Free and forced in-plane vibration of rectangular plates

Farag, N.H.; Pan, Jie

doi:10.1121/1.421120

Cited by 39 publications

(26 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…These results are compared to those computed by Kantorovich method [29], forced response analysis based on two different formulations [27,28], the Fourier series based analytical method [32] and the finite element solutions by using NASTRAN taken from [28]. It is found that the results obtained by the forced response analysis in [27] and Fourier series based analytical methods [32] match better with the current SDSM compared to the other three methods. The Kantorovich method [29], being a weak formulation, always give upper bound solution of the SDSM results, as expected.…”

Section: Applications To Plane Stress Problemsmentioning

confidence: 82%

“…The (k, j) notation is the same as that given in Table 3. a Kantorovich method [29] b Forced response analysis 1 [28] c Forced response analysis 2 [27] d finite element solution using NASTRAN [28] e Fourier series based analytical method [32] Figure 4: The first eight non-zero free inplane vibration mode shapes of a completely free square (a/b = 1) isotropic plate. The (k, j) notation and the meaning of colour of mesh is the same as those in Table 3.…”

Section: Applications To Plane Stress Problemsmentioning

confidence: 99%

“…Next, the current SDSM is used to revisit another interesting problem covered in the literature [27][28][29]32]. This is about a plate with three different combinations of free and clamped boundary conditions.…”

Section: Applications To Plane Stress Problemsmentioning

confidence: 99%

“…Dozio [26] used the Ritz method in conjunction with a set of trigonometric functions to study the free inplane vibration of plates with elastic boundaries. Farag and Pan [27,28] made use of two types of series solution in the forced response analysis to examine the inplane vibration of rectangular plates with a pair of opposite edges clamped and other two edges being either clamped or free. The same cases were solved by Wang and Wereley [29], utilising the Kantorovich variational method.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

Xiang

Banerjee

2017

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

Citation: Liu, X. and Banerjee, J. R. (2017). A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems. Mechanical Systems and Signal Processing, 87, doi: 10.1016/j.ymssp.2016.10.017 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractA highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the exact general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J 0 ) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.

show abstract

Section: Applications To Plane Stress Problemsmentioning

confidence: 82%

Section: Applications To Plane Stress Problemsmentioning

confidence: 99%

Section: Applications To Plane Stress Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

Xiang

Banerjee

2017

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

show abstract

“…At present times piezoelectric ceramic transducers in longitudinal vibration with matching layers and transducers in flexural vibration are both used in a gas environment [81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98][99]. Using transducers in a flexural vibration gives the best possibility to match acoustic impedances of air and the transducer, because flexural transducers have a sufficiently low acoustic impedance.…”

Section: Acoustic Antennas For Devices Using a Direct Ultrasonic Poromentioning

confidence: 99%

Ultrasonic methods and their implementation for evaluating porous materials

Petrauskas

Petrauskas²

2012

ultra

View full text Add to dashboard Cite

In this article application of direct and indirect ultrasonic methods for evaluating and measuring porous materials are reviewed. Ultrasonic waves, due to their physical properties and wide frequency range can successfully be applied when evaluating the porosity of materials. Ultrasonic methods have many advantages when comparing them with other, non-acoustic measurement methods, which are also briefly reviewed in this article. We examine application of the proposed acoustic echolocation method when evaluating porous materials directly and indirectly. The possibilities to apply Lamb waves for evaluation of porous structures are also examined. The application of ultrasonic echolocation measurement method to evaluate porous structures indirectly is presented in depth, along with the process description and various possible implementations. The basic principle along with advantages and shortcomings of such methods are explained. Physical-mechanical properties of porous materials are also described, along with mathematical equations, which are necessary for their theoretical analysis. The ability to determine porosity of various materials is necessary to insure the quality of the final product. We also present a working real-world system, which implements an indirect ultrasonic porosity evaluation method. For indirect porosity determination, we use a very accurate ultrasonic echolocation-based distance meter. Block diagram for such unit is presented. The most important component in the acoustic porosity evaluation system is the electro-acoustic transducer. We describe the most suitable transducers for use in this case, along with acoustic antennas constructed using such transducers. Antennas, designed for measurements in air, consist of transducers vibrating in a flexural mode, which give the best possibility to match acoustic impedances between air and the transducer. Specific type of transducers for acoustic antennas is described, along with their schematic diagrams. The necessary expressions for calculating radiations patterns are also supplied. Schematic diagrams of actual antennas, along with their directivity patterns are presented. A method for eliminating peripheral radiation of these antennas is also described.

show abstract

Simulation der Schalltransmission durch Wände

Ackermann

Antes

2002

Proc. Appl. Math. Mech.

View full text Add to dashboard Cite

Die rechnerische Vorausbestimmung der Schalldämmwirkung von Wänden bereits in der Entwurfs-und Planungsphase durch numerische Simulation gewinnt in Zeiten steigender Lärmbelastungen immer mehr an Bedeutung. Die Erfassung beliebiger geometrischer, bauphysikalischer und bauakustischer Randbedingungen sowie die Berücksichtigung der Interaktion von Fluid und Struktur spielt dabei eine entscheidende Rolle. Die numerische Simulation des Problems erfolgt mit der Finite-Element-Methode. Dabei wird das Körperschallverhalten des Bauteils im wesentlichen durch die Biegewellen bestimmt, welche mit der Mindlinschen Plattentheorie beschrieben werden. Da jedoch auch die Auswirkungen flankierender Bauteile untersucht werden, werden ebenfalls die in-plane Wellen erfaßt. Diese werden durch die dynamische, elastische Scheibengleichung dargestellt. Für die Modellierung komplexer Wandaufbauten kommt ein Homogenisiserungsverfahren zum Einsatz und poröse Dämmstoffe werden mit Hilfe eines äquivalenten Fluid-Ansatzes beschrieben. Das akustische Verhalten der die Wände umgebenden Luft wird durch die Helmholtz-Gleichung erfaßt. Die Kopplung von Struktur und Fluid, also von Körper-und Luftschall, erfolgt an den Koppelflächen über die dort verrichteten virtuellen Arbeiten des Schalldruckes bzw. der Verschiebungen. Das vollständig gekoppelte Berechnungsprogramm ermöglicht z. B. neben der Ermittlung der Schalldruckverteilungen ebenso die Berechnung des Schalldämm-Maßes sowohl einschaliger als auch mehrschaliger Trennbauteile. Es werden Beispielrechnungen vorgestellt, in denen Parameterstudien sowie Vergleiche mit Messungen bzw. anderen numerischen Berechnungen durchgeführt wurden.

show abstract

Free and forced in-plane vibration of rectangular plates

Cited by 39 publications

References 4 publications

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

Ultrasonic methods and their implementation for evaluating porous materials

Simulation der Schalltransmission durch Wände

Contact Info

Product

Resources

About