Showing papers on "Natural frequency published in 1986"
TL;DR: In this paper, a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method was used to obtain the natural frequencies of rectangular plates. But the results for lower modes were not as good as those obtained by other methods.
469 citations
TL;DR: In this article, an experimental study has been made of a circular cylinder in steady and oscillatory flow with non-zero mean velocity up to a Reynolds number of 40000, and the results for the stationary cylinder are in close agreement with previously published data.
Abstract: An experimental study has been made of a circular cylinder in steady and oscillatory flow with non-zero mean velocity up to a Reynolds number of 40000. The results for the stationary cylinder are in close agreement with previously published data. Skin-friction measurements revealed the amplitude of fluctuation of the boundary layer for different angular locations. It has been universally accepted that bluff bodies shed vortices at their natural frequency of shedding (Strouhal frequency), or, when synchronized with an external unsteadiness, at the frequency of the disturbance or half of it, depending of the direction of the unsteadiness. Our findings, instead, indicate that the shedding frequency may vary smoothly with the driving frequency before locking on its subharmonic. Moreover, the present results indicate that, at the lowest frequency limit of lock-on, vortices are shed simultaneously on both sides of the model. A more traditional alternate pattern of vortex shedding is then recovered at higher driving frequencies.
174 citations
TL;DR: Asymptotic equations for the natural frequencies and mode shapes of an elastic, taut, inclined cable were derived from more general asymptotics results by assuming quasi-static stretching.
Abstract: Asymptotic equations are derived for the natural frequencies and mode shapes of an elastic, taut, inclined cable. The equations are derived from more general asymptotic results by assuming quasi‐static stretching. It is shown that for horizontal cables all previous results are recovered, while inclined cables have additional properties which cannot be obtained by using horizontal cable results. The phenomena of avoided crossings and hybrid mode formation are reviewed for inclined cables, in particular because of the significant dynamic tension amplification they induce.
98 citations
TL;DR: In this article, a simple practical procedure is presented for evaluating the dynamic response of an upright circular cylindrical liquid storage tank to a vertical component of ground shaking, considering the flexibility of the supporting medium.
Abstract: A simple practical procedure is presented for evaluating the dynamic response of an upright circular cylindrical liquid storage tank to a vertical component of ground shaking, considering the flexibility of the supporting medium. The tank is presumed to be supported through a rigid circular mat at the surface of a homogeneous elastic half‐space, and it is analyzed approximately by application of Galerkin's method considering the tank‐liquid system to respond as a single‐degree‐of‐freedom system in its fixed‐base condition. Comprehensive numerical data are included that elucidate the actions of both rigidly and flexibly supported tanks, and the effects of the numerous parameters that influence the response. It is shown that soil‐structure interaction reduces the hydrodynamic effects and that the consequences of such interaction may be approximated with good accuracy by a change in the natural frequency of the tank‐liquid system and by an increase in damping. The maximum hydrodynamic effects are related sim...
78 citations
TL;DR: In this article, the authors introduce the concept of resonant heat transfer enhancement based on excitation of shear-layer instabilities present in internal separated flows, which is applicable both in laminar and turbulent flows.
66 citations
Patent•
21 Feb 1986
TL;DR: In this article, a mass flowmeter of the Coriolis-type is conducted through a loop supported on a stationary frame, the loop having a natural resonance frequency, mounted at the vertex of the loop is a ballistic vibrator which is electrically energized to cause the loop to vibrate at its natural frequency on either side of its static plane.
Abstract: A mass flowmeter of the Coriolis-type in which the fluid to be metered is conducted through a loop supported on a stationary frame, the loop having a natural resonance frequency. Mounted at the vertex of the loop is a ballistic vibrator which is electrically energized to cause the loop to vibrate at its natural frequency on either side of its static plane. The fluid passing through the loop is subjected to Coriolis forces, causing the vibrating loop to torsionally oscillate in accordance with the mass flow rate of the fluid. This torsional oscillation is sensed by a pair of strain gauge transducers mounted in balanced relation on opposite legs of the loop, whereby the signals yielded by the transducers have a difference in magnitude therebetween that depends on the amplitude of the torsional oscillation. These signals are applied to a differential amplifier whose output is proportional to the mass flow rate of the fluid.
30 citations
TL;DR: The model of a harmonic oscillator of natural frequency ω0 under the joint action of a periodic driving force of frequency λ and pulsation in mass of frequency Ͻ is considered as a classical or quantized system in this paper.
Abstract: The model of a harmonic oscillator of natural frequency ω0 under the joint action of a periodic driving force of frequency λ and pulsation in mass of frequency ν is considered as a classical or quantized system. Dirac variables are utilized to solve the equations of motion to first and second order in the strength of the mass pulsation and a simple procedure is indicated for extension to any order. The solution contains secular terms and shows resonance behaviour at ν = 2ω0, λ = ω0 or λ = 3 ω0. The fluctuation in energy of the system is examined. At resonance the rotating-wave approximation is shown to furnish an asymptotic solution of the equations of motion for large values of the time. In the same approximation the Green’s function is calculated and the Schrodinger equation is solved.
21 citations
Patent•
13 Jun 1986
TL;DR: In this paper, a method and apparatus for tightening or loosening screw-type connections, in which the screw bolt is stimulated to oscillate longitudinally, the natural frequency of the bolt is measured and the excitation frequency is made to follow the changing natural frequency during the bolting process with a minimum, necessary excitation energy.
Abstract: A method and apparatus for tightening or loosening screw-type connections, in which the screw bolt is stimulated to oscillate longitudinally, the natural frequency of the bolt is measured and the excitation frequency is made to follow the changing natural frequency during the bolting process with a minimum, necessary excitation energy, so that the screw bolt attains a permanent state of resonance.
17 citations
TL;DR: In this article, a method and equipment for qualifying shock absorbers of motor vehicles including the placing of the wheels of the vehicle on suitable supports, measuring the static contact force acting standstill, imposing a forced constant amplitude sinusoidal vibration to, and exceeding the natural resonance frequency of the chassis, then removing this excitation and measuring the contact force as a function of the changing frequency.
Abstract: A method and equipment for qualifying shock absorbers of motor vehicles including the placing of the wheels of the vehicle on suitable supports, measuring the static contact force acting standstill, imposing a forced constant amplitude sinusoidal vibration to, and exceeding the natural resonance frequency of the chassis, then removing this excitation and measuring the contact force as a function of the changing frequency. The positioning of the wheels are checked before the forced vibration, then when the frequency drops below natural frequency, one wheel is vibrated at natural frequency of the chassis by holding the frequency of forced vibration to that value, and at that frequency the minimum contact force is measured, then the value characteristic of the applied shock absorber is determined from the static contact force and minimum contact force. The apparatus has a supporting member to transfer the swinging motion to the wheel of the vehicle chassis, a force-sensing unit coupled to the supporting member, an electronic measuring unit to receive the signals of the force-sensing unit and a unit to check proper adjustment of the pair of wheels, wherein the electronic measuring unit includes dynamometers indicating the forces arising in the supporting member coupled to each unit of the pair of wheels, and a control processor unit to process the output signals of the dynamometers.
15 citations
TL;DR: In this article, a comprehensive analysis of the dynamic response of vertically excited circular ring foundations with mass that are supported at the surface of a homogeneous, linear halfspace is made, and it is shown that both the harmonic and transient responses may, over a wide range of conditions, be compared with good accuracy by considering the foundation-soil system to respond as a single-degree-of-freedom system.
Abstract: A comprehensive analysis is made of the dynamic response of vertically excited circular ring foundations with mass that are supported at the surface of a homogeneous, linear halfspace. The harmonic response of such foundations is evaluated over wide ranges of the parameters involved, and it is shown that both the harmonic and transient responses may, over a wide range of conditions, be compared with good accuracy by considering the foundation-soil system to respond as a single-degree-of-freedom system. Plots are included from which the natural frequency and damping of the equivalent simple oscillator may be determined readily.
12 citations
TL;DR: An exact analytical formula for the complex polarizability of two dipoles constrained to rotate in two dimensions under the influence of their mutual dipole-dipole coupling is derived subject to the condition that the motion is lightly damped and that non-linear effects are weak as discussed by the authors.
TL;DR: In this paper, the authors investigated the tube-TSP interaction dynamics and the fluid excitation forces in shell-and-tube heat exchangers, including nuclear plant steam generators, and derived their support from longitudinally positioned tube support plates (TSPs).
Abstract: Tubes in shell-and-tube heat exchangers, including nuclear plant steam generators, derive their support from longitudinally positioned tube support plates (TSPs). Typically there is a clearance between the tube and TSP hole. Depending on design and fabrication tolerances, the tube may or may not contract all of the TSPs. Noncontact results in an inactive TSP which can lead to detrimental flow induced tube vibrations under certain conditions dependent on the resulting tube-TSP interaction dynamics and the fluid excitation forces. The purpose of this study is to investigate the tube-TSP interaction dynamics. Results of an experimental study of damping and natural frequency as functions of tube-TSP diametral clearance and TSP thickness are reported. Calculated values of damping ratio and frequency of a tube vibrating within an inactive TSP are also presented together with a comparison of calculated and experimental quantities.
01 Jan 1986
TL;DR: In this article, the authors considered the problem of elastic-plastic beam elements joined by hinges with constrained mutual rotations and showed that there exists an optimum value of the limit mutual rotation associated with the maximum elastic strength.
Abstract: Elastic-plastic beam elements joined by hinges with constrained mutual rotations are considered. The problem belongs to mechanics of systems with unilateral boundary conditions. In the pure elastic range, one can observe effects such as nonlinear response of the structure and concavity of the elastic surface in the load space. It appears that there exists an optimum value of the limit mutual rotation associated with the maximum elastic strength. Free elastic vibrations of a portal frame at unilateral boundary conditions are also considered. An important feature of such a structure is the fact that the amplitude may be a double-valued function of the natural frequency. The method of reaching the ultimate load is not unique. In particular cases, one can observe changes in the plastic flow mechanism, even in the range of small displacements. In case of optimum value of limit mutual rotation, the ultimate load is reached in a purely elastic way. The work presented may explain some effects that occur ...
TL;DR: In this article, an experimental modal analysis of tennis racket was carried out at the University of Han Yang in order to obtain the modal parameter of tennis rackets, and the authors compared air and epoxy type rackets to investigate the damping effect due to the existence and/or nonexistence of damping material, by examining its maximum bending moment and logarithmic decrement after impact between racket and ball.
Abstract: A study of spectral analysis as a field of applied engineering has been recently advanced for the identification of structural dynamic characteristics, and many analysis methods to detect vibration sources are under study. In this paper, an experimental modal analysis of tennis racket was carried out at the University of Han Yang in order to obtain the modal parameter. Air type and epoxy type rackets were compared with each other to investigate the damping effect due to the existence and/or nonexistence of damping material, by examining its maximum bending moment and logarithmic decrement after impact between racket and ball. In order to clarify the dynamic behaviour of tennis racket, mode shapes corresponding to each natural frequency were obtained, and its sweet spot was determined by considering the node line at each natural frequency. The final modification was applied in a new prototype and its dynamic behaviour was checked by experimental modal analysis.
Patent•
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30 Jun 1986
TL;DR: In this article, the authors proposed a bar vibrating body with multiple lugs for a vibrating substance, and set the natural frequency of transverse vibration of this lug higher than the vibration frequency of a motor.
Abstract: PURPOSE: To improve the yielding force and speed, by specifying a bar vibrating body with multiple lugs for a vibrating substance, and by setting the natural frequency of transverse vibration of this lug higher than the vibration frequency of a motor. CONSTITUTION: A vibrating wave motor is composed of a group of piezoelectric elements 1, an elastic body 21 as a vibrating substance, a moving body 3, a supporting vibration absorber 4 and an anchor body 5. By the travelling vibrating wave of a group of piezoelectric elements 1, etc. the moving body 3 coming into contact with the elastic body 21 is forced to move in the direction of an arrow A or in the reverse direction. At this moment, multiple lugs 21A extended from the bottom of the elastic body 21 are provided in the whole circuit of the elastic body 21. The form of the lug 21A is selected so that the natural frequency of the transverse vibration of the beam of this lug 21A may become higher than the vibrating frequency of the motor. Thus, the travelling wave is not disturbed and its yielding force is not reduced even if the length 1 of the lug 21A is elongated and the pressure W to apply is increased. COPYRIGHT: (C)1988,JPO&Japio
Patent•
16 Apr 1986
TL;DR: In this paper, a piezoelectric vibrator or vibrator is wired in such a way that they can be excited electrically in or out of phase, which can be used to determine rheological properties of liquids, the damping of the vibration of the strip in the liquid being determined by an amplitude measurement and the change in natural frequency, and also to determine the elastic properties of the liquid.
Abstract: The device determines the vibration parameters of a longitudinally vibrating strip which is excited by a piezoelectric vibrator and whose vibrations are received and evaluated. The notable feature of the device is that the piezoelectric vibrator or vibrators is or are arranged and wired in such a way that they can be excited electrically in or out of phase. The device invented can be used, in particular, for determining the rheological properties of liquids, the damping of the vibration of the strip in the liquid being determined by an amplitude measurement and the change in natural frequency being used to determine the elastic properties of the liquid. However, the device can also be used to determine the chemical composition of a fluid, and furthermore to determine the filling level of a liquid in a container, to determine the complex modulus of elasticity and Young's modulus, to measure the diameter of workpieces or the distance between two edges of a workpiece, and finally, also to measure the expansion of an object such as, for example, a bridge or a building or the like.
TL;DR: In this paper, the use of Dunkerley's first-order method for estimating the fundamental natural frequencies of tower structures is discussed, and an asymmetric geometry may be considered, even though this leads to coupling between bending and torsion.
Patent•
25 Mar 1986
TL;DR: In this paper, the center frequency from the natural frequency of a frequency selecting element itself, such as a ceramic vibrator, was determined to eliminate the fluctuation of center frequency caused by the deviation, etc., of the value of each parts.
Abstract: PURPOSE:To eliminate the fluctuation of the center frequency caused by the deviation, etc., of the value of each parts, by determining the center frequency from the natural frequency of a frequency selecting element itself, such as ceramic vibrator, etc. CONSTITUTION:Oscillation in which the natural frequency of a ceramic vibrator X1 is used as the center frequency, is performed by a positive feedback circuit from the transistor (TR) Q7 of an oscillating circuit section to another TR Q6 through a node P3 and resistance R3. On the other hand, electric currents of the same and opposite polarities to the electric current flowing from the node P3 to a capacitor C3 are respectively produced in the collectors of TRs Q12 and Q13. Thereafter, each current is mixed in a ratio corresponding to a control voltage VCNT and outputted to TRs Q9 and Q11, and then, fed back to the TR Q13 through the node P3 and capacitor C3. Therefore, a positive and negative equivalent capacities are connected with the node P3 in accordance with the value of the control voltage VCNT. Accordingly, fluctuation of the center frequency caused by the deviation, etc., of the constant value of each parts can be eliminated.
Patent•
30 Jan 1986
TL;DR: In this article, the spring constant of a rubber elastic body is varied in response to the resonance frequency of a structural member by means of a spring constant varying means, and this enables effective provision of a vibration preventing effect produced by the rubber body and a mass member.
Abstract: PURPOSE:To effectively prevent production of different types of resonance from a structural member by means of a single damper and to reduce the generation of vibration and noise, by a method wherein the spring constant of a rubber elastic body is varied in response to resonance frequency of a structural member by means of a spring constant varying means. CONSTITUTION:When an engine support member (m) produces resonance with, for example, a low natural frequency occasioned by vibration from an engine, in a spring constant varying means 8, the state is detected by a first detecting means 12 of an electronic control circuit 11. By means of a signal from the electronic circuit 11 (OR circuit 14), a motor 10 is driven, and a control member 9 is rotated in a condition in that the direction of a long axis coincides with the direction of the long axis of a through-hole 7 of a rubber elastic body (rubber 1). In which case, a rubber elastic body 5 is apt to deformation at a portion around the through-hole 7. Spring constant is decreased in response to a lower natural frequency, and this enables effective provision of a vibration preventing effect produced by the rubber elastic body 5 and a mass member 6.
TL;DR: In this paper, an analysis of the natural frequency and dynamic response of a cantilever beam subjected to base motion is presented, and the analysis is extended to a case in which the beam is mounted on a composite support.
TL;DR: In this article, the relationship between the clamped force and the values which show the nature of the dynamic characteristics of a beam containing the junction is presented. But the beam is clamped by a pair of specimens with the asperity on the surface.
Abstract: This paper presents the relationship between the clamped force and the values which show the nature of the dynamic characteristics of a beam containing the junction. The values are the damping ratios, effective stiffness, compliance of the resonance frequency and natural frequency of the 1st and 2nd mode with the beam. The beam with one fixed and other end free is used in the experiments. The beam is clamped by a pair of specimens with the asperity on the surface. Also, FEM is applied to estimated the values of the characteristics theoretically. Herzian theory is applied to calculate the stiffness of the roughness on the specimen. The damping ratios are calculated using the effective stiffness and the compliance of the resonance frequency as the frequency response diagram of the beam containing the junction is given approximately by superposition of a second-order system. The natural frequency and effective stiffness of the each modes increase with and the damping ratios decrease with stronger the clamped force. These theoretical values have the similar tendency and is approximately equal to the experimental one.
Patent•
25 Sep 1986
TL;DR: In this article, a pair of enclosed vessels 3, 3' capable of expansion and contraction by bellows etc are installed on both sides of a frame 1 and filled with liquid fully.
Abstract: PURPOSE:To prevent resonance of a structure without losing the anti-vibrational effect for external vibration having a higher frequency than the natural frequency by applying damping force through oscillation of a liquid in a connecting pipe first when the amplitude of structure exceeds a certain value CONSTITUTION:A pair of enclosed vessels 3, 3' capable of expansion and contraction by bellows etc are installed on both sides of a frame 1 These vessels 3, 3' are put in communication through a narrow and long connecting pipe 4 and filled with liquid fully A gap g is provided between the frame 1 and vessels 3, 3' in order to suppress generation of vibration in the liquid along said connecting pipe 4 until the amplitude of the frame 1 as structural member attains a certain specified value
01 Jan 1986
TL;DR: In this paper, a special nonlinearity of the Jeffcott equations in rotordynamics is examined and the immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing.
Abstract: The special nonlinearities of the Jeffcott equations in rotordynamics are examined. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing. Deadband, side force and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency is defined and used to develop the solutions of the nonlinear Jeffcott equations as asympotic expansions. This nonlinear natural frequency which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies. Numerical solutions are included for comparison with the analysis. Also, nonlinear frequency-response tables are made for a typical range of values.
Journal Article•
TL;DR: Based on the classical beam theory, a simple method for calculating the natural frequency of unequally spanned tubes is presented in this article, where the method is suitable for various boundary conditions and accuracy of the calculations is sufficient for practical applications.
Abstract: Based on the classical beam theory, a simple method for calculating the natural frequency of unequally spanned tubes is presented. The method is suitable for various boundary conditions. Accuracy of the calculations is sufficient for practical applications. This method will help designers and operators estimate the vibration of tubular exchangers. In general, there are three reasons why a tube vibrates in cross flow: vortex shedding, fluid elasticity and turbulent buffeting. No matter which is the cause, the basic reason is that the frequency of exciting force is approximately the same as or equal to the natural frequency of the tube. To prevent the heat exchanger from vibrating, it is necessary to select correctly the shell-side fluid velocity so that the frequency of exciting force is different from the natural frequency of the tube, or to vary the natural frequency of the heat exchanger tube. So precisely determining the natural frequency of the heat exchanger, especially its foundational frequency under various supporting conditions, is of significance.
TL;DR: In this paper, it was shown numerically as well as experimentally that the resonance causing a head positioning error results from a coincidence of rotor natural frequency and the ball bearing excitation frequency.
Abstract: Large capacity magnetic disks require a head postioning accuracy in the order of a few micro-meters. This implies a technology to master the difficult problems of the disk-spindle assembly vibration. The following subjects are studied in this paper : (1) The gyroscopic effect on the natural frequency of the rotor-bearing system is experimentally made clear by exciting a rotating spindle. (2) The whirling force acting on the spindle system is dominantly caused by slight deformations on the ball bearing races. (3) It is shown numerically as well as experimentally, considering whirling direction, that the resonance causing a head positioning error results from a coincidence of rotor natural frequency and the ball bearing excitation frequency.
TL;DR: Theoretical analysis based on the energy principle is presented in a generalised form for predicting damped and undamped natural frequencies as well as logarithmic decrement of such beams as discussed by the authors.
Abstract: In order to control the intensity of troublesome vibration in the modern day structures, viscoelastic materials are sometimes bonded to one or both sides of those structures. This type of unconstrained damping layer treatment is quite effective for abating structural vibration. In this paper both theoretical and experimental investigation has been made on the dynamic characteristics of such beam-like structures in order to get sufficient design data. Theoretical analysis based on the energy principle is presented in a generalised form for predicting damped and undamped natural frequencies as well as logarithmic decrement of such beams. Expressions for the loss-factor and static stiffness are also found out in order to evaluate dimensional inter-relationship between base metal and damping layer for maximizing damping capacity of the structure without losing its stiffness. Experimental measurements for natural frequency and log-decrement bear out the fact that theoretical predictions are indeed accurate. It...
01 Aug 1986
TL;DR: In this article, a simple mathematical model of nonlinear axial force-displacement behavior in jointed members is presented for the sample case of solid structural members of circular section.
Abstract: Hertzian contact theory is applied to a butt joint with specially mismatched bearing surfaces to devise a simple mathematical model of nonlinear axial force-displacement behavior in jointed members. Normalized tangent stiffness-force plots, for several values of a joint imperfection parameter, are presented for the sample case of solid structural members of circular section. The results illustrate the potential problem of high joint compliance at low axial-force levels, as well as the generally desirable stiffening and linearizing effects of preload. A nonlinear oscillator problem based on the static model is also formulated and solved to illustrate the effect of amplitude on natural frequency. As expected, natural frequency is low when amplitude is small. The results call attention to the important roles that tight tolerances and preload are expected to play in the design and fabrication of deployable and erectable truss-type space structures.
Patent•
30 Oct 1986
TL;DR: In this paper, a ring-like elastic unit is disposed in a casing body of a supersonic wave motor, and an annular hard rubber 14 secured to the end 12a of a rotor shaft is pressed and contacted with one side of the unit 10.
Abstract: PURPOSE:To maximize the efficiency of a motor by providing a piezoelectric detector for monitoring the vibration of an elastic unit and control means for switching the frequency of a high frequency voltage through a frequency modulator. CONSTITUTION:A ringlike elastic unit 10 is disposed in a casing body of a supersonic wave motor, and an annular hard rubber 14 secured to the end 12a of a rotor shaft 12 is pressed and contacted with one side of the unit 10. An electrostrictive ring 16 is fixedly arranged on the opposite outer periphery of the unit 10, and a supersonic wave vibrator 18 is formed of the both 10, 16. A traveling wave which rotates in the prescribed direction is generated on the surface of the unit 10 with the high frequency voltage applied thereto to rotate the rotor 12. In this case, a ringlike piezoelectric detector 32 for monitoring the vibration mode is bonded to one side of the unit 10. A driver 34 which contains the detector 32 has a frequency regulator 36 and control means 42 in addition to an oscillator 24, and finely regulates the exciting frequency to be applied to the ring 16 even if the natural frequency of the unit 10 varies.
TL;DR: In this paper, a numerical approach for estimating the mode shape and natural frequency of an orthotropic plate is proposed by applying an iterative method similar to Stodola's method to the governing equation not of a free vibration but of a forced one.
Abstract: A numerical approach is proposed for estimating the mode shape and natural frequency of an orthotropic plate. By applying an iterative method similar to Stodola's method to the governing equation not of a free vibration but of a forced one, a series solution is derived. By using this solution as a trial function, the application of Galerkin's technique to the governing equation of a free vibration yields approximate equations for estimating the natural frequency and the mode shape. It is a merit of this approach that one can estimate directly the arbitrary order natural frequency and mode shape. For the discussion of the convergency and accuracy of the solution, a simply supported orthotropic rectangular plate with an intermediate support is demonstrated. From these results, it follows that one can estimate values with sufficient accuracy. As numerical examples, natural frequencies are computed for various flexural rigidities and aspect ratios.