Hydrodynamic impact of a system with a single elastic mode I : theory and generalized solution with an application to an elastic airframe Page: 1 of 17
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HYDRODYNAMIC IMPACT OF A SYSTEM WITH A SINGLE ELASTIC MODE
I-THEORY AND GENERALIZED SOLUTION WITH AN APPLICATION
TO AN ELASTIC AIRFRAME '
By ILBUR L. IMAYO
Solutions of impact of a rigid prismatic float connected by a
massless spring to a rigid upper mass are presented. The
solutions are based on hydrodynamic theory which has been
experimentally con formed for a rigid structure.
Equations are giren for defining the spring constant and the
ratio of the sprung mass to the lower mass so that the two-mass
systemm protides representation of the fundamental mode of an
airplane wing. The forces calculated are more accurate than
the forces which would be predicted for a rigid airframe since
the effect of the fundamental mode on the hydrodynamic force
is taken into account. The response of the tuw-mnass system
gives the response of the represented mode and, although no
prorisn is made for taking into account the effect of secondary
nideN on the hydrodynamic force, means are indicated whereby
the results may be used to approximate the response of modes
other than the fundamental mode.
Time histories of the hydrodynamic force and structural
response are given for wide ranges of mass distribution and
ratio of natural period to the period of the impact. By use of
nondimensional coefficients these results are made applicable
to different combinations of velocity, weight, angle of dead rise,
and fluid density. Although the equations permit solutions for
different combinations of flight-path angle and trim, an approxi-
mation is given for correcting the results for the combination for
which solutions are given to other conditions within a narrow
range indicated to be of primary interest to the design engineer.
In a comparison of the theoretical data with data for a severe
flight-test landing impact, the effect of the fundamental mode on
the hydrodynamic force is considered and response data are
compared with experimental data. Consideration of the funda-
mehtal mode alone fails to account for the fact that during the
impact partial failure of the inboard-engine mounts occurred,
but use of the theoretical solutions to approximate the effects of
further wIing torsion leads to substantial agreement.
In recent years the development of large airplanes has
caused the elastic behavior of airframe structures during
landing impact to become important. The work which has
been done on this problem has been handicapped by lack of
proper knowledge of the time history of applied ground
reaction. This situation has been particularly acute for
seaplanes because of difficulties. in measuring the hydro-
dynamic force, the seaway, and the manner of contact with
In order to facilitate the interpretation of flight data and
to lead to the prediction of design loads on a rational basis,
a theoretical hydrodynamic study was made and tests of a
rigid float were conducted at the Langley impact basin.
Since the results of these tests agree with the theoretical
results for wide ranges of the pertinent variables in numerous
force time histories (reference 1), it is assumed that the
theory may also be used in considering the effect of the
upper-structure elasticity of a seaplane on the motion and
force characteristics of the hull proper, which is assumed to
The bending of wings during impact, which for modem
flying boats is the primary structural action, is considered in
the present report by reducing the fundamental mode to an
equivalent two-mass system. The results are presented in
a form suited to general application and are compared with
experimental results for a particular case. The equations
showing the method of solution are included in appendix A,
and a sample data sheet is given as table I.
t, time required for one-fourth cycle of natural
t, time between initial contact and maximum hydro-
dynamic force for rigid structure
t time elapsed after initial contact
mL lower, or hull, mass of two-mass system
ms upper, or sprung, mass of two-mass system
m gross mass (W/g or ms+ mL)
W gross weight
g acceleration due to gravity
K spring constant of spring connecting ms and mL,
force per unit deflection
n, acceleration normal to water surface of nodal point
of elastic system, multiples of acceleration of
gravity; for two-mass system, acceleration of
center of gravity
n, oscillatory acceleration of hull about center of gravity
of two-mass system or nodal point of represented
mode, multiples of the acceleration of gravity
t Supersedes NACA TN 1316, "Solatfons for Hydrodynamic Impct Force and Response of a Two-Mass System with an Application to an Elastei Airframe" by Wilbur L. Mayo, 1947.
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Mayo, Wilbur L. Hydrodynamic impact of a system with a single elastic mode I : theory and generalized solution with an application to an elastic airframe, report, January 1, 1952; (digital.library.unt.edu/ark:/67531/metadc60433/m1/1/: accessed January 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.