Modal properties and stability of centrifugal pendulum vibration absorber systems with equally spaced, identical absorbers

Vibration mode structure and simplified modelling of cyclically symmetric or rotationally periodic systems

“…The relation between the submatrices M (1) cs and M (i) cs in equation (3.8) is exactly the same as that expressed in equation (3.7). This property can also be observed in the gyroscopic and stiffness matrices of cyclically symmetric CPVA systems [23][24][25], where the submatrices are related according to…”

“…Invoking equations (3.20) and (3.7), the second term of equation (3.21) is [23]. Therefore, the second term in equation (3.21) vanishes for k = 2, 3, .…”

“…Substitution of u kl in equation (2.5) for a chosen k into the equation that governs the motion of each substructure in equation (2.1) (that is, the L equations defined by each A The eigenvectors in equation (2.5) show that all vibration modes of a cyclically symmetric system with non-vibrating central components consist of identical motions for each substructure (i.e. the v kl ), but the substructures vibrate out of phase with the phase difference determined by the integer k, known as the phase index of the vibration mode [2,3,[23][24][25], and the spacing angles β i . (a) An example system with cyclic symmetry…”

“…In a free-body diagram and kinematic analysis, these relative force and acceleration vectors for degrees of freedom in substructure i, when calculated in the basis {e We take the absorber acceleration in cyclically symmetric CPVA systems as an example ( figure 3). The matrix equations of motion of CPVA systems are in [23]. The tangential acceleration of the ith absorber relative to its pivot point acceleration expressed in the {e 2 , where s i is the absorber displacement along its path (figure 3).…”

“…, N − 2. In planetary gears [6,[19][20][21][22]34] and CPVA systems [23][24][25] In cases like planetary gears [6,[19][20][21][22]34] and CPVA systems [23][24][25] where the substructures do not connect with each other but only connect to the central components, the submatrix A s is block-diagonal. The A i (defined in equations (2.3) and (2.4)) vanish for i = 1.…”