Free Vibration Analysis of Sandwich Beams with Functionally-Graded-Cores by Complementary Functions Method

Yıldırım, Sefa

doi:10.2514/1.j059587

Cited by 16 publications

(4 citation statements)

References 46 publications

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“…Different studies have been conducted for sandwich structures to understand the vibration behavior and propagation of waves. [5][6][7][8] Sandwich beams having different type of resonators has been studied to obtain wider attenuation bandgap. 9, 10 Sharma et al studied the band structure of a sandwich beam by making an equivalent single beam model.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation study in metamaterial sandwich structure with periodically inserted hourglass resonators

Gupta¹,

Singh²,

Bhattacharya³

2023

Active and Passive Smart Structures and Integrated Systems XVII

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Low-frequency bandgaps are generally achieved by using locally resonant metamaterials at much higher wavelengths than the lattice constant. However, it remains a challenge to control wave propagation and vibration in these structures due to the limited number of conventional options available as periodic unit cell arrangements. This work investigates the band structure of flexural waves in a metamaterial sandwich beam with an hourglass lattice core using the transfer matrix method. The double dome-shaped hourglass unit cell is modelled with different non-dimensional geometric ratios. A sandwiched metamaterial beam model is then established using a periodic finite hourglass array, considered under the flexural wave propagation. The complete hourglass sandwiched system is further studied to obtain the bandgaps corresponding to the microstructure of the hourglass which is varied in the frequency domain. Subsequently, parametric analysis is performed using some specific non-dimensional geometric parameters that are found to be sensitive towards tailoring the mechanical properties of such unit cells. This study builds a foundation for modelling lightweight hourglass lattice sandwich beams with complex dome shape structures and presents guidelines for designing sandwich beams to control wave propagation.

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Section: Introductionmentioning

confidence: 99%

Wave propagation study in metamaterial sandwich structure with periodically inserted hourglass resonators

Gupta¹,

Singh²,

Bhattacharya³

2023

Active and Passive Smart Structures and Integrated Systems XVII

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“…Tis study also introduces the complementary function method (CFM) as an efcient solution. Continuing the exploration of composite structures, Yildirim [25] investigates the free vibration characteristics of composite sandwich beams, emphasizing isotropic face sheets and an orthotropic core. Teir use of the complementary function method in solving diferential equations enhances precision.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Isotropic Homogeneous Beams Using the Method of Initial Functions and Comparison with Classical Beam Theories and FEM

Namdeo,

Dubey,

Dorji

2023

Complexity

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The main aim of this study is the dynamic analysis of isotropic homogeneous beams using the method of initial functions (MIFs) and comparison with classical beam theories and FEM. Also, this research employs the state space methodology, with a special emphasis on isotropy, to analyse simply supported beam systems. A mathematical model for the dynamic response of beams is constructed using the method of initial functions. The novelty of this study lies in its approach to dynamic analysis, where isotropic homogeneous beams are explored without making assumptions, thus ensuring increased precision using the method of initial functions. Importantly, the approach remains free from restrictive assumptions and relies solely on mathematical formulations, yielding results superior to classical beam theories such as Euler–Bernoulli, Timoshenko, and Rayleigh beam theories. In this work, the application of MIFs of various orders (4th, 6th, 8th, and 10th) to calculate natural frequencies is explored, enabling a thorough examination of the beam’s dynamic characteristics. In addition, parameters such as normal stresses, shear stresses, and deflections in different directions are considered to provide a comprehensive understanding of beam behaviour. To validate the findings, a detailed comparison with a finite element method (FEM) is conducted, achieving excellent agreement between the analytical results and FEM solutions. Furthermore, the influence of Poisson’s ratio (μ) on natural frequencies is investigated by varying its value from 0.18 to 0.30. The research also explores the deviation of plane stress values of the beam section from those estimated using the FEM for the corresponding components.

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“…Zghal ve arkadaşları, kalınlık yönünde FD boşluklu kirişlerin statik eğilme davranışını karışık sonlu elemanlar yöntemi ile araştırmıştır [19]. Literatürde çeşitli mühendislik mekaniği problemleri TFY kullanarak araştırılmıştır [20][21][22][23][24][25][26].…”

Section: Introductionunclassified

Winkler Tipi Elastik Zemine Oturan Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Statik Analizi

ASLAN,

NOORI,

SİVRİ

et al. 2023

Çukurova Üniversitesi Mühendislik Fakültesi Dergisi

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Bu çalışmada, Winkler tipi elastik zemine oturan ve kalınlık boyunca fonksiyonel derecelenmiş (FD) malzemeli kirişlerin eğilme davranışı üzerine bir inceleme yapılmıştır. Farklı mesnet koşullarının, malzeme değişim katsayılarının ve Winkler zemin katsayısının FD kirişlerin statik davranışı üzerine etkileri parametrik olarak incelenmiştir. Ele alınan problemin davranışını idare eden denklemler Euler-Bernoulli kiriş teorisine (EBKT) dayanan minimum toplam potansiyel enerji ilkesinin yardımıyla ilk defa bu çalışmada elde edilmiştir. Elde edilen bu kanonik denklem takımının sayısal çözümünde Tamamlayıcı Fonksiyonlar Yöntemi (TFY) ile Runge-Kutta 5 (RK5) algoritması kullanılmıştır. Önerilen yöntemin doğruluğu ve uygulanabilirliği, literatürde verilen mevcut çalışmaların değerleri ile bu yöntemin sonuçlarının karşılaştırılmasıyla gösterilmiştir. Malzeme değişim katsayısı, Winkler zemin katsayısı ve sınır koşulları ele alınan probleme önemli ölçüde etki etmektedir.

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Free Vibration Analysis of Sandwich Beams with Functionally-Graded-Cores by Complementary Functions Method

Cited by 16 publications

References 46 publications

Wave propagation study in metamaterial sandwich structure with periodically inserted hourglass resonators

Wave propagation study in metamaterial sandwich structure with periodically inserted hourglass resonators

Dynamic Analysis of Isotropic Homogeneous Beams Using the Method of Initial Functions and Comparison with Classical Beam Theories and FEM

Winkler Tipi Elastik Zemine Oturan Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Statik Analizi

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