Quantitative Assessment of Mass Discretization in Structural Dynamic Modeling

1986 ◽  
Vol 108 (4) ◽  
pp. 401-405 ◽  
Author(s):  
K. M. Vashi
Keyword(s):  
Degrees Of Freedom ◽  
Quantitative Assessment ◽  
Natural Frequencies ◽  
Exact Analytical Solution ◽  
Discrete Problem ◽  
Span Length ◽  
Structural Dynamic ◽  
Simply Supported ◽  
Parametric Studies ◽  
Modeling Rule

For dynamic analysis of majority of structures, a dynamic model is developed by discretizing the distributed mass and elastic properties. For assessing the adequacy of mass discretization, several procedures are used. These procedures include a comparison of analysis with test, parametric studies using finer mass discretizations, and lump mass spacing according to a frequency-controlled span length of a simply supported beam. This paper presents a quantitative assessment of mass discretization by utilizing exact analytical solution to the discrete problem of beam and bar vibrations. The assessment examines the effect of mass discretization on the accuracy of natural frequencies, modes and participation factors. In one modeling rule, the total number of dynamic degrees of freedom is taken to be twice the number of lower frequencies to be computed with a reasonable amount of accuracy. The assessment in this paper provides support for this rule.

Investigation of Engine–Airframe Vibration Due to Main Rotor Hub Loads Using a Substructuring Framework

2019 ◽  
Vol 64 (4) ◽  
pp. 1-16
Author(s):  
Stacy Sidle ◽  
Ananth Sridharan ◽  
Inderjit Chopra ◽  
Matt Feshler ◽  
Peter Kull
Keyword(s):  
Degrees Of Freedom ◽  
Transfer Functions ◽  
Element Model ◽  
Forced Response ◽  
Main Rotor ◽  
Structural Dynamic ◽  
Engine Vibration ◽  
Parametric Studies ◽  
Engine Mount ◽  
Stiffness And Damping

This paper presents a methodology to analyze the coupled structural dynamic response of an elastic airframe and engines of a helicopter in response to main rotor hub loads. Transfer functions of individual components (airframe, engine, mount struts, and torque tube) are coupled together using a substructuring approach to obtain consistent coupled solutions of the entire system. Using this approach, a twin-engine, four-bladed helicopter is analyzed using NASTRAN-based models of the airframe and engines. This efficient substructuring approach is validated against the fully coupled NASTRAN model using forced response studies. Characteristics of the mount properties, i.e., the torque tube stiffness, and aft mount stiffness and damping are systematically varied to study their effect on the engine vibration response. The fore and aft mount element properties for minimizing the 8P engine response are identified without increasing 4P response. A compromise between 4P and 8P response is also identified from parametric studies of rear mount properties, using just three parameters to represent the design space. Using the substructuring approach presented here, future studies can be performed to rapidly match airframe characteristics with available engines at approximately 1000 times the speed of running a detailed finite element model (millions of degrees of freedom), without any reduction in accuracy.

scholarly journals VIBRATION ANALYSIS OF A ROTATING TAPERED COMPOSITE BEAM WITH TIP MASS

2013 ◽  
pp. 61-64
Author(s):  
R. VASUDEVAN ◽  
B. PARTHASARADHI
Keyword(s):  
Composite Beam ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Equation Of Motion ◽  
Beam Element ◽  
Mass Matrices ◽  
Vibration Responses ◽  
Parametric Studies ◽  
Tip Mass ◽  
Kinetic And Potential Energies

In this study, free vibration responses of a rotating tapered composite beam with tip mass are investigated. The energy expressions for the kinetic and potential energies of a rotating composite beam with tip mass have been formulated. The energy expressions are then applied in Lagrange’s equations to develop the equation of motion of a composite beam with tip mass. The stiffness and mass matrices for a standard composite beam element with two end nodes with two degrees of freedom at each node are derived. Various parametric studies are performed to investigate the effect of tip mass and the rotational speed on the variation of natural frequencies of the composite beam. The investigations are also done to study the effect of hub radius on the natural frequencies. It is shown that the addition of tip mass increases the stiffness of the structure and consequently increases the natural frequencies.

scholarly journals Spatially Resolved Experimental Modal Analysis on High-Speed Composite Rotors Using a Non-Contact, Non-Rotating Sensor

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4705
Author(s):  
Julian Lich ◽  
Tino Wollmann ◽  
Angelos Filippatos ◽  
Maik Gude ◽  
Juergen Czarske ◽  
...  
Keyword(s):  
High Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Fiber Reinforced ◽  
Structural Dynamic ◽  
Spatially Resolved ◽  
Glass Fiber Reinforced ◽  
Vibration Responses ◽  
And Performance

Due to their lightweight properties, fiber-reinforced composites are well suited for large and fast rotating structures, such as fan blades in turbomachines. To investigate rotor safety and performance, in situ measurements of the structural dynamic behaviour must be performed during rotating conditions. An approach to measuring spatially resolved vibration responses of a rotating structure with a non-contact, non-rotating sensor is investigated here. The resulting spectra can be assigned to specific locations on the structure and have similar properties to the spectra measured with co-rotating sensors, such as strain gauges. The sampling frequency is increased by performing consecutive measurements with a constant excitation function and varying time delays. The method allows for a paradigm shift to unambiguous identification of natural frequencies and mode shapes with arbitrary rotor shapes and excitation functions without the need for co-rotating sensors. Deflection measurements on a glass fiber-reinforced polymer disk were performed with a diffraction grating-based sensor system at 40 measurement points with an uncertainty below 15 μrad and a commercial triangulation sensor at 200 measurement points at surface speeds up to 300 m/s. A rotation-induced increase of two natural frequencies was measured, and their mode shapes were derived at the corresponding rotational speeds. A strain gauge was used for validation.

Natural Frequency of Laminated Composite Plates Using a Sinusoidal Theory

2014 ◽  
Vol 709 ◽  
pp. 148-152
Author(s):  
Guo Qing Zhou ◽  
Ji Wang ◽  
Song Xiang
Keyword(s):  
Differential Equations ◽  
Analytical Method ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Sinusoidal Shear Deformation Theory

Sinusoidal shear deformation theory is presented to analyze the natural frequencies of simply supported laminated composite plates. The governing differential equations based on sinusoidal theory are solved by a Navier-type analytical method. The present results are compared with the available published results which verify the accuracy of sinusoidal theory.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

Natural Frequencies of Parallelogrammic Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method

1992 ◽  
Author(s):  
L. T. Lee ◽  
W. F. Pon
Keyword(s):  
Boundary Conditions ◽  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Energy Functional ◽  
Comprehensive Treatment ◽  
Energy Functionals ◽  
Simply Supported ◽  
Cartesian Coordinate

Abstract Natural frequencies of parallelogrammic plates are obtained by employing a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The orthogonal polynomials are generalted by using a Gram-Schmidt process, after the first member is constructed so as to satisfy all the boundary conditions of the corresponding beam problems accompanying the plate problems. The strain energy functional and kinetic energy functionals are transformed from Cartesian coordinate system to a skew coordinate system. The natural frequencies obtained by using the orthogonal polynomial functions are compared with those obtained by other methods with all four edges clamped boundary conditions and greet agreements are found between them. The natural frequencies for parallelogrammic plates with other boundary conditions, such as four edges simply supported, clamped-free and simply supported-free, are also obtained. This method is considered as a better and accurate comprehensive treatment for this type of problems.

The Natural Frequencies of Free and Constrained Non-Uniform Beams

1960 ◽  
Vol 64 (599) ◽  
pp. 697-699 ◽  
Author(s):  
R. P. N. Jones ◽  
S. Mahalingam
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Normal Modes ◽  
Iteration Process ◽  
Conservative System ◽  
Basic System ◽  
Orthogonal Functions ◽  
Added Masses ◽  
The Given

The Rayleigh-Ritz method is well known as an approximate method of determining the natural frequencies of a conservative system, using a constrained deflection form. On the other hand, if a general deflection form (i.e. an unconstrained form) is used, the method provides a theoretically exact solution. An unconstrained form may be obtained by expressing the deflection as an expansion in terms of a suitable set of orthogonal functions, and in selecting such a set, it is convenient to use the known normal modes of a suitably chosen “ basic system.” The given system, whose vibration properties are to be determined, can then be regarded as a “ modified system,” which is derived from the basic system by a variation of mass and elasticity. A similar procedure has been applied to systems with a finite number of degrees of freedom. In the present note the method is applied to simple non-uniform beams, and to beams with added masses and constraints. A concise general solution is obtained, and an iteration process of obtaining a numerical solution is described.

Free Vibration of Thin-Walled Open Section Beams With Unconstrained Damping Treatment

1981 ◽  
Vol 48 (1) ◽  
pp. 169-173 ◽  
Author(s):  
S. Narayanan ◽  
J. P. Verma ◽  
A. K. Mallik
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Simply Supported ◽  
Clamped Beams ◽  
Thin Walled ◽  
Open Cross Section

Free-vibration characteristics of a thin-walled, open cross-section beam, with unconstrained damping layers at the flanges, are investigated. Both uncoupled transverse vibration and the coupled bending-torsion oscillations, of a beam of a top-hat section, are considered. Numerical results are presented for natural frequencies and modal loss factors of simply supported and clamped-clamped beams.

scholarly journals Characteristic Constraint Modes for Component Mode Synthesis

1999 ◽  
Author(s):  
Matthew P. Castanier ◽  
Yung-Chang Tan ◽  
Christophe Pierre
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Component Mode Synthesis ◽  
Complex Structures ◽  
Cantilever Plate ◽  
Vibration Transmission ◽  
Stiffness Matrices ◽  
Physical Insight ◽  
Insight Into

Abstract In this paper, a technique is presented for improving the efficiency of the Craig-Bampton method of Component Mode Synthesis (CMS). An eigenanalysis is performed on the partitions of the CMS mass and stiffness matrices that correspond to the so-called constraint modes. The resultant eigenvectors are referred to as “characteristic constraint modes,” since they represent the characteristic motion of the interface between the component structures. By truncating the characteristic constraint modes, a CMS model with a highly-reduced number of degrees of freedom may be obtained. An example of a cantilever plate is considered. It is shown that relatively few characteristic constraint modes are needed to yield accurate approximations of the lower natural frequencies. This method also provides physical insight into the mechanisms of vibration transmission in complex structures.

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