EXPERIMENTAL AND NUMERICAL MODAL ANALYSIS OF COMPOSITE LAMINATED SHELLS WITH CUT-OUT

2021 ◽  
Vol 161 (A1) ◽  
Author(s):  
A Mandal ◽  
C Ray ◽  
S Haldar
Keyword(s):  
Heat Dissipation ◽  
Mass Matrix ◽  
Experimental Studies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Lumped Mass ◽  
Auxiliary Equipment ◽  
Mass Model ◽  
Laminated Shells

The presence of cutouts at different positions of laminated shell component in marine and aeronautical structures facilitate heat dissipation, undertaking maintenance, fitting auxiliary equipment, access ports for mechanical and electrical systems, damage inspection and also influences the dynamic behaviour of the structures. The aim of the present study is to establish a comprehensive perspective of dynamic behavior of laminated deep shells (length to radius of curvature ratio less than one) with cut-out by experiments and numerical simulation. The glass epoxy laminated composite shell has been prepared in the laboratory by resin infusion. The experimental free vibration analysis is carried out on laminated shells with and without cut-out. The mass matrix is developed by considering rotary inertia in a lumped mass model in the numerical modeling. The results obtained from numerical and experimental studies are compared for verification and the consistency between mode shapes is established by applying modal assurance criteria.

Experimental and Numerical Modal Analysis of Composite Laminated Shells

2019 ◽  
Vol 161 (A1) ◽  
Keyword(s):  
Heat Dissipation ◽  
Mass Matrix ◽  
Experimental Studies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Lumped Mass ◽  
Auxiliary Equipment ◽  
Mass Model ◽  
Laminated Shells

The presence of cut outs at different positions of laminated shell component in marine and aeronautical structures facilitate heat dissipation, undertaking maintenance, fitting auxiliary equipment, access ports for mechanical and electrical systems, damage inspection and also influences the dynamic behaviour of the structures. The aim of the present study is to establish a comprehensive perspective of dynamic behavior of laminated deep shells (length to radius of curvature ratio less than one) with cut-out by experiments and numerical simulation. The glass epoxy laminated composite shell has been prepared in the laboratory by resin infusion. The experimental free vibration analysis is carried out on laminated shells with and without cut-out. The mass matrix is developed by considering rotary inertia in a lumped mass model in the numerical modeling. The results obtained from numerical and experimental studies are compared for verification and the consistency between mode shapes is established by applying modal assurance criteria.

Critical Speed Analysis of Multi-Cylider Engines As Spatial Elastic Linkage Systems

1996 ◽  
Author(s):  
Sirihari Kurnool ◽  
Cemil Bagei
Keyword(s):  
Critical Speed ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Lumped Mass ◽  
Constant Frequency ◽  
Elastic Mechanism ◽  
Finite Line ◽  
Crankshaft Rotation

Abstract A multi-cylinder engine is a cluster of slider-crank linkages. Presently used conventional pure torsional shaft models predict results far from the results predicted considering actual three-dimensional linkage and crankshaft geometries. Pure torsional model doesn’t sense the variation in frequency with the variation in engine geometry. It predicts one constant frequency value for each mode; it does not permit the use of flexible bearings. Article offers a finite element method for performing frequency and critical speed analysis of multi-cylinder engines considering three-dimensional geometries of the linkage loops, crankshaft, and the crankshaft throws, as a spatial elastic mechanism system. Any number of cylinders in any angular orientations with respect to each other may be considered. A three-dimensional flexural finite-line element with isoparametric joint freedom irregularity is developed and used to formulate the eigenvalue equations of motion for the system. Consistent mass matrix as well as lumped mass matrix methods can be used. The element can be restrained to perform coupled torsional and flexural or pure torsional frequency analysis of geared rotor model of engines and shafts on many rigid or flexible bearings. Geared connections can also be considered flexible. A generalized computer program is made available for industrial use. It determines frequencies, mode shapes and critical speed bands of an engine for complete crankshaft rotation for as many modes as desired. The frequency and critical speed analysis of a four-cylinder MGB automobile engine with in-plane crank throws, with and without bearing flexibilities, is performed and the results are compared with those obtained using the conventional pure torsional shaft model. Geared tandem ship drive system is studied to test the reliability of the developments.

Experimental and numerical analysis of vibration frequency in sandwich composites with different radii of curvature

2017 ◽  
Vol 21 (8) ◽  
pp. 2870-2886
Author(s):  
Melis Yurddaskal ◽  
Buket Okutan Baba
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Experimental Studies ◽  
Sandwich Panels ◽  
Mode Shapes ◽  
Sandwich Composite ◽  
Radius Of Curvature ◽  
Finite Element Software

In this study, free vibration responses of sandwich composite panels with different radius of curvature were presented numerically. The studies were carried out on square flat and curved sandwich panels made of E-glass/epoxy face sheets and polyvinyl chloride foam with three different radii of curvature. Experimental studies were used to verify the numerical results. Vibration tests were performed on flat and curved sandwich panels under free–free boundary conditions. The experimental data were then compared with finite element simulation, which was conducted by ANSYS finite element software and it was shown that the numerical analysis results agree well with the experimental ones. Effect of the curvature on natural frequencies under different boundary conditions (all edge free, simply supported, and fully clamped) was investigated numerically. Results indicated that the natural frequencies and corresponding mode shapes were affected by boundary conditions and curvature of the panel. For all boundary conditions, the variation of curvature had smaller effect on the natural frequency of the first mode than those of the other modes.

scholarly journals Effects of the Radius of Curvature on Natural Frequency and Mode Shape

2019 ◽  
Vol 7 (12) ◽  
Author(s):  
Can Gonenli ◽  
Hasan Ozturk ◽  
Oguzhan Das
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Curvature Radius ◽  
Finite Element Program ◽  
Plane Theory ◽  
Element Type

In this study, the effect of radius of curvature on the natural frequency of isotropic square thin plate is investigated. The models examined are obtained by simply changing the radius of curvature by keeping the length constant from the flat plate to the semicircle model. The free vibration analysis of the plates fixed on two straight edges is performed by the finite element method. As a finite element type, the four-node quadrilateral rectangular element type, which has a total of 24 generalized coordinates, is used. Out-of-plane theory and in-plane theory are used together to form the curve model. The accuracy and validity of the theory are controlled with the data obtained from the finite element program. The effect of the curvature radius on the first five natural frequencies and the mode shapes of these natural frequencies is given in tables and graphs.

scholarly journals Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks

2013 ◽  
Vol 81 (3) ◽  
Author(s):  
Jong-Shyong Wu ◽  
Foung-Tang Lin ◽  
Huei-Jou Shaw
Keyword(s):  
Free Vibration ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Natural Mode ◽  
Lumped Mass ◽  
Rotating Shaft ◽  
Disk System ◽  
Mass Moment ◽  
Rigid Disks ◽  
Equivalent Mass

The purpose of this paper is to present an approach for replacing the effects of each rigid disk mounted on the spin shaft by a lumped mass together with a frequency-dependent equivalent mass moment of inertia so that the whirling motion of a rotating shaft-disk system is similar to the transverse free vibration of a stationary beam and the technique for the free vibration analysis of a stationary beam with multiple concentrated elements can be used to determine the forward and backward whirling speeds, along with mode shapes of a distributed-mass shaft carrying arbitrary rigid disks. Numerical results reveal that the characteristics of whirling motions are significantly dependent on the slopes of the associated natural mode shapes at the positions where the rigid disks are located. Furthermore, the results obtained from the presented analytical method and those obtained from existing literature or the finite element method (FEM) are in good agreement.

Free Flexural Vibration of Composite Plates in Different Situations Using a High Precision Triangular Element

2004 ◽  
Vol 10 (3) ◽  
pp. 371-386 ◽  
Author(s):  
A. H. Sheikh ◽  
S. Haldar ◽  
D. Sengupta
Keyword(s):  
High Precision ◽  
Mass Matrix ◽  
Free Vibration Analysis ◽  
Flexural Vibration ◽  
Composite Plates ◽  
Triangular Element ◽  
Transverse Displacement ◽  
Lumped Mass ◽  
Concentrated Mass ◽  
Independent Field

A high precision, thick-plate element developed by D. Sengupta has been applied to the free vibration analysis of laminated composite plates with necessary addition and modification. The effect of shear deformation has been incorporated in the formulation, taking the transverse displacement and rotations of the normal as independent field variables. These are approximated with polynomials of different orders, which has made the element free from locking in shear. The element contains internal nodes. The degrees of freedom of these nodes have been eliminated through condensation in its final form. To facilitate the condensation, an efficient mass lumping scheme has been recommended to form the mass matrix having zero mass for the internal nodes. Recommendation has also been made for the inclusion of the rotary inertia in the lumped mass matrix. Numerical examples of plates having different shapes, boundary conditions, thickness ratios, fiber orientations and number of layers have been solved. Examples of plates having internal cutout and concentrated mass have also been studied. The results obtained in all cases have been compared with those obtained from other sources to show the accuracy and range of applicability of the element.

scholarly journals A High Precision Shear Flexible Triangular Element for Vibration of Composite Shells

2004 ◽  
Vol 11 (5-6) ◽  
pp. 585-596
Author(s):  
A.H. Sheikh ◽  
S. Haldar ◽  
D. Sengupta
Keyword(s):  
High Precision ◽  
Mass Matrix ◽  
Free Vibration Analysis ◽  
Rotary Inertia ◽  
Triangular Element ◽  
Future Research ◽  
Lumped Mass ◽  
Efficient Manner ◽  
Static Condensation ◽  
Wide Range

A high precision triangular shallow shell element is proposed and it is applied to free vibration analysis of composite and isotropic shells. The Mindlin's hypothesis is followed to include the effect of shear deformation. The formulation is made in an efficient manner to make the element free from shear locking problem. The element has some internal nodes, which are eliminated through static condensation technique to improve the computational elegance of the element. In the present vibration problem, the implementation of the static condensation became possible with the help of an efficient mass lumping scheme. It is quite interesting that the effect of rotary inertia can be included in the recommended scheme for lumped mass matrix. Numerical examples covering a wide range of problems are solved and the results obtained are compared with the published results in many cases, which show the precision and range of applicability of the proposed element. The performance of the proposed technique for rotary inertia is found to be excellent. Some new results are produced, which may be useful in future research.

Free Vibration Analysis of Arbitrarily Shaped Plates With Smoothly Varying Free Edges Using NDIF Method

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
S. W. Kang ◽  
I. S. Kim ◽  
J. M. Lee
Keyword(s):  
Boundary Condition ◽  
Free Boundary ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Free Boundary Condition ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Polar Coordinate System ◽  
Boundary Node

The so-called non-dimensional influence function method that was developed by the authors is extended to free vibration analysis of arbitrarily shaped plates with the free boundary condition. A method proposed in this paper can be applied to plates with only smoothly varying boundary shapes. In the proposed method, a local polar coordinate system has been employed at each boundary node to effectively consider the free boundary condition, which is much more complex than the simply supported or clamped boundary condition. The local coordinates system devised allowed us to successfully deal with the radius of curvature involved in the free boundary condition, and, as a result, the accuracy of the proposed method has been reinforced. Finally, verification examples showed that the natural frequency and mode shapes obtained by the proposed method agree excellently with those given by other analytical or numerical methods.

scholarly journals Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2288
Author(s):  
Hongming Luo ◽  
Guanhua Sun
Keyword(s):  
Structural Dynamics ◽  
Interpolation Method ◽  
Mass Matrix ◽  
Time Integration ◽  
Partition Of Unity ◽  
Implicit Time ◽  
Lumped Mass ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Consistent Mass Matrix

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

Study on Kinetic Energy for Saving Materials with Analysis of Lumped Mass Matrix of Variable Cross-Section Beam Element

2013 ◽  
Vol 675 ◽  
pp. 158-161
Author(s):  
Lv Zhou Ma ◽  
Jian Liu ◽  
Yu Qin Yan ◽  
Xun Lin Diao
Keyword(s):  
Kinetic Energy ◽  
Cross Section ◽  
Mass Matrix ◽  
Nonlinear Problems ◽  
Variable Cross Section ◽  
Beam Element ◽  
Variable Cross ◽  
Lumped Mass ◽  
Geometrical Nonlinear ◽  
Properties Of Materials

Based on positional finite element method (FEM), a new, simple and accurate lumped mass matrix to solve dynamic geometrical nonlinear problems of materials applied to variable cross-section beam element has been proposed. According to Hamilton theory and the concept of Kinetic energy, concentrate the beam element mass to the two nodes in certain proportion, the lumped mass matrix is deduced. The lumped mass matrix is diagonal matrix and its calculated quantity is less than using consistent mass matrix about properties of materials under the same calculation precision.

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