Showing papers in "Journal of Vibration and Acoustics in 1992"

A Spectral Element Approach to Wave Motion in Layered Solids

Abstract: A matrix methodology similar to that of the finite element method is developed for the analysis of stress waves in layered solids. Because the mass distribution is modeled exactly, the approach gives the exact frequency response of each layer. The fast Fourier transform and Fourier series are used for inversion to the time/space domain. The impact of a structured medium with multiple layers is used to demonstrate the method. Comparison with existing propagator and direct global matrix methods show the present approach to be computationally more efficient.

Optimal Semi-Active Suspension with Preview Based on a Quarter Car Model

Abstract: This paper deals with the synthesis of an optimal yet practical finite preview controller for a semi-active dissipative suspension system based on a two - degree - of - freedom (2-DOF) vehicle model. The proposed controller utilises knowledge about approaching road disturbances obtained from preview sensors to minimise the effect of these disturbances. A truly optimal control law, which minimises a quadratic performance index under passivity constraints, is derived using a variational approach. The optimal closed loop system becomes piecewise linear varying between two passive systems and a fully active one. It is shown that the steady state system response to a periodic input is also periodic and its amplitude is proportional to the amplitude of the input. Therefore, frequency domain characteristics in a classical sense can be generated. The problem formulation and the analytical solution are given in a general form and hence they apply to any bilinear system with system disturbances that are a priori unknown but some preview information is possible. The results of this analysis are applied to a quarter car model with semi-active suspension whose frequency domain and time domain performances are evaluated and compared to those of fully active and passive models. The effect of preview time on the system performance is also examined.

Coupled Vibration of Cracked Shafts

Abstract: The coupling of vibration modes of vibration of a clamped-free circular cross-section Timoshenko beam with a transverse crack is investigated in this paper. A 6 × 6 local flexibility matrix is used to simulate the crack. The nondiagonal terms of this matrix cause coupling between the longitudinal, torsional, and bending vibrations. Coupling is apparent in all spectra obtained with a harmonic sweeping excitation throughout the frequency range. The method is very sensitive even for small cracks.

Consistent Modeling of Rotating Timoshenko Shafts Subject to Axial Loads

Abstract: The equations of motion of a flexible rotating shaft have been typically derived by introducing gyroscopic moments, in an inconsistent manner, as generalized work terms in a Lagrangian formulation or as external moments in a Newtonian approach. This paper presents the consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load. The coupling between flexural and torsional vibration due to mass eccentricity is not considered. In addition, a new approach for calculating correctly the effect of an axial load for a Timoshenko beam is presented based on the change in length of the centroidal line. It is found that the use of either a floating frame approach with the small strain assumption or a finite strain beam theory is necessary to obtain a consistent derivation of the terms corresponding to gyroscopic moments in the equations of motion. However, the virtual work of an axial load through the geometric shortening appears consistently in the formulation only when using a finite strain beam theory.

Vibration Damping Through Liquid Sloshing, Part I: A Nonlinear Analysis

Abstract: Energy dissipation due to sloshing liquid in rigid torus shaped containers is studied using the potential flow model in conjunction with the boundary layer correction. The analysis is based on the perturbation method to solve for the nonlinear free surface equation. Special consideration is given to the case of resonant interactions which yield interesting damping characteristics. The results suggest that large diameter ratios and low liquid heights lead to efficient damper design. The concept is applicable to a wide spectrum of problems characterized by low frequency oscillations as encountered in wind, ocean and earthquake engineering.

Spectral Analysis of Wave Motion in Plane Solids With Boundaries

Abstract: A spectral formulation is employed whereby in-plane stress waves are synthesized from the superposition of components at discrete frequencies and wavenumbers. The summations are performed using the fast Fourier transform and the Fourier series, respectively. Because the components are discrete, the solution to problems (over the entire field) with completely arbitrary loading, both in time and space, is made tractable. Waves generated from a line load acting on an infinite and semiinfinite plane are first considered. A cascade approach is then adopted for the treatment of these waves incident on a free, fixed, and elastic boundary. At each stage, the results are compared with those obtained from the available classical solutions and/or finite element results. These studies will form the basis for the investigation of in-plane stress waves in multiply layered media.

On the use of momentum balance and the assumed modes method in transverse impact problems

Abstract: The objective of this investigation is to examine the validity of applying the assumed modes method and the generalized impulse momentum approach that involves the coefficient of restitution in the analysis of transverse impact in constrained elastic systems. A simple impact model that consists of a rotating beam which is subjected to a transverse impact by a mass (impact hammer) moving with a constant velocity is used. For the purpose of comparison and in order to check the validity of using the proposed technique, the transverse deformation of the beam with respect to the beam coordinate system is described using three different assumed sets of orthogonal functions. The different sets of modes are the clamped-free modes, pin-free modes, and a set of assumed harmonic functions. The system mass matrix that accounts for the coupling between the rigid body motion and the elastic deformation is identified and used with the Jacobian matrix of the kinematic constraints and the coefficient of restitution to define the algebraic generalized impulse momentum equations that describe the transverse impact. The series solution obtained using the generalized impulse momentum equations is used to define the generalized impulse, the jump discontinuity in the system reference and modal velocities, and the jump discontinuities in the generalized joint reaction forces. It is shown in this investigation, that by increasing the number of elastic degrees of freedom, the jump discontinuity in the angular velocity of the rod as well as the generalized impulse converge to zero regardless of the assumed complete set of modes used. The effect of the coefficient of restitution and the mass ratio on the jump in the system velocities and the generalized reaction forces is also examined.

Coriolis Effect on the Vibration of a Cantilever Plate With Time-Varying Rotating Speed

Abstract: A method for investigating the Corilois effect on the vibration of a cantilever plate rotating at a time-varying speed is presented in this paper. Due to this time-dependent speed, parametric instability occurs in the system. Furthermore, owing to the existence of the Coriolis force, the system equation is transformed, by a special modal analysis procedure, into independent sets of first-order simultaneous differential equations. This set of simultaneous differential equations is solved by the method of multiple scales, yielding the system response and the expressions for the boundaries of the unstable regions. Finally, the Coriolis effect on the changes in the boundaries of the unstable regions is investigated numerically.

Effect of a vibrating substructure on acoustic radiation from a cylindrical shell

Abstract: The presence of a substructure in a cylindrical shell gives rise to dynamic interactions, including resonance effects, which have an influence on the radiated acoustic field. The lowest mode of the substructure may interact vigorously with a higher order mode of the shell. In this paper a Lagrangian formulation is used to analyze the forced motion of the immersed shell/substructure system. In addition, the frequency window method is used to reduce the complexity of the resulting expressions and to obtain approximate solutions in a frequency range of interest. The particular example is concerned with a spring-mass system, which is attached to the shell. Three cases of forced harmonic motion are considered. The radiated pressure is computed as a function of the frequency. The radiated pressure for the shell/substructure system is compared with that for a shell without an oscillator subjected to the same input force.