1,721,121 research outputs found
Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials
No full textThis book presents the most recent advances on the mechanics of soft and composite shells and their nonlinear vibrations and stability, including advanced problems of modeling human vessels (aorta) with fluid-structure interaction. It guides the reader into nonlinear modelling of shell structures in applications where advanced composite and complex biological materials must be described with great accuracy. To achieve this goal, the book presents nonlinear shell theories, nonlinear vibrations, buckling, composite and functionally graded materials, hyperelasticity, viscoelasticity, nonlinear damping, rubber and soft biological materials. Advanced nonlinear shell theories, not available in any other book, are fully derived in a simple notation and are ready to be implemented in numerical codes. The work features a blend of the most advanced theory and experimental results, and is a valuable resource for researchers, professionals and graduate students, especially those interested in mechanics, aeronautics, civil structures, materials, bioengineering and solid matter at different scales
Shell-plate interaction in the free vibrations of circular cylindrical tanks partially filled with a liquid: The artificial spring method
No full textThe free vibrations of a circular cylindrical tank partially filled with an inviscid and incompressible liquid with a free surface orthogonal to the tank axis are analytically studied. The tank is modelled by a simply supported circular cylindrical shell connected to a simply supported circular plate by an artificial rotational distributed spring of appropriate stiffness. The plate is considered to be resting on a Winkler elastic foundation. The effects of the free surface waves and the hydrostatic liquid pressure are neglected. The bulging modes (where the tank walls oscillate with the liquid) of the structure are investigated and the solution is obtained as an eigenvalue problem by using the Rayleigh-Ritz expansion of the mode shapes and then minimizing the Rayleigh quotient for coupled vibrations. The effects of the liquid level inside the tank, of the stiffness of the Winkler foundation and of the spring stiffness at the shell-plate joint are investigated for shallow and tall water-filled tanks. Comparison with available results is also given. © 1997 Academic Press Limited
Free vibration of partially filled, horizontal cylindrical shells
No full textThe exact solution to the free vibration problem of circular cylindrical shells half-filled with liquid and with the shell axis orthogonal to the gravitational field is analytically obtained and approximate models are proposed to estimate natural frequencies and mode shapes of partially filled shells. In the problem considered, the free surface of the liquid is parallel to the shell axis with lack of the axisymmetry of the liquid-shell system. The shell is considered to be simply supported at both ends. The kinetic energy of the system is analytically evaluated for an inviscid and incompressible liquid. Natural frequencies and mode shapes are found by using a Galerkin equation obtained by minimizing the Rayleigh quotient. The study is based on the development of the radial displacement in a Fourier series and it is independent of the shell theory. Numerical data are presented for both eigenvalues and eigenvectors. The curves of natural frequencies as functions of the water level in the shell are shown. The theoretical study is validated through comparison with results of experimental modal analyses performed on a AISI 304 stainless steel pipe supported by two thin diaphragms and filled with water to different levels. © 1996 Academic Press Limited
Nonlinear damping in large-amplitude vibrations: modelling and experiments
No full textExperimental data clearly show a strong and nonlinear dependence of damping from the maximum vibration amplitude reached in a cycle for macro- and microstructural elements. This dependence takes a completely different level with respect to the frequency shift of resonances due to nonlinearity, which is commonly of 10–25% at most for shells, plates and beams. The experiments show that a damping value over six times larger than the linear one must be expected for vibration of thin plates when the vibration amplitude is about twice the thickness. This is a huge change! The present study derives accurately, for the first time, the nonlinear damping from a fractional viscoelastic standard solid model by introducing geometric nonlinearity in it. The damping model obtained is nonlinear, and its frequency dependence can be tuned by the fractional derivative to match the material behaviour. The solution is obtained for a nonlinear single-degree-of-freedom system by harmonic balance. Numerical results are compared to experimental forced vibration responses measured for large-amplitude vibrations of a rectangular plate (hardening system), a circular cylindrical panel (softening system) and a clamped rod made of zirconium alloy (weak hardening system). Sets of experiments have been obtained at different harmonic excitation forces. Experimental results present a very large damping increase with the peak vibration amplitude, and the model is capable of reproducing them with very good accuracy
Free Vibration of a Fluid-Filled Circular Cylindrical Shell with Lumped Masses Attached, Using the Receptance Method
Full text linkThe receptance method is applied to the analytical study of the free vibrations of a simply supported circular cylindrical shell that is either empty or filled with an in viscid, incompressible fluid and with lumped masses attached at arbitrary positions. The receptance of the fluid-filled shell is obtained using the added virtual mass approach to model the fluid–structure interaction. The starting data for the computations is the modal properties of the cylinder that can be obtained using any theory of shells. Numerical results are obtained as roots of the frequency equation and also by considering the trivial solution. They are compared to data obtained by experimental modal analysis performed on a stainless steel tank, empty, or filled with water, with a lead mass attached
Vibrations of Base Plates in Annular Cylindrical Tanks: Theory and Experiments
No full textIn this paper, the bulging modes (i.e., modes where the walls oscillate moving the liquid) of the flexible bottom annular plate of an otherwise rigid annular cylindrical container are studied. The tank has a vertical axis and is partially filled with liquid, so that the free surface of the liquid is orthogonal to the tank axis. The volume occupied by the liquid is delimited by two coaxial rigid cylinders and the liquid deformation potential is obtained by using variables separation. First, by using the simplifying hypothesis that the mode shapes of the plate in contact with the liquid (wet modes) are the same in vacuo, the approach based on the non-dimensionalized added virtual mass incremental (NAVMI) factor is applied, so that all numerical computations can be made non-dimensional. Second, the accuracy of this method is checked by using the Rayleigh-Ritz method, which removes the restrictive hypothesis on the wet mode shapes. Finally, several experimental modal analyses were performed on two different test tanks filled with different water levels in order to verify the accuracy of the theoretical results. © 1998 Academic Press Limited
Nonlinear damping in nonlinear vibrations of rectangular plates: Derivation from viscoelasticity and experimental validation
No full textEven if still little known, the most significant nonlinear effect during nonlinear vibrations of continuous systems is the increase of damping with the vibration amplitude. The literature on nonlinear vibrations of beams, shells and plates is huge, but almost entirely dedicated to model the nonlinear stiffness and completely neglecting any damping nonlinearity. Experiments presented in this study show a damping increase of six times with the vibration amplitude. Based on this evidence, the nonlinear damanaping of rectangular plates is derived assuming the material to be viscoelastic, and the constitutive relationship to be governed by the standard linear solid model. The material model is then introduced into a geometrically nonlinear plate theory, carefully considering that the retardation time is a function of the vibration mode shape, exactly as its natural frequency. Then, the equations of motion describing the nonlinear vibrations of rectangular plates are derived by Lagrange equations. Numerical results, obtained by continuation and collocation method, are very successfully compared to experimental results on nonlinear vibrations of a rectangular stainless steel plate, validating the proposed approach. Geometric imperfections, in-plane inertia and multi-harmonic vibration response are included in the plate model
Derivation of nonlinear damping from viscoelasticity in case of nonlinear vibrations
No full textExperiments show a strong increase in damping with the vibration amplitude during nonlinear vibrations of beams, plates and shells. This is observed for large size structures but also for micro- and nanodevices. The present study derives nonlinear damping from viscoelasticity by using a single-degree-of-freedom model obtained from standard linear solid material where geometric nonlinearity is inserted in. The solution of the problem is initially reached by a third-order harmonic balance method. Then, the equation of motion is obtained in differential form, which is extremely useful in applications. The damping model developed is nonlinear and the parameters are identified from experiments. Experimental and numerical results are compared for forced vibration responses measured for two different continuous structural elements: a free-edge plate and a shallow shell. The free-edge plate is interesting since it represents a case with no energy escape through the boundary
Nonlinear vibrations and stability of laminated shells using a modified first-order shear deformation theory
No full textAn original and consistent first-order shear deformation theory that retains all the nonlinear terms in the in-plane displacements and rotations is presented here. The theory is developed for dynamics and is applied to study large-amplitude, geometrically nonlinear vibrations. The numerical application to a simply supported, composite laminated circular cylindrical shell is implemented for illustration and validation purposes. Initially the theory is compared to an accurate third-order nonlinear shear deformation theory for the case of pressurized shell. This comparison validates the theory for buckling, which arises in case of external pressure, and post-buckling. The pressure is accurately modelled as displacement-dependent. Then, the nonlinear vibrations due to harmonic forcing around a resonance are studied in detail. The coupling between driven and companion mode gives a chaotic oscillation region near the linear resonance associated to a travelling-wave vibration. Results are presented in the frequency and time domains, in addition to sections of Poincaré maps
Breathing Vibrations of a Horizontal Circular Cylindrical Tank Shell, Partially Filled With Liquid
No full textA theoretical approach to study breathing vibrations of cylindrical shells with horizontal axis, partially fdled with liquid, is delineated and the results of some modal tests conducted on an industrially-manufactured tank are presented and discussed. The good agreement between theoretical and experimental results is preliminarily verified in the case of both an empty and completely full shell, in order to confirm that it is possible to apply the theoretical approach to real structures. The modal properties of a partially-filled shell as a function of liquid level are then experimentally studied, the mode shapes are compared using the Modal Assurance Criterium and a qualitative explanation of the dynamic behavior is proposed. © 1995 by ASME
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