INFLUENCE OF THE INPLANE BOUNDARY CONDITIONS ON THE VIBRATION FREQUENCIES AND BUCKLING LOAD OF RIBBED PLATES

2002 ◽  
Vol 02 (01) ◽  
pp. 25-43 ◽  
Author(s):  
EVANGELOS J. SAPOUNTZAKIS ◽  
JOHN T. KATSIKADELIS
Keyword(s):  
Boundary Conditions ◽  
Mass Matrix ◽  
Buckling Load ◽  
Vibration Frequencies ◽  
Lumped Mass ◽  
Analog Equation Method ◽  
Axial Forces ◽  
Adopted Model ◽  
Dynamic Criterion ◽  
Analog Equation

In this paper, the influence of the inplane boundary conditions on the vibration frequencies and the buckling load of plates reinforced with a system of parallel beams is presented. The adopted model for the dynamic analysis of the ribbed plate takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists in isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The analysis of the vibration problem of a ribbed plate subjected to inplane forces is based on the capability to establish a flexibility matrix with respect to a set of nodal mass points using the Analog Equation Method (AEM) for the static ribbed plate problem. Moreover, a lumped mass matrix is constructed from the tributary mass areas to the nodal mass points. The buckling load is established using the dynamic criterion. From the obtained results it is shown that both the vibration frequencies and the buckling load may be significantly influenced by the inplane boundary conditions.

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.

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.

scholarly journals Analysis of Monolithic and Sandwich Panels Subjected To Non-Uniform Thickness-Wise Boundary Conditions

2016 ◽  
Vol 5 (1) ◽  
pp. 232-249
Author(s):  
Riccardo Vescovini ◽  
Lorenzo Dozio
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Sandwich Plate ◽  
Sandwich Plates ◽  
Vibration Frequencies ◽  
Thickness Direction ◽  
Finite Element Analyses ◽  
Uniform Thickness ◽  
Bending Problems ◽  
High Degree

Abstract The analysis of monolithic and sandwich plates is illustrated for those cases where the boundary conditions are not uniform along the thickness direction, and run at a given position along the thickness direction. For instance, a sandwich plate constrained at the bottom or top face can be considered. The approach relies upon a sublaminate formulation,which is applied here in the context of a Ritz-based approach. Due to the possibility of dividing the structure into smaller portions, viz. the sublaminates, the constraints can be applied at any given location, providing a high degree of flexibility in modeling the boundary conditions. Penalty functions and Lagrange multipliers are introduced for this scope. Results are presented for free-vibration and bending problems. The close matching with highly refined finite element analyses reveals the accuracy of the proposed formulation in determining the vibration frequencies, as well as the internal stress distribution. Reference results are provided for future benchmarking purposes.

Research on Dynamic Simulation of AUV Launching a Towed Navigation Buoyage

2013 ◽  
Vol 433-435 ◽  
pp. 1170-1174
Author(s):  
Guang Pan ◽  
Zhi Dong Yang ◽  
Xiao Xu Du
Keyword(s):  
Angular Momentum ◽  
Boundary Conditions ◽  
Dynamic Simulation ◽  
Numerical Scheme ◽  
Mathematic Model ◽  
Dynamic Equations ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
Towed Cable ◽  
Undersea Vehicle

A mathematic model was established to simulate the process of AUV (autonomous undersea vehicle) launching a towed buoyage. Based on the lumped mass method and moment theorem and angular momentum theorem, dynamic equations of the cable and the buoyage were developed, respectively. Then the boundary conditions and the numerical scheme to deal with the cable with non-fixed length were presented. Moreover, the process of AUV launching a towed cable was simulated. By using the model, the results show the trajectory of buoyage and shape of towed cable can be well predicted.

Hydroelastic Vibration of Rectangular Plates

1996 ◽  
Vol 63 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Moon K. Kwak
Keyword(s):  
Boundary Conditions ◽  
Approximate Formula ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Ritz Method ◽  
Plate Boundary ◽  
Rigid Wall ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Virtual Mass

This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

scholarly journals Generalized straight and curved beam theories with isogeometric analyis

2017 ◽  
Author(s):  
Ιωάννης Τσιπτσής
Keyword(s):  
Isogeometric Analysis ◽  
Computer Aided Design ◽  
State Of The Art ◽  
Curved Beam ◽  
Analog Equation Method ◽  
B Splines ◽  
Aided Design ◽  
Analog Equation ◽  
Beam Theories ◽  
Element Method

Στη διατριβή αυτή διερευνάται και επιλύεται σειρά προβλημάτων μέσω της ανάπτυξης εξελιγμένων προσομοιωμάτων ευθύγραμμης και καμπύλης δοκού. Πιο συγκεκριμένα, αντιμετωπίζονται τα προβλήματα ανομοιόμορφης στρέψης, γενικευμένης στρέβλωσης λόγω διάτμησης και στρέψης (μέσω των οποίων μελετάται το φαινόμενο της διατμητικής υστέρησης), διαστρέβλωσης (παραμόρφωση των διατομών της δοκού στο επίπεδό τους) καθώς και το πρόβλημα της δυναμικής ανάλυσης ευθύγραμμων και καμπύλων δοκών. Η αντιμετώπιση των προβλημάτων αυτών βασίζεται στη γενικευμένη διατύπωση καινοτόμων θεωριών δοκού (Generalized Beam Theories - GBT), με τις οποίες το πεδίο μετατοπίσεων και οι συνιστώσες των τανυστών παραμόρφωσης και τάσης διατυπώνονται ως γραμμικοί συνδυασμοί γινομένων μονοδιάστατων και διδιάστατων συναρτήσεων.Η αναλυτική λύση των μονοδιάστατων και διδιάστατων προβλημάτων συνοριακών και αρχικών-συνοριακών τιμών που μορφώνονται εν γένει δεν είναι εφικτή. Ως εκ τούτου, τα προβλήματα αυτά επιλύονται αριθμητικά εφαρμόζοντας τη Μέθοδο Συνοριακών Στοιχείων (Boundary Element Method - BEM), τη Μέθοδο Αναλογικής Εξίσωσης (Analog Equation Method - AEM), η οποία αποτελεί εξέλιξη της BEM, καθώς και τη Μέθοδο Πεπερασμένων Στοιχείων (Finite Element Method - FEM). Όσον αφορά στην επίλυση μονοδιάστατων προβλημάτων, οι αριθμητικές μέθοδοι που χρησιμοποιoύνται (AEM και FEM) συνδυάζονται με εργαλεία της Ισογεωμετρικής Ανάλυσης (Isogeometric Analysis - IGA) ώστε να επιτευχθεί μία προσέγγιση με χαμηλότερο υπολογιστικό κόστος καθώς και πιο διαδραστική μεταξύ ανάλυσης και γεωμετρίας που θα επιτυγχάνει πιο αξιόπιστα αποτελέσματα περιορίζοντας το σφάλμα που πηγάζει από την προσέγγιση της γεωμετρίας. Συγκεκριμένα, οι παραμετρικές καμπύλες B-splines και NURBS (Non-Uniform Rational B-Splines) που έχουν υιοθετήσει τα λογισμικά πακέτα μοντελοποίησης με υπολογιστή (Computer-Aided Design - CAD) εφαρμόζονται στην παρούσα διατριβή. Με βάση τις αναπτυχθείσες αναλυτικές και αριθμητικές διαδικασίες συντάσσονται καινοτόμα προγράμματα ηλεκτρονικού υπολογιστή για την ανάλυση τρισδιάστατων ευθύγραμμων και καμπυλόγραμμων ραβδωτών φορέων. Κάθε κύριο κεφάλαιο της διατριβής αποτελείται από την εισαγωγή, τη διατύπωση του προβλήματος, την αριθμητική επίλυση, αντιπροσωπευτικά αριθμητικά παραδείγματα και τα συμπεράσματα. Στην εισαγωγή κάθε κύριου κεφαλαίου περιέχεται η βιβλιογραφική επισκόπηση του ερευνητικού έργου (State of the Art) του αντίστοιχου εξεταζόμενου προβλήματος και παρουσιάζονται τα πρωτότυπα σχετικά στοιχεία της εργασίας. Τέλος, στο τελικό κεφάλαιο παρουσιάζονται τα συμπεράσματα και προτάσεις για μελλοντική έρευνα.

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