Static and Dynamic Studies on Fg Porous Sandwich Structures With Viscoelastic Boundary Conditions In Thermal Environment

Abstract

The present study investigates the static bending, buckling, and vibration behavior of functionally graded (FG) sandwich beams and plates with a viscoelastic interlayer. Finite element (FE) and analytical methods are used for the formulations. The metal- ceramic gradation of FG stiff layers along the thickness is governed by the rule of mixture and power law index. The kinematics of the sandwich beam stiff layers are based on the Euler-Bernoulli beam theory. The viscoelastic interlayer is assumed to undergo only shear. Lagrange density functions for sandwich beams have been deduced, taking into account the effect of strain energies of the stiff and core layers along with the corresponding translational energies and work done by external forces. Static and dynamic equilibrium equations of sandwich beams are derived using Euler- Lagrange equations. FE solutions are developed to solve equilibrium equations. The developed FE sandwich beam model is validated with an analytical model. Navier’s solution method is used to solve simply supported sandwich beams. Further porosity models and viscoelastic boundary conditions (VBCs) are incorporated into the study; bending, buckling, and vibration studies are carried out. A complex stiffness model is adopted for VBCs. Various types of porosity patterns, such as H, O, V, and X, across the thickness directions are assumed. The effect of porosities and VBCs on transverse deflection, natural frequency (NF), and loss factor (LF) of the FG sandwich beam is investigated. The results convey that VBCs contribution to vibration damping is more predominant when the supports are less stiff (more viscous). In addition, the effect of temperature on buckling and free vibration of FG porous sandwich beams with VBCs is discussed. The study also addresses the geometric nonlinearity of sandwich beams due to thermal stresses. Accordingly, temperature-dependent material properties are considered for FG stiff layers and viscoelastic interlayers. The study investigates the sandwich beam’s critical buckling temperature (CBT), natural frequency, and loss factors in thermal environment. Further, the proposed sandwich beam model is used to study the vibration and damping behavior of the disc brake pad. In the first case, only the back plate with brake insulator is considered as a sandwich beam. iiiA comparison study is presented in terms of the free and forced vibration characteristics of different back plate-brake insulator sandwich beams such as Steel-Acrylic-Steel, FGM-Acrylic-Steel, FGM-Acrylic-Aluminium, and Steel-Acrylic-Aluminium. The study reveals that the natural frequency, loss factor, and with regard to dynamic loading, the imaginary part of transverse deflection, axial displacement, stress, and strain of FGM-Acrylic-Steel are higher. As a result, FGM-Acrylic-Steel is a suitable combination for back plate and brake insulator assembly that enhances the overall disc brake system’s damping capacity and helps to reduce brake squeal problems associated with the operation of the disc brake system. In the second case, a complete brake pad (including friction material) is considered as a sandwich plate. Free and forced vibration studies are carried out on the brake pad for simply supported case (SSSS) using an analytical sandwich plate model. A comparative examination is provided among the brake pads with conventional steel and Al-Al2O3 FG back plates. The influence of several parameters on fundamental frequency and loss factors is also discussed. In addition, transient and steady-state analysis is carried out for the brake pad subjected to uniformly distributive transverse load (UDL) using the Newmark method. The results and analysis reveal that the brake pad with an Al-Al2O3 FG back plate having 0 to 100% Al2O3 variation is as stiff as a pad with a steel back plate and withstands the transverse load (brake load) effectively. The replacement of the steel back plate with an Al-Al2O3 FG enhances energy dissipation in the brake pad and is more efficient in vibration reduction.