The dynamic analysis of the elastic response of marine structures to intense, localized, transient, hydrodynamic impact loads is important in the design of marine vessels. A dry and wet dynamic analysis of vibration of a square Kirchhoff’ s plate is presented. The dry and wet natural frequencies and modeshapes of the plate have been evaluated by Galerkin’s method. The transient loads are of two kinds: a uniform stretching load and a hydrodynamic impact load (at different deadrise angles). The stretching load sets the plate into small-amplitude high-frequency vibrations. The computationally efficient normal mode analysis has been used to evaluate the dynamic deflections. Three different boundary conditions of the plate have been used. The response of the plate to these loads has been investigated for a wide range of impact speeds and material properties. The response characteristics have been established, namely (a) maximum deflection, (b) maximum dynamic overshoot relative to the static deflection, (c) quasi-static and dynamic zones of the response over the range of time-scales. The dependency of these characteristics on parameters like the deadrise angles, damping ratios, boundary conditions and forcing configurations have also been studied, to aid the designer. A separate study of the modal participation factor is used to establish modal truncation limits for the analysis, with subsequent increases in the computational efficiency.

Dynamic response of Kirchhoff’s plates to transient hydrodynamic impact loads

Hydroelastic Response of Marine Structures to Impact-induced Vibrations

HYDROELASTIC RESPONSE OF MARINE STRUCTURES TO IMPACT-INDUCED VIBRATIONS by Nabanita Datta Chair : Armin W. Troesch This research deals with the numerical analysis of the hydroelastic behavior of marine vessels under hydrodynamic impact loads, which causes potentially detrimental local flexural vibrations in the vessel. The objective is to provide the dynamic response spectra for transient water-structure dynamics subject to typical impact loads and time scales, using one-way coupling between the fluid and the structure. The hydrodynamic pressure is assumed to be applied on the rigid plate, and then the plate is modelled to respond elastically. The structural vibrations are assumed not to influence the hydrodynamic pressure field. The changing wetted surface is the prime complexity of the problem. The sweeping load sets the plate into small amplitude vibrations, exciting all its natural frequencies (fundamental and overtones). The time-scales of the problem are : (a) the duration of the forcing when sweeping across the plate, and (b) the natural period of the structure. Assuming small deflections of the structure, normal mode summation is used to calculate the vibratory response. The total deflection is assumed to be a series summation of the modal deflections. When the amplitude of the vibrations is small, the dynamic stresses are directly proportional to the flexural displacement. xx Two configurations of the moving load, i.e. (i) uniform stretching load and (ii) impact load, are applied. The coupled system of modal governing differential equation is non-dimensionalized in space and time, and the Dynamic Loading Factor (DLF) of the loading is numerically evaluated by the fourth-order Runge-Kutta method. The corresponding static deflections are calculated by Galerkin’s method. The ratio of the maximum dynamic deflection to the maximum static deflection is the DLF. This analysis provides recommendations to the structural designer, who typically relies on static analysis. The modal participation spectra relative to the dominant fundamental mode for various impact speeds is used to establish modal truncation guidelines. The variation of the response with respect to space and time, and with respect to various parameters like the aspect ratio, damping ratio, boundary conditions, and deadrise angles has been studied. The change in natural frequencies of the structure due to these parameters, and immersion, has also been evaluated.

Hydroelastic Response of Marine Structures to Impact-induced Vibrations. Hydroelastic Reponse of Marine Structures to Impact-induced Vibrations.

Dynamic analysis of thin rectangular elastically supported stiffened plates with axial loads is presented. A floating airport is modeled as a horizontal Kirchhoff’s plate, which is elastically supported at the ends; and is subjected to the impact of aircrafts landing and deceleration over its length. This sets the free-free-free-free plate into high-frequency vibration, causing flexural stress waves to travel over the plate. First, the beam natural frequencies and modeshapes in either direction are generated with these complexities. The Eigen value analysis of the governing differential equation is done, using the weighted summation of the product of the beam modes. The accuracy of the frequencies is compared with those from FEA studies. The radiation pressure on the bottom side of the plate is included to reduce the frequencies by the added-mass effect. The plate is then subjected to decelerating shock loads. The vibratory response is analyzed by the computationally efficient normal mode analysis. The amplification factor vs. the taxiing time of the moving load is generated.Copyright © 2013 by ASME

Paul Joseph

Papers

Vibrations of generally orthotropic plates in fluids