Linear and autoparametric modal analysis of aeroelastic structural systems

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Title: Linear and autoparametric modal analysis of aeroelastic structural systems
Author: Woodall, Tommy Dale
Abstract: This investigation deals with the linear modal analysis and autoparametric interaction of aeroelastic systems such as an airplane fuselage and wing with fuel storage . The mathematical modeling is derived by applying Lagrange's equations taking into consideration the Christoffel symbol of the first kind to account for the nonlinear coupling of the system coordinates , velocities , and accelerations . The linear modal analysis will be obtained by considering the linear , conservative portion of the equations of motion . The normal mode frequencies and the associated mode shapes are obtained in terms of the system parameters . The main objective of the linear analysis is to explore the critical regions of autoparametric (or internal ) resonance conditions , £kiwi=0 (where ki are integers and wi are the normal mode frequencies ) . The results show that for certain system parameters the condition of internal resonance is satisfied . The dynamic behavior of the structure in the neighborhood of internal resonance conditions is obtained by considering the nonlinear coupling of the normal modes . The asymptotic approximation technique due to Struble is employed . Three groups of internal and normal resonance conditions are obtained from the secular terms of the first -order perturbational equations . The transient and steady -state responses cure obtained numerically by using the IBM Continuous System Modeling Program (CSMP ) with double precision Milne integration . The transient response shows a build up in the interacted modes to a level which exceeds the steady -state response . In addition , the excited mode is suppressed by virtue of the nonlinear feedback of other modes . Under certain conditions , the steady -state response is derived analytically . It is concluded that the nonlinear modal analysis reveals certain types of response characteristics which cannot be interpreted within the framework of the linear theory of small oscillations .
URI: http : / /hdl .handle .net /2346 /21210
Date: 1984-05


Linear and autoparametric modal analysis of aeroelastic structural systems. Master's thesis, Texas Tech University. Available electronically from http : / /hdl .handle .net /2346 /21210 .

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