Sound Enhancement of Orthotropic Sound Radiation Plates Using Line Loads and Considering Resonance Characteristics

A new vibro-acoustic method is presented to analyze the sound radiation behavior of orthotropic panel-form sound radiators using strip-type exciters to exert line loads to the panels for sound radiation. The simple first-order shear deformation theory together with the Ritz method is used to formulate the proposed method that makes the vibro-acoustic analysis of elastically restrained stiffened orthotropic plates more computationally efficient than the methods formulated on the basis of the other shear deformation theories. An elastically restrained orthotropic plate consisting of two parallel strip-type exciters was tested to measure the experimental sound pressure level curve for validating the effectiveness and accuracy of the proposed method. The resonance characteristics (natural frequency and mode shape) detrimental to sound radiation are identified in the vibro-acoustic analysis of the orthotropic plate. For any orthotropic sound radiation plate, based on the detrimental mode shapes, a practical procedure is presented to design the line load locations on the plate to suppress the major sound pressure level dips for enhancing the smoothness of the plate sound pressure level curve. For illustration, the sound radiation enhancement of orthotropic plates with different fiber orientations for aspect ratios equal to 3, 2, and 1 subjected to one or two line loads is conducted using the proposed procedure. The results for the cases with two line loads perpendicular to the fiber direction and located at the nodal lines of the major detrimental mode shape may find applications in designing orthotropic panel-form speakers with relatively smooth sound pressure level curves.

Adjustable positive and negative hygrothermal expansion metamaterial inspired by the Maltese cross

A metamaterial that can manifest both positive and negative coefficients of moisture and thermal expansion is presented herein, based on inspiration from the Maltese cross. Each unit of the metamaterial consists of a pair of equal-armed crosses pin-joined at their junctions to permit rotation, but elastically restrained by a bimaterial spiral spring, and four pairs of hinge rods to translate the relative rotational motion of the pair of equal-armed crosses into translational motion of the connecting rods. The effective coefficients of moisture and thermal expansion models were developed for small and large changes in the hygrothermal conditions using infinitesimal (approximate) and finite (exact) motion analyses, respectively, with the former giving constant effective coefficients with respect to environmental changes. Results indicate that the approximate method underestimates the magnitude of both the effective expansion coefficients under cooling and drying but overestimates magnitudes of both coefficients during heating and moistening, and that the change in both expansion coefficients is more drastic during cooling and drying than during heating and moistening. In addition to providing another micro-lattice geometry for effecting expansion coefficients of either signs, this metamaterial exhibits auxetic property.

Dynamic Analysis of Two Parallel Rectangular Plates Coupled with Mechanical Links

The plate-type structures are classical configurations in many engineering applications. A comprehensive understanding of the structural dynamic mechanisms is of great significance. An analytical modeling approach is established and applied to investigate the dynamic characteristics of a plate system. The model encompasses two parallel elastically restrained rectangular plates coupled through mechanical links. The linear stiffness parameters are used to simulate various structural boundary conditions and mechanical links. The wave propagation of the plate structure is considered based on the improved Fourier series method. And the theoretical formulations for the dynamic performance of the plate system are obtained by employing the energy principle and Rayleigh–Ritz method. The stability and efficiency of the proposed model are firstly validated for the plate system with classical boundary conditions by comparing the results obtained from FEM software. Subsequently, the boundary restraining parameters are analyzed to figure out their effects on the modal characteristics of the plate system. In addition, the influence of mechanical link distributions on the forced response properties of the plate system is presented and discussed. Numerical results show that the importance of both the boundary conditions and the mechanical link distributions on the dynamic behavior of the plate system. The obtained results of the dynamic investigation and parametric analysis of the plate system can be useful for the further work of vibration and noise control technology of engineering applications.

INVESTIGATION OF THE INFLUENCE OF AN INTERMEDIATE HINGE SUPPORT IN THE PROBLEM OF BENDING OF AN ELASTICALLY RESTRAINED ORTHOTROPIC BEAM

In this paper, based on the refined theory of orthotropic plates of variable thickness, a system of differential equations is obtained for solving the problem of bending of an elastically restrained beam with an intermediate condition. The beam thickness is constant and is subject to a uniformly distributed load. The effects of transverse shear are also taken into account. Passing to dimensionless quantities, an analytical closed solution is obtained. The question of the influence of changing the place of application of the intermediate condition on the solution is discussed. Depending on the location of the hinge bearing, the question of optimality was posed and resolved according to the principle of minimum maximum deflection. The results are presented in both tabular and graphical form. Based on the results obtained, appropriate conclusions are drawn.

An Auxetic System Based on Interconnected Y-Elements Inspired by Islamic Geometric Patterns

A 2D mechanical metamaterial exhibiting perfectly auxetic behavior, i.e., Poisson’s ratio of , is proposed in this paper drawing upon inspiration from an Islamic star formed by circumferential arrangement of eight squares, such as the one found at the exterior of the Ghiyathiyya Madrasa in Khargird, Iran (built 1438–1444 AD). Each unit of the metamaterial consists of eight pairs of pin-jointed Y-shaped rigid elements, whereby every pair of Y-elements is elastically restrained by a spiral spring. Upon intermediate stretching, each metamaterial unit resembles the north dome of Jameh Mosque, Iran (built 1087–1088 AD), until the attainment of the fully opened configuration, which resembles a structure in Agra, India, near the Taj Mahal. Both infinitesimal and finite deformation models of the effective Young’s modulus for the metamaterial structure were established using strain energy approach in terms of the spiral spring stiffness and geometrical parameters, with assumptions to preserve the eight-fold symmetricity of every metamaterial unit. Results indicate that the prescription of strain raises the effective Young’s modulus in an exponential manner until full extension is attained. This metamaterial is useful for applications where the overall shape of the structure must be conserved in spite of uniaxial application of load, and where deformation is permitted under limited range, which is quickly arrested as the deformation progresses.