamic stiffness method