EFFECTS OF CENTRIFUGAL STIFFENING ON THE VIBRATION FREQUENCIES OF A CONSTRAINED FLEXIBLE ARM

✍ Scribed by E.H.K. FUNG; D.T.W. YAU

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 495 KB
• Volume: 224
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2212

✦ Synopsis

A clamped-free rotating #exible robotic arm is modelled by the Euler}Bernoulli beam theory. The arm rotates horizontally about the clamped axis while the other end is constrained to move against a curve. The arm has an end mass attached at its tip. An axial compressive force, which is derived from the contact force between the tip of the arm and the constrained curve, is applied at the free end. When the #exible robotic arm rotates, a centrifugal force is produced on the arm by the centrifugal sti!ening e!ect. Hamilton's principle is used to derive the equation of motion of the arm together with the associated boundary conditions. The non-homogeneous boundary condition is transformed into a homogeneous one by de"ning a new variable. The equation of motion and the boundary conditions are then expressed in non-dimensional form. The power series method is used to solve the equation of motion. A frequency equation is derived giving the relationship between the non-dimensional modal frequencies and the four non-dimensional parameters, i.e. the axially compressed force, the end mass, the angular velocity of the arm and the total moment of inertia about the hub. The numerical bisection method is used to solve for the natural frequencies under di!erent values of axial force, end mass, angular velocity of the arm and the total moment of inertia about the hub. Results are prersented for the "rst three modes of vibration. These results are useful in the understanding of the dynamic behavior of the rotating constrained #exible beam with an end mass.