Influence of Large Amplitude on Response to Sonic Booms
01 Dec 1975-AIAA Journal (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 13, Iss: 12, pp 1549-1550
TL;DR: In this article, the influence of large amplitude on the dynamic response of rectangular isotropic plate with special reference to glass panel subjected to sonic boom is studied for several boom parameters like overpressure, waveform duration, and rise time.
Abstract: Theme ^CONSIDERABLE amount of literature exists on the \^inear dynamic response of discrete and continuous systems subjected to sonic booms.' In the present investigation the influence of large amplitude on the dynamic response of rectangular isotropic plate with special reference to glass panel subjected to sonic boom is studied for several boom parameters like overpressure, waveform duration, and rise time. The solution procedure adopted in the present investigation consists of expressing the governing nonlinear differential equations in the rate form, a method adopted by the authors earlier, and in the process these equations are reduced to a set of linear differential equations. These linear equations are solved approximately spacewise by Galerkin method and time-wise using the Houbolt scheme. The influence of nonlinearity is presented in the form of a ratio of maximum linear to maximum nonlinear dynamic response. It should be mentioned that the rate form linearization has a specific advantage that the resulting linear equations are themselves exact without any approximations, and it can be used equally well for both static and dynamic nonlinear problems. An investigation on nonlinear dynamic behavior of shells of revolution using a similar technique has recently appeared.
Citations
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TL;DR: In this article, the non-linear dynamic responses of both clamped and simply supported rectangular plates have been investigated for uniform pulse loadings, and the numerical results obtained by the present technique compare well with the results available in the literature.
Abstract: The non-linear dynamic responses of both clamped and simply supported rectangular plates have been investigated for uniform pulse loadings. The non-linear partial differential equations have been linearized by expressing one or more of the product terms constituting the non-linearity in the differential equations in Taylor's series. By using a finite difference scheme for space-wise and the Houbot scheme for time-wise integrations, the differential equations are transformed into a set of linear algebraic equations which has been solved by matrix methods without using any iterative techniques. The numerical results obtained by the present technique compare well with the results available in the literature. In addition, the influence of damping on the non-linear dynamic response has been studied.
9 citations
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TL;DR: In this article, the Berger method was used in conjunction with the iso-amplitude contour lines method to analyze the large amplitude response of elliptical plates under various types of dynamic loading, namely a step function, a sinusoidal pulse and an N-wave.
Abstract: The large amplitude vibrations of elastic plates of arbitrary plan form subjected to transient pressure loading are analyzed in a relatively simple fashion by using the Berger method in conjunction with the iso-amplitude contour lines method. The analysis provides for both clamped and simply supported edge conditions. By way of illustration, the large amplitude response of elliptical plates under various types of dynamic loading, namely a step function, a sinusoidal pulse and an N-wave, is investigated and the results are presented graphically. Some comparison is made with previously obtained results for circular plates, as available in the literature.
6 citations
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TL;DR: In this paper, the dynamic response of one of the walls of a full-scale plaster-wood room to sonic-boom loading is investigated using a series solution, and the response of the wall to either N-waves or resulting room pressure is presented.
Abstract: The dynamic response of one of the walls of a full-scale plaster-wood room to sonic-boom loading is investigated using a series solution. The response of the wall to either N-waves or resulting room pressure is presented. The numerical results were confirmed experimentally by measuring the wall strain resulting from subjecting the room with an opening to simulated sonic booms. The agreement between the measured and predicted strains at several locations of the wall for different window sizes and N-wave durations is very satisfactory in terms of amplitude, signature and phase. The possibility of damage to a wall is more critical when a window in the room is open than when it is closed. It is shown analytically and confirmed experimentally, for the plaster-wood wall described herein, that no damage is expected under the pressure loadings from sonic booms produced by current supersonic transport.
5 citations
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TL;DR: In this article, a multi-mode approach based on the Galerkin technique is employed for the analysis of the large amplitude dynamic response of rectangular plates under transient loads, where the plate edges which may be clamped or simply supported are assumed constrained against inplane translation.
Abstract: A multi-mode approach based on the Galerkin technique is employed for the analysis of the large amplitude dynamic response of rectangular plates under transient loads. The plate edges which may be clamped or simply supported are assumed constrained against inplane translation. The nonlinear forces arising from inplane and transverse motions are grouped into a single vector which is added to the forcing vector. The resulting initial value problem is solved numerically in the time domain. By way of illustration, a solution is obtained for a square plate subjected to uniform step loading and the results compare favourably with those available in the literature.
2 citations
References
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TL;DR: A systematic procedure is developed for the calculation of the structural response of an airplane subject to dynamic loads, with particular attention given to determining the stresses developed due to flight through gusts.
Abstract: A systematic procedure is developed for the calculation of the structural response of an airplane subject to dynamic loads. Particular attention is given the problem of determining the stresses developed due to flight through gusts. Difference equivalents for derivatives and matrix notation are used to develop a recurrence relation that permits step-by-step calculation of the response and of the loads that occur on the structure. The chief feature of this recurrence approach is that the generality and physical aspects of the basic equilibrium relations of the problem are preserved without loss of ease in application. The use of difference equivalents for derivatives in the solution of dynamic problems is first illustrated by means of a simple damped oscillator example, and the application to the flexible aircraft structure is then made. For brevity, the case of wing bending and vertical motion of the airplane is treated, although the method may be readily extended to take into account also wing torsional deformations, pitching motion of the airplane, fuselage deflections, and tail forces of known character. Either a sharp-edge gust or a gust of arbitrary shape in the spanwise or flight directions may be treated. Some results obtained by application of the recurrence matrix relation are presented, and the advantages of this method over other methods of evaluating the dynamic response of an aircraft are discussed.
543 citations
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TL;DR: In this article, a partially filled, cylindrical tank was used to study the dynamics of liquid sloshing and pressure distribution in a hydrodynamic theory for breathing vibrations.
Abstract: Hydrodynamic theory for breathing vibrations of a partially filled, cylindrical tank, giving natural frequencies of liquid sloshing as well as pressure distribution
65 citations
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TL;DR: In this article, the response of a damped mass spring system to an N wave is examined in terms of dynamic magnification factors which are expressed as functions of the non-dimensionalized frequency fτ.
Abstract: The response of a damped mass spring system to an N wave is examines. In particular, the dependence of the response upon structural damping, upon the radio of total to positive phase duration, and upon the rise time of the N wave is determined. The cases of response to N waves with shock reflection and to repeated N waves are also studied. The results in this paper are given in terms of dynamic magnification factors which are expressed as functions of the non-dimensionalized frequency fτ. A final curve of dynamic magnification factor against fτ is produced which envelopes the effects of varying positive to negative phase duration, rise time, shock reflections and structural damping. This curve may be used to determine the possibility of damage due to overflights of a supersonic transport.
28 citations
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TL;DR: A detailed theoretical study of the response of a uniform flat rectangular panel to a sonic boom (or “N” wave) is presented in this article, where the N wave arrives normal to the panel surface and where the shock front arrives at any angle of incidence and crosses the panel parallel to one side.
Abstract: A detailed theoretical study of the response of a uniform flat rectangular panel to a sonic boom (or “N” wave) is presented. Both cases, where the N wave arrives normal to the panel surface and where the shock front arrives at any angle of incidence and crosses the panel parallel to one side, are considered. Closed‐form solutions (for individual modes) are given for the cases of simply supported panel response to normal and traveling N waves; an approximate solution is presented for the response of a panel with fully fixed edges to a normal N wave. The Duhamel integral method used gives panel displacement‐, strain‐, and stress‐time histories for any point on the panel. The analyses derived have engineering applications in the computation of window or wall‐panel response to sonic boom. Some comparison made between theory and experiment. Good agreement is shown to exist between measured and predicted strain maxima and fair agreement to exist between the early parts of the strain‐time histories, despite some differences between the experimental and theoretical models. The necessity to include the contributions due to the higher modes is clearly borne out in theory and experiment, particularly for accuracy in strain‐time histories.
22 citations
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