Patent Publication Number: US-11645436-B2

Title: Mode-shaped components

Description:
This application claims priority to European Patent Application EP19175620.4 filed May 21, 2019, the entirety of which is incorporated by reference herein. 
     The present disclosure relates to a method for designing a component, to a method for manufacturing a component, and to a component. 
     A common problem, in particular in the field of rotating machinery, is controlling the level of vibration. Vibration may be caused by imbalances of components of the machinery, such as, e.g., a shaft, compressor and turbine discs and blades in gas turbine engines, and also external forcing such as, e.g., aircraft maneuvers and aerodynamic forces in an aircraft with the gas turbine engine. Damping systems such as fluid dampers are commonly employed to reduce vibrations. 
     Vibrations are specifically pronounced at particular rotational speeds and/or frequencies, known as “critical” speeds, in view of resonances of the rotating system. At the critical speeds systems commonly vibrate in resonance, a condition at which vibrations are sustained by the system internal vibratory response determined by the designed stiffness, inertia and damping. The damping system is commonly designed such that its capabilities are not exceeded in use. In many cases the damping system and other components, such as a supporting structure, correspondingly have a relatively high weight. In many fields however, for example, aerospace, weight is an important consideration. 
     It is an object to reduce vibrations with a lightweight component design. 
     According an aspect there is provided a method for manufacturing a component. The method comprises designing or receiving a model of the component (e.g., a 3d-CAD model); determining, e.g., by computer simulation, at least one mode shape of the model; redesigning the model based on the determined at least one mode shape to obtain a redesigned model of the component; and manufacturing the component in accordance with the redesigned model. 
     This is based on the finding that a vibrational response of a component may particularly effectively be reduced by adapting the geometry of the component to one or more of the mode shapes it has without the modification. 
     The method provides a component design that allows to reduce vibration in resonance by means of variating the distribution of stiffness and/or mass at one or more components (e.g., of an engine), following the paths that are defined by one or more of its mode shapes. 
     Given a certain object or structure, e.g. an engine component, a mode shape (defined by an eigenvector) corresponds to the characteristic deformation pattern at which the component vibrates when a correspondent natural frequency (defined by an eigenvalue) is excited in resonance. In addition to resonances, which are commonly unwanted conditions during operation, aircraft engines repeatedly undergo vibration excited by transient loads such as aircraft maneuvers, speed regulations or control systems interactions, which might be repeated several time per flight, causing fatigue and a eventually loss of the engine structural integrity. 
     The mode shapes of a mechanical arrangement completely define the free and forced response of a mechanical system, being the free vibratory response defined a linear combination of mode shapes (Eq. 1), which depends on the boundary conditions (e.g., initial deformation and velocity).
 
 Y   i ( t )=Σ i   A   i  sin ω i   t−φ   i    Eq. 1
 
     A peculiar property of the mode shapes is the orthogonality with respect to the mass and stiffness matrixes of the mechanical arrangement (e.g., a component or a sub assembly). 
     
       
         
           
             
               
                 
                   
                     
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     The property of the mode shape orthogonality that is defined by Eq. 2 implies that the product of two different mode shapes over a period of the vibration is always equal to zero. In the physical domain of the vibration this represents the antagonism between two different mode shapes that cannot coexist at the same time. 
     In fact, when the initial deformation of an unforced system is given reproducing one of the mode shapes, the response at the other mode is, as the peculiar inertia and stiffness equilibrium cannot take place at the same time. Hence the transient vibration takes place at the frequency of the mode shape that has been used for the initial excitation. 
     Similarly, if a mode shape deformation is forced into the component by means of design, the other modes shapes can be advantageously disrupted, with the benefit of reducing critical vibration in a broad speed range. 
     The Finite Element Modal Analysis is a calculation that can be carried out on engine subsystems and components in order to obtain their natural frequencies (eigenvalues) and correspondent mode shapes (eigenvectors). The characteristic vibratory response of a component includes a complex deformation that is a linear combination of its mode shapes, each one vibrating on at its own frequency. When, in the example of an engine, the engine speed is being variating and a resonance condition, or critical speed, is hit, the deformation of the component that generates vibration becomes coincident with the mode shape correspondent to the natural frequency that is being excited, as determined by the connections with the other engine components. 
     The model may be redesigned in accordance with a pattern of the at least one mode shape. For example, the model is redesigned so that a stiffness and/or mass distribution follows the particular deformation pattern of the at least one mode shape. 
     The at least one mode shape may be a non-critical mode shape. Optionally, one mode shape (e.g., a non-critical mode shape) is selected out of a plurality of mode shapes. The selected mode shape may be one that is able to disrupt the vibration due to one or more critical mode shapes excited in resonance. 
     Determining one or more mode shapes of the component may be performed outside of a normal operating range of an operating condition of the component. This may comprise determining vibrational frequencies experienced in an operating range of the component. The operating condition may be a speed of an engine, wherein the component is a part of the engine. The operating condition may alternatively be a frequency of an excitation of the component (which, in turn may depend of an engine speed). 
     Redesigning the model can be performed so as to adjust a stiffness of the component in accordance with the at least one out-of-operating-range mode shape. It is possible to reduce or eliminate vibrations and/or critical harmonics, at several speeds e.g. of a gas turbine having the component, within the operating range. It has been found that by taking into account mode shapes outside of operational ranges, the vibrational response of components within their operational range may be tuned so that potentially critical mode shapes within the operational range may be effectively disrupted. 
     Redesigning the model may comprise modifying a geometry and/or a mass distribution of the component and/or the choice of a material of the component. For example, the shape and/or material thickness may be adapted to the at least one mode shape. 
     Redesigning the model may also comprise modifying a stiffness, in particular a global stiffness and/or a local stiffness. 
     The stiffness can be modified in a simple way by adding or removing reinforcement and/or by opportunely modifying the shape of the existing surface. 
     The method optionally further comprises checking that a vibrational response of the component within an operating range is reduced after the redesigning, in particular below a predetermined threshold. If this is not the case, the method may repeat the step of determining a mode shape and/or of redesigning the model. 
     The method optionally further comprises iteratively performing the steps of determining and/or redesigning and/or checking several times, e.g., two, three, four, five or more times. 
     Optionally, the component is selected from a plurality of components before the model of this component is redesigned (in particular before the model of the component is designed). For example, the component is selected from a plurality of components of a gas turbine by determining one or more components of the gas turbine which produce(s) vibration and/or critical harmonics by a design failure mode and effects analysis, DFMEA, and/or by a finite element analysis, FEA. Alternatively or in addition, determining one or more mode shapes of the selected model may be performed by DFMEA and/or FEA. 
     After manufacturing the component or of a plurality of components, the component or the plurality of such components may be mounted at a machine, e.g. at a gas turbine, in particular a gas turbine engine of an aircraft. 
     According to an aspect, a component manufactured in accordance with the above method is provided. As a result, the shape of the component corresponds to a mode shape, e.g. with alternating local variations of the shape and/or stiffness. 
     The component may particularly be a component of a gas turbine engine, in particular of a power gearbox thereof, driven by a compressor via a shaft. For example, the component is a ring gear mounting, in particular of such a power gearbox. Vibrations may be particularly difficult to reduce in such gearboxes, in particular vibrations of the ring gear mounting. By designing and manufacturing particularly the ring gear mounting in accordance with the methods described herein, it is possible to substantially decrease vibrations and the weight of the ring gear mounting (and, eventually, also further components). This may increase the lifetime of the power gearbox and/or the time between two maintenances. 
     According to an aspect, a gas turbine, in particular a gas turbine engine for an aircraft is provided, which comprises one or more components as described herein. 
     The skilled person will appreciate that except where mutually exclusive, a feature or parameter described in relation to any one of the above aspects may be applied to any other aspect. Furthermore, except where mutually exclusive, any feature or parameter described herein may be applied to any aspect and/or combined with any other feature or parameter described herein. 
    
    
     
       Embodiments will now be described by way of example only, with reference to the Figures, in which: 
         FIG.  1    shows various mode shapes for components with basic circular geometries; 
         FIG.  2    is a method for designing and manufacturing a component; 
         FIG.  3    is a method for designing and manufacturing a component; 
         FIGS.  4 A to  4 C  show a component without excitation ( FIG.  4 A ), with excitation of a mode shape ( FIG.  4 B ) and a cross section of  FIG.  4 B  ( FIG.  4 C ); 
         FIGS.  5 A and  5 B  show a component in the form of a ring gear mount without excitation ( FIG.  5 A ) and with excitation of a mode shape ( FIG.  5 B ); 
         FIG.  6    is a sectional side view of a gas turbine engine; 
         FIG.  7    is a close up sectional side view of an upstream portion of a gas turbine engine; 
         FIG.  8    is a partially cut-away view of a gearbox for a gas turbine engine; and 
         FIG.  9    (Prior Art) is an aircraft having a plurality of gas turbine engines. 
     
    
    
     For a dynamical system, a mode is a standing wave state of excitation, in which all parts of the system will be affected sinusoidally under a specified fixed frequency. A mode of vibration is characterized by a modal frequency and a mode shape. Given a certain component (in particular a certain engine component), a mode shape corresponds to a characteristic deformation at which the component vibrates when one of its natural frequencies is excited. The vibratory response of the component corresponds to a linear combination of all mode shapes. 
       FIG.  1    shows in four rows examples of different components generally having the shape of a disc. The different columns each show the excitation of a certain mode of vibration, wherein the corresponding mode shapes are indicated. 
     Referring to the first row showing a component in the form of a disc with a hole in the middle as an example, the first mode has a mode shape comprising a symmetric U-shaped deformation. The second mode has a mode shape with two upward deformations and two downward deformations (i.e., each two maxima and minima). The third mode has a mode shape with four maxima and minima, the mode shape shown in the fourth column of the first row has each six maxima and minima. 
     According to aspects described herein, a component, such as one of the components shown in  FIG.  1   , may be redesigned in accordance with one or more of the mode shapes. As a result, the response of the component at other frequencies and thus the overall strength of vibrations of the component may be reduced. Due to eigenvalues orthogonality and Fourier theory applied to system dynamics, a possibility to polarize a system response is based on the idea to force the deformation of a structure to assume a shape similar to one of its mode shapes. 
       FIG.  2    shows a method  100  for designing and manufacturing a component. The method comprises the following steps: 
     Step  101 : designing or receiving a model of the component. The model may be a geometric representation of the component, e.g. in the form of a CAD drawing. The model may be specifically designed or retrieved, e.g., from a database. 
     Step  102 : determining one or more mode shapes of the model. This may comprise performing a finite elements modal analysis. The mode shape may be a non-critical mode shape. The component may be adapted to operate at a predetermined operating range of a given parameter, such as the frequency of an excitation. In gas turbines, for example, a shaft may rotate at a specific range of speeds, wherein the rotation of the shaft may excite a vibration of the component. The determination of the mode shape may be made at values of the parameter outside the operating range (and therefore unlikely to be excited during operation of the machine having the component). 
     Step  103 : redesigning the model based on the determined at least one mode shape (e.g., one mode shape or a combination of several mode shapes) to obtain a redesigned model of the component. This may comprise modifying the geometry and/or other parameters of the model. In particular, redesigning the model may be based on a pattern of the at least one mode shape. This can be done by adjusting a stiffness of the component in accordance with the at least one (e.g., out of operating range) mode shape. As an example, redesigning the model may comprise modifying the geometry and/or mass distribution defined by the model. Optionally, redesigning the model comprises modifying a stiffness defined by the model. The stiffness may be modified by adding or removing a reinforcement structure, e.g., a rib and/or locally increased thickness, and/or by a local hardening of the material. Purely by way of example, it may be found that for the component shown in the first row of  FIG.  1   , the operating range comprises frequencies and intensities that lead to the first, second and third modes. The third mode, e.g., may be found to be a critical mode (e.g., potentially leading to increased wear and/or reduced lifetime). The fourth mode may be found to be outside the operating range and non-critical. The model of the component may be redesigned so as to have the form described by the fourth mode shape. This may disturb the vibrational response of the component in such a way that the third mode becomes no longer critical under the same operating conditions as before. Indeed, a plurality of critical mode shapes may be addressed at the same time by providing the redesigned, modified component geometry. 
     Step  104 : Checking that a vibrational response of the component is reduced, e.g., within the operating range. This may include the comparison of a parameter of the vibrational response with a predetermined threshold. When it is determined at step  104  that the vibrational response is reduced, e.g., to a predetermined extend, the method continues to step  105 . Otherwise, it can optionally repeat steps  102  to  104  at least one time, e.g., iteratively. 
     Step  105 : providing the redesigned model. As an example, the model may be provided in the form of computer-readable instructions being indicative for the geometry of the component. The computer-readable instructions may be provided to a manufacturing machine or the like. 
     Step  106 : manufacturing the component in accordance with the redesigned model. This may be done by means of a machine that received the redesigned model. 
       FIG.  3    shows a method  200  to design and manufacture a component. 
     The method  200  starts at step  201  (component design). At step  201 , a component is designed by providing, designing or otherwise creating a model of the component. The model may comprise a set of definitions that characterize the physical properties, in particular the geometry of the component to be manufactured. 
     The model is provided to a finite elements modal analysis performed at step  202  (FE modal analysis to determine mode shapes and natural frequencies). Therein the modal analysis may determine mode shapes and natural frequencies of a component having the design of the model. This may be performed by a computer. 
     At optional step  203  (harmonic response), a harmonic response is determined, e.g., by a harmonic response analysis. 
     At optional step  205  (maximum stress profiles), maximum stress profiles may be determined and/or provided, e.g. a maximum stress profile of the component to be manufactured. At further optional step  206  (speed envelope), a speed envelope, e.g., of a gas turbine for which the component is to be manufactured for (and during a flight), may be determined and/or provided. At further optional step  207  (dimensional tolerances), dimensional tolerances of the component to be manufactured and/or of adjacent components in the engine are determined and/or provided. 
     The results of the analyses at steps  202  and, optionally  203 , and, optionally, the outcome of steps  205 ,  206  and/or  207  are provided to a critical mode shapes identification at step  204 . Therein, a mode shape may be determined to be critical when it creates or potentially leads to a critical resonance, e.g. having a destructive effect on the component or adjacent components in the engine (or, in general, machine). 
     Further input to the critical mode shapes identification at step  204  may be provided as test results from tests in steps  211  (engine subsystem test),  212  (engine test) and/or  213  (flight test, in particular for a retrofit). 
     At steps  202  and  203 , computer simulations may be applied. For example, a design failure mode and effects analysis, DFMEA, and/or a finite element analysis, FEA. Steps  211  to  213  may provide hardware-based tests that are performed based on a given component design, represented by the model provided in step  201  (or step  101  in  FIG.  1   ). 
     Based on some of, or all of the results provided, at step  204 , critical mode shapes are identified. 
     The mode shape(s) on which to variate the geometry of the component may be identified upon conjoint consideration of an operational speed range and the identification of critical mode shapes that require to be eliminated, or reduced to a maximum extent. The mode shape chosen for altering the geometry may be a non-critical one, out of range and able to mismatching the geometrical periodicities expected to excite resonances during operation. In addition, the mode shape for the stiffness paths may be chosen in order to optimize the disruption of other critical mode shapes at other frequencies. 
     In case that critical mode shapes are identified at step  204 , the method proceeds to step  208 . At step  208  (identification of the mode shape for modal stiffening), a mode shape to be used for a mode-shape specific component stiffening is identified. To this end, the results or a subset of the results of the performance of step  202  may be provided to be used at step  208 . 
     The identified mode shape (e.g., as shown in the first row, third column of  FIG.  1   ), is then provided to a mode-shaped design application at step  209 . Therein, the component design, i.e., the model of the component, is redesigned (modified) so as to at least partially follow the form of the mode shape. An excitation of the mode shape (e.g., a maximum deflection) may be translated to or “frozen” in the redesigned model of the component. 
     The redesigned model and the outcome of step  204  are provided and analyzed at step  210  (vibration reduced to target evaluation). At step  210 , it is evaluated whether or not the vibration of the component according to the redesigned model in response to a given excitation meets a given target, e.g., is reduced so as to be below a predefined threshold. When this is the case, the redesigned model is provided (indicated as  214 ), for manufacturing the component in accordance with the redesigned model at step  215  (manufacturing). 
     If, however, the target is not met, the method may return to step  209  (and from there either to step  201  or to step  210 ) or to step  201 . 
       FIGS.  4 A to  4 C  show geometries of two versions of a component  50 , in the present example a ring gear front diaphragm, having a disc portion  51  and a cylindrical portion  52 .  FIG.  4 A  shows the component  50  in accordance with a model M. The model M is provided at step  101  or  201  of the method  100 ;  200  of  FIG.  2  or  3   . The method  100  of  FIG.  2    or the method  200  of  FIG.  3    is then performed, wherein a redesigned model M′ is created. The component  50  is manufactured in accordance with the redesigned model M′. This is shown in  FIGS.  4 B and  4 C , wherein it becomes apparent that a portion of the model M′, in this example, an outer ring section of the disc portion  51 , has been modified with respect to the original model M such that it assumes the pattern of a mode shape of the component  50 . In the example of  FIGS.  4 B and  4 C , the outer ring section is periodically bent inwards and outwards (in a 7-nodal diameter mode shape). The surface of the outer ring section follows the mode shape deformation of the unmodified component (see  FIG.  4 A ). 
       FIG.  4 C  shows an optional way of stiffening portions in accordance with a mode shape by adding one or more reinforcements  53  in a pattern that corresponds to the mode shape (indicated by dashed lines). The reinforcements  53  may be formed as stiffening ribs and/or local thickness variations. Another option is to arrange a composite material (or portions thereof) along the mode shape. 
       FIGS.  5 A and  5 B  show two versions of another component  60 . This component  60  is a ring gear mount for mounting a ring gear  38  of a gearbox of a gas turbine engine to a stationary structure of the gas turbine engine by means of a flange  61 . The gas turbine engine, gearbox and ring gear  38  will be described in greater detail below with reference to  FIGS.  6  to  8   . 
       FIG.  5 A  shows the component  60  designed in accordance with a model M that has not yet been tuned on a mode shape, and excited in an operating range of frequencies and intensities. Local deformations are very pronounced and lead to stresses on the component  60  which may reduce its lifetime. The mode shape is a critical 8-diameter mode shape. 
       FIG.  5 B  shows a version of the component  60  manufactured in accordance with the method  100 ;  200  of  FIG.  2  or  3    (in accordance with a redesigned model M′) at the excitation as shown in  FIG.  5 A . Stresses are more smoothly distributed over the component  60 , so that it can withstand the stresses more stably. Thus, the lifetime of the component  60  according to the redesigned model M′ may be increased. Alternatively or additionally, the weight of the component  60  may be reduced. 
     It becomes apparent that by means of the method described herein, vibrations of the component can be optimized. Manufacturing a component  50 ;  60  in accordance with the method  100 ;  200  allows to reproduce a non-critical mode shape stiffness distribution. 
     In the methods  100 ;  200 , the whole distribution of stiffness of a non-critical mode shape can be used in order to alter the component stiffness and geometry so that the vibration due other, critical mode shapes cannot take place any longer, even if the natural frequency remains within the operational range. 
     This can be achieved particularly due to the principle of antagonism between different mode shapes. Stating in simplified words, if a mode shape exists, other mode shapes cannot take place at the same time or are minimized by being disrupted due to the presence of the other, non-critical mode shape. By this, the vibration by critical resonances due to other mode shapes may be damped. The non-critical mode shape becomes dominant at all speed as its stiffness has been “shaped” in the geometry. From the integration of the functional requirements of the component and the stiffness variation along the areas identified by a well-defined mode shape, it is possible to reduce the vibration in the frequency ranges where it is most needed. Thereby, several resonances may be addressed at the same time. 
       FIG.  6    illustrates a gas turbine engine  10  for an aircraft. The gas turbine engine  10  has a principal rotational axis  9 . The engine  10  comprises an air intake  12  and a propulsive fan  23  that generates two airflows: a core airflow A and a bypass airflow B. The gas turbine engine  10  comprises a core  11  that receives the core airflow A. The engine core  11  comprises, in axial flow series, a low pressure compressor  14 , a high-pressure compressor  15 , combustion equipment  16 , a high-pressure turbine  17 , a low pressure turbine  19  and a core exhaust nozzle  20 . A nacelle  21  surrounds the gas turbine engine  10  and defines a bypass duct  22  and a bypass exhaust nozzle  18 . The bypass airflow B flows through the bypass duct  22 . The fan  23  is attached to and driven by the low pressure turbine  19  via a shaft  26  (low-pressure shaft) and an epicyclic gearbox. 
     In use, the core airflow A is accelerated and compressed by the low pressure compressor  14  and directed into the high pressure compressor  15  where further compression takes place. The compressed air exhausted from the high pressure compressor  15  is directed into the combustion equipment  16  where it is mixed with fuel and the mixture is combusted. The resultant hot combustion products then expand through, and thereby drive, the high pressure and low pressure turbines  17 ,  19  before being exhausted through the nozzle  20  to provide some propulsive thrust. The high pressure turbine  17  drives the high pressure compressor  15  by a suitable interconnecting shaft  27  (high-pressure shaft). The fan  23  generally provides the majority of the propulsive thrust. The epicyclic gearbox  30  is a reduction gearbox. 
     The gas turbine engine  10  comprises one or more components designed in accordance with the method  100 ;  200  of  FIGS.  2  and/or  3   , e.g. a ring gear mount of the gearbox  30 . 
     An exemplary arrangement for a geared fan gas turbine engine  10  is shown in  FIG.  7   . The low pressure turbine  19  (see  FIG.  6   ) drives the shaft  26 , which is coupled to a sun wheel, or sun gear,  28  of the epicyclic gear arrangement  30 . Radially outwardly of the sun gear  28  and intermeshing therewith is a plurality of planet gears  32  that are coupled together by a planet carrier  34 . The planet carrier  34  constrains the planet gears  32  to precess around the sun gear  28  in synchronicity whilst enabling each planet gear  32  to rotate about its own axis. The planet carrier  34  is coupled via linkages  36  to the fan  23  in order to drive its rotation about the engine axis  9 . Radially outwardly of the planet gears  32  and intermeshing therewith is an annulus or ring gear  38  that is coupled, via the ring gear mount  60  and linkages  40 , to a stationary supporting structure  24 . 
     Note that the terms “low pressure turbine” and “low pressure compressor” as used herein may be taken to mean the lowest pressure turbine stages and lowest pressure compressor stages (i.e. not including the fan  23 ) respectively and/or the turbine and compressor stages that are connected together by the interconnecting shaft  26  with the lowest rotational speed in the engine (i.e. not including the gearbox output shaft that drives the fan  23 ). In some literature, the “low pressure turbine” and “low pressure compressor” referred to herein may alternatively be known as the “intermediate pressure turbine” and “intermediate pressure compressor”. Where such alternative nomenclature is used, the fan  23  may be referred to as a first, or lowest pressure, compression stage. 
     The epicyclic gearbox  30  is shown by way of example in greater detail in  FIG.  8   . Each of the sun gear  28 , planet gears  32  and ring gear  38  comprise teeth about their periphery to intermesh with the other gears. However, for clarity only exemplary portions of the teeth are illustrated in  FIG.  8   . There are four planet gears  32  illustrated, although it will be apparent to the skilled reader that more or fewer planet gears  32  may be provided within the scope of the claimed invention. Practical applications of a planetary epicyclic gearbox  30  generally comprise at least three planet gears  32 . 
     The epicyclic gearbox  30  illustrated by way of example in  FIGS.  7  and  8    is of the planetary type, in that the planet carrier  34  is coupled to an output shaft via linkages  36 , with the ring gear  38  fixed. However, any other suitable type of epicyclic gearbox  30  may be used. By way of further example, the epicyclic gearbox  30  may be a star arrangement, in which the planet carrier  34  is held fixed, with the ring (or annulus) gear  38  allowed to rotate. In such an arrangement the fan  23  is driven by the ring gear  38 . By way of further alternative example, the gearbox  30  may be a differential gearbox in which the ring gear  38  and the planet carrier  34  are both allowed to rotate. 
     It will be appreciated that the arrangement shown in  FIGS.  7  and  8    is by way of example only, and various alternatives are within the scope of the present disclosure. Purely by way of example, any suitable arrangement may be used for locating the gearbox  30  in the engine  10  and/or for connecting the gearbox  30  to the engine  10 . By way of further example, the connections (such as the linkages  36 ,  40  in the  FIG.  7    example) between the gearbox  30  and other parts of the engine  10  (such as the input shaft  26 , the output shaft and the fixed structure  24 ) may have any desired degree of stiffness or flexibility. By way of further example, any suitable arrangement of the bearings between rotating and stationary parts of the engine (for example between the input and output shafts from the gearbox and the fixed structures, such as the gearbox casing) may be used, and the disclosure is not limited to the exemplary arrangement of  FIG.  7   . For example, where the gearbox  30  has a star arrangement (described above), the skilled person would readily understand that the arrangement of output and support linkages and bearing locations would typically be different to that shown by way of example in  FIG.  7   . 
     Accordingly, the present disclosure extends to a gas turbine engine having any arrangement of gearbox styles (for example star or planetary), support structures, input and output shaft arrangement, and bearing locations. 
     Optionally, the gearbox may drive additional and/or alternative components (e.g. the intermediate pressure compressor and/or a booster compressor). 
     Other gas turbine engines to which the present disclosure may be applied may have alternative configurations. For example, such engines may have an alternative number of compressors and/or turbines and/or an alternative number of interconnecting shafts. By way of further example, the gas turbine engine shown in  FIG.  6    has a split flow nozzle  20 ,  22  meaning that the flow through the bypass duct  22  has its own nozzle that is separate to and radially outside the core engine nozzle  20 . However, this is not limiting, and any aspect of the present disclosure may also apply to engines in which the flow through the bypass duct  22  and the flow through the core  11  are mixed, or combined, before (or upstream of) a single nozzle, which may be referred to as a mixed flow nozzle. One or both nozzles (whether mixed or split flow) may have a fixed or variable area. Whilst the described example relates to a turbofan engine, the disclosure may apply, for example, to any type of gas turbine engine, such as an open rotor (in which the fan stage is not surrounded by a nacelle) or turboprop engine, for example. In some arrangements, the gas turbine engine  10  may not comprise a gearbox  30 . 
     The geometry of the gas turbine engine  10 , and components thereof, is defined by a conventional axis system, comprising an axial direction (which is aligned with the rotational axis  9 ), a radial direction (in the bottom-to-top direction in  FIG.  6   ), and a circumferential direction (perpendicular to the page in the  FIG.  6    view). The axial, radial and circumferential directions are mutually perpendicular. 
       FIG.  9    shows an aircraft  8  in the form of a passenger aircraft. Aircraft  8  comprises several (i.e., two) gas turbine engines  10  in accordance with  FIGS.  6  to  8   . 
     The identification of the out-of-range mode shape(s) may target the stiffness and mass distributions may result in an effective reduction of the vibration throughout wide gas turbine engine  10  speed ranges where vibrations are deemed to be critical for the engine operation. 
     It will be understood that the invention is not limited to the embodiments above-described and various modifications and improvements can be made without departing from the concepts described herein. Except where mutually exclusive, any of the features may be employed separately or in combination with any other features and the disclosure extends to and includes all combinations and sub-combinations of one or more features described herein. 
     For example, the invention may be applied particularly to components of gas turbines, such as gas turbine engines, and power plants, rigs, engine mounts, large frames, buildings, civil structures, as well as in turbines, pumps, bearings, accessory and power gearboxes and others, but it can also be applied to components of other machines, in particular any type of engine. It is also worth noting that the methods described herein can optionally be used to redesign a component for retrofitting a part, e.g., when it has been found that the part vibrates critically in use. 
     For aircraft engines, such as gas turbine engines, components particularly suitable for being redesigned as described herein are housings, static structures, struts, vanes and blades. The modification of geometry upon mode-shape patterns may further be combined with the use of composite materials or single crystals (e.g. for blades). 
     LIST OF REFERENCE NUMBERS 
     
         
           8  airplane 
           9  principal rotational axis 
           10  gas turbine engine 
           11  engine core 
           12  air intake 
           14  low-pressure compressor 
           15  high-pressure compressor 
           16  combustion equipment 
           17  high-pressure turbine 
           18  bypass exhaust nozzle 
           19  low-pressure turbine 
           20  core exhaust nozzle 
           21  nacelle 
           22  bypass duct 
           23  propulsive fan 
           24  stationary support structure 
           26  shaft 
           27  interconnecting shaft 
           28  sun gear 
           30  gearbox 
           32  planet gears 
           34  planet carrier 
           36  linkages 
           38  ring gear 
           40  linkages 
           50  component 
           51  disc portion 
           52  cylindrical portion 
           53  reinforcement 
           60  component 
           61  flange 
         A core airflow 
         B bypass airflow 
         M model 
         M′ redesigned model