Dynamic characteristic analysis of the constrained beams

Yunn-Lin Hwang; Wei-Hsin Gau

doi:10.1117/12.905135

15 November 2011 Dynamic characteristic analysis of the constrained beams

Yunn-Lin Hwang, Wei-Hsin Gau

Proceedings Volume 8321, Seventh International Symposium on Precision Engineering Measurements and Instrumentation; 83212S (2011) https://doi.org/10.1117/12.905135
Event: Seventh International Symposium on Precision Engineering Measurements and Instrumentation, 2011, Yunnan, China

Abstract

A procedure is developed in this investigation to study the propagation of impact-induced axial waves in the constrained beams that undergo large rigid body displacements. The solution of the wave equations is obtained using the Fourier method. Kinematic conditions which describe mechanical joints in the system are formulated using a set of nonlinear algebraic constraint equations that are introduced to the dynamic formulation using the vector of Lagrange multipliers. The initial conditions which represent the jump discontinuity in the elastic coordinates as the result of impact are predicted using the generalized impulse momentum equations that involve the coefficient of restitution as well as the Jacobian matrix of the kinematic constraints. The convergence of the series solutions presented in this paper is examined and the analytical and numerical results are found to be consistent with the solutions obtained by the use of the classical theory of elasticity in the case of plastic impact. The cases in which without and with the gravity are also examined and it is shown that the generalized impulse momentum equations can be used with confidence to study the propagation of elastic waves in applications related to multibody dynamic systems.

Citation Download Citation

Yunn-Lin Hwang and Wei-Hsin Gau "Dynamic characteristic analysis of the constrained beams", Proc. SPIE 8321, Seventh International Symposium on Precision Engineering Measurements and Instrumentation, 83212S (15 November 2011); https://doi.org/10.1117/12.905135

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KEYWORDS

Wave propagation

Kinematics

Silicon

Phase velocity

Beam shaping

Complex systems

Differential equations

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