TY - GEN
T1 - Approximate general responses of multi-degree-of-freedom systems with parametric stiffness
AU - Acar, Gizem
AU - Feeny, Brian F.
N1 - Publisher Copyright:
© The Society for Experimental Mechanics, Inc. 2016.
PY - 2016
Y1 - 2016
N2 - In the work presented, the solutions and stability of multi-degree-of-freedom Mathieu-type systems are investigated. An approach combining Floquet theory with harmonic balance is used to find the system response. The assumed Floquet-type solution consists of a product between an exponential part and a periodic part. The periodic part is approximated with a finite number of harmonics, and without making further assumptions, this solution is directly applied the original differential equations of motion. A harmonic balance analysis results in an eigenvalue problem. The characteristic exponents are the eigenvalues and the corresponding eigenvectors provide the Fourier coefficients of the harmonic part of the solution. By examining the solutions of the eigenvalue problem, the initial conditions response, frequency content, and stability characteristics can be determined. The approach is applied to two and three DOF examples. For a few parameter sets, the results obtained from this method are compared to the numerical solutions.
AB - In the work presented, the solutions and stability of multi-degree-of-freedom Mathieu-type systems are investigated. An approach combining Floquet theory with harmonic balance is used to find the system response. The assumed Floquet-type solution consists of a product between an exponential part and a periodic part. The periodic part is approximated with a finite number of harmonics, and without making further assumptions, this solution is directly applied the original differential equations of motion. A harmonic balance analysis results in an eigenvalue problem. The characteristic exponents are the eigenvalues and the corresponding eigenvectors provide the Fourier coefficients of the harmonic part of the solution. By examining the solutions of the eigenvalue problem, the initial conditions response, frequency content, and stability characteristics can be determined. The approach is applied to two and three DOF examples. For a few parameter sets, the results obtained from this method are compared to the numerical solutions.
KW - Floquet theory
KW - Harmonic balance
KW - Mathieu equation
KW - Parametric stiffness
KW - Stability
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U2 - 10.1007/978-3-319-29910-5_22
DO - 10.1007/978-3-319-29910-5_22
M3 - Conference contribution
AN - SCOPUS:84978689397
SN - 9783319299099
T3 - Conference Proceedings of the Society for Experimental Mechanics Series
SP - 211
EP - 219
BT - Special Topics in Structural Dynamics - Proceedings of the 34th IMAC, A Conference and Exposition on Structural Dynamics 2016
A2 - Tarazaga, Pablo A.
A2 - Castellini, Paolo
A2 - di Miao, Dario
T2 - 34th IMAC, Conference and Exposition on Structural Dynamics, 2016
Y2 - 25 January 2016 through 28 January 2016
ER -