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In order to provide information for flutter and dynamic stress calculations on an aircraft a knowledge of the normal modes of vibration is required. In the following paper a matrix method, due to Dr Traill‐Nash, is extended and used to obtain a general expression for the complete aircraft normal modes, and is applicable to most aircraft configurations. The method is considered to be eminently suitable for use with modern digital electronic computational equipment. Methods arc discussed vthcrcby the degrees of freedom may be economized without significant loss of accuracy. By restriction of the degrees of freedom allowed, important subsidiary cases arc drawn from the general expressions, allowing standard matrix solutions suitable for normal oflicc routine.

The purpose of this paper is establish a model of the equations of a two‐dimensional problem of fluid saturated porous medium for a half space.

A state space approach has been applied to solve the problem. Normal mode analysis is used to obtain the exact expressions for normal stress, tangential stress and pore pressure.

A computer programme is developed and numerical results are obtained for normal stress, tangential stress and pore pressure and depicted graphically for a special model. A particular case of interest has also been deduced from the present investigation.

The disturbance due to force in normal and tangential direction and porosity effect have been observed by the method of normal mode analysis.

This paper aims to deal with the problem of vibration in an aircraft engine turbine shaft shield. The physical model of the system under study is inspired by the PZL-10W aviation jet engine shaft shield and is a structure of the profile circular arc. The main goal of the presented research is to develop a modal model of the discussed object. Another task is to determine the impact of the shaft shield damage on the change of dynamic parameters (the values of the natural frequencies and changing of the shape of the corresponding natural forms) of the discussed object. Finally, the task is connected with the calculation of the excitation speeds of the discussed shaft shield’s respective natural frequencies.

To realize the main goal finite element method simulation and experimental investigation were conducted. The quality of the achieved models is determined based on the relative error of natural frequencies and the similarity to normal modes established on the basis of the modal assurance criterion (MAC) indicator. The Campbell diagram was used to calculate the excitation speeds of the discussed shaft shield’s respective natural frequencies.

The obtained results indicate the changes in the dynamic properties of the shaft shield as a result of its cracking. On the basis of the adopted measurement (MAC indicator), the level of similarity was established between the numerical simulation results and the measurement results for the undamaged shield. Verification of the different mode shapes using the CrossMAC tool is an effective method, which allows comparing of the shape of the natural form and may be helpful in the process of adjusting modal models to the results of experimental tests.

It is important to note that as a result of using commercial software (ANSYS program) and a commercial measuring system (Bruel and Kjaer), the presented analysis can be attractive for design engineers dealing with the dynamics of aviation systems.

The paper presents the authors’ original approach to the dynamic analysis of the aviation engine turbine shaft shield, which can be useful for engineers dealing with the issue of vibration in shaft shield systems.

The purpose of the present paper is to investigate the thermo-mechanical interactions in an initially stressed nonlocal micropolar thermoelastic half-space having void pores under Lord–Shulman model. A moving thermal shock is applied to the formulation.

The normal mode technique is adopted to obtain the exact expressions of the physical quantities.

Numerical computations for stresses, displacement components, temperature field and change in the volume fraction field are performed for suitable material and are depicted graphically. Some comparisons have been shown in figures to estimate the effects of micropolarity, initial stress, voids, nonlocal parameter and time on the resulting quantities.

The exact expressions for the displacement components, stresses, temperature and change in the volume fraction field are obtained in the physical domain. Although numerous investigations do exist to observe the disturbances in a homogeneous, isotropic, initially stressed, micropolar thermoelastic half-space, the work in its current form has not been established by any scholar till now. The originality of the present work lies in the formulation of a fresh research problem to investigate the dependence of different physical fields on nonlocality parameters, micropolarity, initial stress, porosity and time due to the application of a moving thermal shock.

The dual-phase-lag (DPL) model is applied to study the effect of the gravity field and micropolarity on the wave propagation in a two-temperature generalized thermoelastic problem for a medium. The paper aims to discuss this issue.

The exact expressions of the considered variables are obtained by using normal mode analysis.

Numerical results for the field quantities are given in the physical domain and illustrated graphically to show the effect of angle of inclination. Comparisons of the physical quantities are also shown in figure to study the effect of gravity and two-temperature parameter.

This paper is concerned with the analysis of transient wave phenomena in a micropolar thermoelastic half-space subjected to inclined load. The governing equations are formulated in the context of two-temperature generalized thermoelasticity theory with DPLs. A medium is assumed to be initially quiescent and under the effect of gravity. An analytical solution of the problem is obtained by employing normal mode analysis. Numerical estimates of displacement, stresses and temperatures are computed for magnesium crystal-like material and are illustrated graphically. Comparisons of the physical quantities are shown in figures to study the effects of gravity, two-temperature parameter and angle of inclination. Some particular cases of interest have also been inferred from the present problem.

A two‐dimensional coupled problem in electromagneto‐thermoelasticity for a thermally and electrically conducting half‐space solid whose surface is subjected to a thermal shock is considered. The problem is in the context of the Lord and Shulman’s generalized thermoelasticity with one relaxation time. There acts an initial magnetic field parallel to the plane boundary of the half‐space. The medium deformed because of thermal shock and due to the application of the magnetic field, there result an induced magnetic and an induced electric field in the medium. The Maxwell’s equations are formulated and the electromagneto‐thermoelastic coupled governing equations are established. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the considered variables are represented graphically. From the distributions, it can be found the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier’s in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in medium. Comparisons are made with the results predicted by the coupled theory for two values of time.

The finite element model developed for a new-designed aircraft was used to solve some problems of structural dynamics. The key purpose of the task was to estimate the critical flutter velocities of the light airplane by performing numerical analysis with application of MSC Software.

Flutter analyses processed by Nastran require application of some complex aeroelastic model integrating two separate components – structural model and aerodynamic model. These sub-models are necessary for determining stiffness, mass and aerodynamic matrices, which are involved in the flutter equation. The aircraft structural model with its non-structural masses was developed in Patran. To determine the aerodynamic coefficient matrix, some simplified aerodynamic body-panel geometries were developed. The flutter equation was solved with the PK method.

The verified aircraft model was used to determine its normal modes in the range of 0-30 Hz. Then, some critical velocities of flutter were calculated within the range of operational velocities. As there is no certainty that the computed modes are in accordance with the natural ones, some parametric calculations are recommended. Modal frequencies depend on structural parameters that are quite difficult to identify. Adopting their values from the reasonable range, it is possible to assign the range of possible frequencies. The frequencies of rudder or elevator modes are dependent on their mass moments of inertia and rigidity of controls. The critical speeds of tail flutter were calculated for various combinations of stiffness or mass values.

The task described here is a preliminary calculational study of normal modes and flutter vibrations. It is necessary to prove the new airplane is free from flutter to fulfil the requirement considered in the type certification process.

The described approach takes into account the uncertainty of results caused by the indeterminacy of selected constructional parameters.

A low-cost but credible method of low-subsonic flutter analysis based on ground vibration test (GVT) results is presented. The purpose of this paper is a comparison of two methods of immediate flutter problem solution: JG2 – low cost software based on the strip theory in aerodynamics (STA) and V-g method of the flutter problem solution and ZAERO I commercial software with doublet lattice method (DLM) aerodynamic model and G method of the flutter problem solution. In both cases, the same sets of measured normal modes are used.

Before flutter computation, resonant modes are supplied by some non-measurable but existing modes and processed using the author’s own procedure. For flutter computation, the modes are normalized using the aircraft mass model. The measured mode orthogonalization is possible. The flutter calculation made by means of both methods are performed for the MP-02 Czajka UL aircraft and the Virus SW 121 aircraft of LSA category.

In most cases, both compared flutter computation results are similar, especially in the case of high aspect wing flutter. The Czajka T-tail flutter analysis using JG2 software is more conservative than the one made by ZAERO, especially in the case of rudder flutter. The differences can be reduced if the proposed rudder effectiveness coefficients are introduced.

The low-cost methods are attractive for flutter analysis of UL and light aircraft. The paper presents the scope of the low-cost JG2 method and its limitations.

In comparison with other works, the measured generalized masses are not used. Additionally, the rudder effectiveness reduction was implemented into the STA. However, Niedbal (1997) introduced corrections of control surface hinge moments, but the present work contains results in comparison with the outcome obtained by means of the more credible software.

A variational procedure is developed, in the form of an extension of the Rayleigh‐Ritz method, leading to a rapid estimation of the flapwise vibration modes and frequencies of a helicopter rotor blade. The initial data required are the blade mass and stiffness distribution and the angular velocity of the rotor blade. The normal modes and frequencies are subsequently used to determine blade shapes in flight. The aerodynamic forces only enter at a late stage of the analysis, and the effect of differing flight conditions is readily assessed. The method makes extensive use of matrix formulation and particularly lends itself to electronic computation techniques. A numerical example is given for the special case of constant spanwise blade mass distribution, although the method may readily be extended to cover this restriction. The bending moment distribution is also worked out, and flexible and rigid blades are compared.

The purpose of this paper is to study two-dimensional deformations in a nonlocal, homogeneous, isotropic, rotating thermoelastic medium with temperature-dependent properties under the purview of the Green-Naghdi model II of generalized thermoelasticity. The formulation is subjected to a mechanical load.

The normal mode analysis technique is adopted to procure the exact solution of the problem.

For isothermal and insulated boundaries, discussions have been made to highlight the influences of rotational speed, nonlocality, temperature-dependent properties and time on the physical quantities.

The exact expressions for the displacement components, stresses and temperature field are obtained in the physical domain. These are also calculated numerically for a magnesium crystal-like material and depicted through graphs to observe the variations of the considered physical quantities. The present study is useful and valuable for the analysis of problems involving mechanical shock, rotational speed, nonlocal parameter, temperature-dependent properties and elastic deformation.