N. Ganesan

A note on vibration of a cantilever plate immersed in water

Abstract The added mass of the fluid surrounding it plats an important role in the dynamic behaviour of a submerged structure. The first few mode shapes and the respective natural frequencies of a submerged cantilever plate are found by using a finite element procedure, eigenvalues being obtained by a simultaneous iteration technique. The influence of the water depth below the plate and also of the waters lateral extent is considered, in order to test the convergency of the results. Results on the effects of the depth of immersion on the natural frequencies and mode shapes of the cantilever plate for different aspect ratios are presented.

Vibration analysis of a rectangular plate subjected to a thermal gradient

The dynamic free response of thin rectangular plates subjected to one and two dimensional steady state temperature distributions satisfying Laplaces equation is analyzed. The governing equations of motionare derived by a finite difference method and solved by a simultaneous iteration technique to obtain eigenvalues and eigenvectors. The accuracy of the method is assessed by comparing the results for some typical cases with those obtained by classical methods. The finite element method is also employed for the problem and the results obtained compare well with those of the finite difference method. From the results an attempt is made to correlate the non-dimensional frequency parameter and the temperature. Plates of different boundary conditions, with at least one edge clamped, free to expand or contract in their planes, are studied.

Partial coverage of rectangular plates by unconstrained layer damping treatments

Theoretical and experimental investigations have been made to study the damping effectiveness of unconstrained partially applied damping treatments applied to rectangular plates. By using the finite element approach, different configurations of partially applied damping layer treatments have been analyzed for their effectiveness in realizing maximum system damping with minimum mass of the applied damping material. The effects of partial application on the modal frequencies, loss factors and mode shapes are discussed. The theoretical results are validated by suitable experiments. Specific recommendations are made for the near-optimum distribution of the damping material on the panel surface which is effective for many modes of panel response.

Response of plates with unconstrained layer damping treatment to random acoustic excitation, part I: Damping and frequency evaluations

Abstract For theoretical evaluation of the response of a structure under random acoustic excitation a complete understanding is required of the various modes of vibration and the modal damping associated with each mode. In order to evaluate these parameters for plates with unconstrained layer damping treatment, some of the theoretical approaches applicable are used. Experimentally observed modal frequencies and associated loss factors are compared with those estimated by different theories for all edges simply supported and all edges clamped boundaries, after accounting for the damping at supports. The modes of vibration used in the theoretical analysis for these boundaries are compared with those observed in the experiments. These results are made use of in Part II for the evaluation of response under random acoustic excitation.

Transmission line vibrations

Various forms of dampers are used to suppress vibrations in transmission lines. In the present paper a study has been made on vibrations of transmission lines having one or more dampers (Stockbridge type) near each end of the span for different cable lengths. An attempt is made here to study the effect of the location of dampers on maximum strains produced in the line. A comparative study of the maximum strains produced is also made for various wind power input assumptions. In addition, a finite difference method is used to find the natural frequency and a finite element method is used to find the natural frequency and mode shapes of the cable with and without a damper.

Torsional vibrations of prismatic shells

Prismatic shells find wide application in mechanical, civil and aeronautical engineering. The object of this paper is to propose a method of analysing such shells having different internal ribbing for their torsional vibrations. The governing equations of motion are derived by using a finite difference method and solved by the simultaneous iteration technique. The accuracy of the method is ascertained by comparing the results for some wellknown boundary conditions with the results obtained by classical methods. Shells of square cross-section and rectangular shells of variable and constant cross-section have been analysed. The effects of introduction of diaphragms on the eignefrequencies have been analysed. The effects of variations in shell thickness and length on the dynamic behaviour also have been studied.

Free vibration characteristics of periodically stiffened panels with damped stringers

Abstract Free vibration characteristics of a periodically stiffened panel with unconstrained viscoelastic damping layers applied to the flanges of the stringers are analyzed by using the wave propagation approach. Periodic structure theory in conjunction with the concept of damped forced waves is used in the determination of resonant frequencies and the associated loss factors of the composite structure. The complex nature of the rotational and transverse stiffnesses of the stringers is taken into consideration in the analysis. Numerical results showing the effect of the geometric and material properties of the damping layer treatment on the resonant frequencies and loss factors of the composite panel are presented.

Conditions for backward whirling motion of a flexible rotor supported on hydrodynamic journal bearings

The necessary conditions for backward whirling motion of a Jeffcott rotor supported in identical hydrodynamic journal bearings are investigated in this paper. Backward whirling motion of the rotor centre is shown to occur if and only if the load parameter is greater than a limiting value corresponding to the flexibility parameter. In spite of the backward whirling motion of the rotor centre, the journal centre is shown to orbit only in the forward sense.

The effect of modified inlet boundary conditions on the stiffness and damping characteristics of finite hydrodynamic journal bearings

Abstract The well-known solutions for the pressure distribution in the lubricating film of a hydrodynamic journal bearing, satisfying the Reynolds boundary conditions, show a sudden change in the pressure gradient at the position of maximum film thickness, which is possible only if the lubricant is supplied precisely at this location. Since the pressure develops smoothly because of hydrodynamic action, a correction in the boundary conditions is applied and a modified solution for the pressure distribution is obtained. The stiffness and damping characteristics of a finite hydrodynamic journal bearing using the new boundary conditions are compared with the wellknown characteristics incorporating the Reynolds boundary conditions. There is a significant change in the dynamic characteristics particularly at low values of the eccentricity ratio which can influence the characteristics of rotor-bearing systems.

Response of clamped sandwich panels with viscoelastic core under random acoustic excitation

Abstract Both theoretical and experimental studies have been made to evaluate the acceleration response of square sandwich panels with clamped boundaries under a specific random acoustic excitation. Generalized harmonic analysis was used to compute the response spectrum. The modal frequencies and associated loss factors of the composite used in the analytical estimation of the response were obtained by applying Galerkins procedure. The effects of modal cross coupling and of the core thickness on the response have been studied. The theoretical estimates of the response are compared with the results from the experiments for certain core thicknesses.