Dynamic Responses of Two Beams Connected by a Spring-Mass Device

Abstract

This paper deals with the transverse free vibrations of a system in which two beams are coupled with a spring-mass device. The dynamics of this system are coupled through the motion of the mass. The entire system is modeled as two two-span beams and each span of the continuous beams is assumed to obey the Euler-Bernoulli beam theory. Considering the compatibility requirements across each spring connection position, the eigensolutions (natural frequencies and mode shapes) of this system can be obtained for different boundary conditions. Some numerical results and experimental validations are presented to demonstrate the method proposed in this article.

Coupling effects with vibration-based estimation of individual bolt tension in multi-bolt structures

“…Different approaches to determine eigensolutions have been proposed. In the work of [14], two clamped-clamped beams, connected with a spring-mass system are analyzed. In [15], two pinned-pinned beams connected with a spring and damper subjected to a moving force are considered.…”

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

“…Therefore, methods predominantly based on numerical techniques are not always suitable for modal analysis in the high frequency range [11] . To circumvent the above problem, many analytical models have been proposed for beam structures connected to various types of attachments such as lumped concentrated mass [12][13][14][15][16] and/or rotatory inertia [17] , spring and damper [18] , single spring-mass [14,[19][20][21][22][23][24][25][26] , double spring-mass [27][28][29][30][31][32] , spring-mass chain [33,34] which all have wide ranging applications in engineering. The attachment as lumped mass used in these publications is by and large assumed to be a concentrated point mass without any consideration to the size or dimension of the mass or its mass moment of inertia.…”

“…Thus, there are some difficulties to apply these existing methods to complex multibody systems. For example, unlike the numerical method where the stiffness and mass matrices can be formulated separately [9] , almost all existing analytical methods [45][46][47][48][49][50]2,6,13,52,14,15,[22][23][24]26,27,[29][30][31]55,[32][33][34][35][37][38][39][40]42,44,61,62] apply the usual determinant method for non-trivial solution of the eigenvalue problem for which the determinant of the coefficient matrix vanishes. The determinant method needs the evaluation of the determinant numerically for one frequency at a time.…”

Dynamics of a beam with multiple spring/mass attachments using binary asymptotic admissible functions

“…Lin and Yang 12 used a transfer matrix method for studying the dynamics of two beams connected by a spring-mass-spring device. The method was extended to n spring-mass-spring devices at different locations of the beam for all classical boundary conditions.…”