Vibrations of Orthogonally Stiffened Panels

1978 ◽  
Vol 22 (02) ◽  
pp. 100-109 ◽  
Author(s):  
Niels FI. Madsen
Keyword(s):  
Numerical Method ◽  
Cross Section ◽  
Natural Frequencies ◽  
Axial Deformation ◽  
Linear Combinations ◽  
Stiffened Panels ◽  
Natural Frequencies And Modes ◽  
Modes Of Vibration

A general numerical method for the determination of natural frequencies and modes of vibration for orthogonally stiffened panels is presented. The panel is considered as an assembly of prismatic beams and plate strips rigidly connected along their longitudinal edges and transversely stiffened by beams of varying cross section. The modes of vibration are approximated by linear combinations of the analytically calculated modes of vibration for the prismatic panel, resulting from neglecting the transverse stiffening and assuming simple end supports. For the transverse stiffening, the effects of shear deflection, axial deformation, and St. Venant torsion are taken into account. As a practical example, the natural frequencies of a deep girder in a tanker have been calculated.

Natural frequencies of cooling tower shells

1967 ◽  
Vol 2 (2) ◽  
pp. 127-133 ◽  
Author(s):  
B G Neal
Keyword(s):  
Cooling Tower ◽  
Natural Frequencies ◽  
Support Condition ◽  
Theoretical Determination ◽  
Electro Deposition ◽  
Horizontal Fracture ◽  
Natural Frequencies And Modes ◽  
Modes Of Vibration ◽  
Hyperbolic Cooling Tower

A theoretical determination of the lowest natural frequencies of inextensional vibrations of hyperbolic cooling tower shells is first presented. It is shown that inextensional behaviour is only possible for certain types of support condition at the base, one of which consists of four pairs of inclined columns evenly spaced round the circumference which, at their points of attachment, only permit displacements normal to the plane of the shell. Experiments to determine the natural frequencies and modes of vibration of a model shell are then described. This model, which was made by the electro-deposition of copper on a Perspex mould, could be supported at its base by up to forty pairs of inclined columns. Using only four evenly spaced pairs of columns the lowest natural frequencies of inextensional vibrations were first determined, and found to agree well with the theoretical values. The natural frequencies and modes of the extensional vibrations which occurred when the shell was supported by forty pairs of columns were then explored. Finally, the effect of removing some of the supports, thereby simulating a horizontal fracture in part of the shell, was studied. The possibility of wind-induced vibrations occurring in practice is then considered. It is concluded that these are unlikely to occur unless the shell has already suffered damage, as for example by experiencing a horizontal fracture over part of its circumference near the base.

On the Determination of the Dynamic Characteristics of a Vibrating System

1967 ◽  
Vol 71 (683) ◽  
pp. 793-796 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Dynamic Characteristics ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Experimental Investigations ◽  
Aircraft Industry ◽  
Natural Frequencies And Modes ◽  
Vibrating System ◽  
Modes Of Vibration

The natural frequencies and modes of vibration of a structure may be obtained more or less directly from experiments. The generalised masses and stiffnesses, however, are usually obtained indirectly from experimental investigations of the dynamic behaviour of the system. One of the techniques widely used for this purpose in the aircraft industry is known as the method of displaced frequenciesm.Stated briefly, the method consists of observing the changes in the natural frequencies caused by the addition of one or more small masses to the vibrating system.

Effect of the Material Types on the Fundamental Frequencies of Uniaxial Composite Conical Springs

1999 ◽  
Author(s):  
Vebil Yildirim ◽  
Erol Sancaktar ◽  
Erhan Kiral
Keyword(s):  
Transfer Matrix Method ◽  
Pitch Angle ◽  
Natural Frequencies ◽  
Axial Deformation ◽  
Helical Springs ◽  
Fundamental Frequencies ◽  
Helix Pitch ◽  
Constant Pitch ◽  
Α Helix

Abstract This paper deals with the effect of the material types (Graphite-Epoxies and Kevlar-Epoxy) on the fundamental frequencies of uniaxial constant-pitch composite conical helical springs with solid circle section and fixed-fixed ends. The transfer matrix method is used for the determination of the fundamental natural frequencies. The rotary inertia, the shear and axial deformation effects are taken into account in the solution. The free vibrational charts for each material presented in this study cover the following vibrational parameters: n (number of active turns) = 5–10, α = (helix pitch angle) = 5° and 25°, R2/R1, (minimum to maximum radii of the cylinder) = 0.1 and 0.9, and Dmax/d (maximum cylinder to wire diameters) = 5 and 15. These charts can be used for the design of uniaxial composite conical springs.

Free Vibration of Continuous Skin-Stringer Panels

1960 ◽  
Vol 27 (4) ◽  
pp. 669-676 ◽  
Author(s):  
Y. K. Lin
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Structural Configuration ◽  
Modes Of Vibration ◽  
Fuselage Skin

The determination of the natural frequencies and normal modes of vibration for continuous panels, representing more or less typical fuselage skin-panel construction for modern airplanes, is discussed in this paper. The time-dependent boundary conditions at the supporting stringers are considered. A numerical example is presented, and analytical results for a particular structural configuration agree favorably with available experimental measurements.

Deformation Compensation During Buoyancy-Enabled Inkjet Printing of Three-Dimensional Soft Tubular Structures

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Kyle Christensen ◽  
Zhengyi Zhang ◽  
Changxue Xu ◽  
Yong Huang
Keyword(s):  
Cross Section ◽  
Inkjet Printing ◽  
Three Dimensional ◽  
Structural Deformation ◽  
Tubular Structures ◽  
Axial Deformation ◽  
Buoyant Force ◽  
Drop On Demand ◽  
Biological Studies

Of various tissues being fabricated using bioprinting, three-dimensional (3D) soft tubular structures have often been the focus since they address the need for printable vasculature throughout a thick tissue and offer potential as perfusable platforms for biological studies. Drop-on-demand inkjetting has been favored as an effective technique to print such 3D soft tubular structures from various hydrogel bioinks. During the buoyancy-enabled inkjet fabrication of hydrogel-based soft tubular structures, they remain submerged in a solution, which crosslinks the printed structures and provides a supporting buoyant force. However, because of the low stiffness of the structures, the structural deformation of printed tubes poses a significant challenge to the process effectiveness and efficiency. To overcome this structural deformation during buoyancy-enabled inkjet printing, predictive compensation approaches are developed to incorporate deformation allowance into the designed shape. Circumferential deformation is addressed by a four-zone approach, which includes base, circular, vertical, and spanning zones for the determination of a designed cross section or compensated printing path. Axial deformation is addressed by the modification of the proposed circumferential compensation based on the distance of a given cross section to the junction of a branching tube. These approaches are found to enable the successful fabrication of straight and branching alginate tubular structures with nearly ideal geometry, providing a good foundation for the wide implementation of the buoyancy-enabled inkjetting technique. While inkjetting is studied herein as a model bioprinting process, the resulting knowledge also applies to other buoyancy-enabled bioprinting techniques.

Experimental Determination of the Complete Dynamical Properties of a Two-Degree-Of-Freedom Model Having Nearly Coincident Natural Frequencies

1967 ◽  
Vol 9 (5) ◽  
pp. 402-413 ◽  
Author(s):  
R. W. Traill-Nash ◽  
G. Long ◽  
C. M. Bailey
Keyword(s):  
Experimental Investigation ◽  
Experimental Determination ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Influence Coefficients ◽  
Stiffness Properties ◽  
Modes Of Vibration ◽  
Dynamical Properties ◽  
Two Degree Of Freedom

Existing techniques of resonance testing have shown a marked inability to find the principal modes, natural frequencies and levels of damping in a structure which possesses two or more close natural frequencies (1)§. This paper describes an experimental investigation on a two-degree-of-freedom model of a technique which makes use of dynamical influence coefficients (or receptances) measured at a number of stations on the structure (2) (3) (4) (5). The measured coefficients are used to calculate natural frequencies and modes of vibration, and the mass, damping and stiffness properties of the system. Several model configurations having different natural frequency separations were tested and no special difficulty resulted when natural frequencies were close or even coincident.

Effect of a Change in Position of a Support on the Natural Frequencies and Modes of Vibration of a System

1965 ◽  
Vol 7 (3) ◽  
pp. 271-278 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Torsional Vibration ◽  
Simple Formula ◽  
Natural Frequencies ◽  
Static Deflection ◽  
Deflection Curve ◽  
Natural Frequencies And Modes ◽  
Method Of Solution ◽  
Modes Of Vibration ◽  
Frequency Changes ◽  
Small Change

The effect of a small change in position of one of the supports on the natural frequencies and modes of a structure, which is ‘continuous’ over a number of supports, is examined in this paper. Using energy and receptance methods a simple formula is obtained for the change in natural frequency of a beam when the support displacement is infinitesimal. The corresponding displacements of other nodal points are also obtained. When the support displacement is finite, but not large, changes in mode and frequency are determined by iteration. The method of solution is extended to the coupled flexural and torsional vibration of a non-symmetrical beam. In the case of a rectangular plate with stiffeners parallel to an edge, frequency changes due to the change in position of a stiffener may be determined by the same method. Alternative approximate formulae, based on the static deflection curve, are derived for the change of fundamental frequency.

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