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By the application of Noether's theorem, conservation laws in linear elastodynamics are derived by invariance of the Lagrangian functional under a class of infinitesimal transformations. The recent work of Gupta and Markenscoff (2012) providing a physical meaning to the dynamic J-integral as the variation of the Hamiltonian of the system due to an infinitesimal translation of the inhomogeneity if linear momentum is conserved in the domain, is extended here to the dynamic Mand L-integrals in terms of the "if" conditions. The variation of the Lagrangian is shown to be equal to the negative of the variation of the Hamiltonian under the above transformations for inhomogeneities, which provides a physical meaning to the dynamic J-, Land M-integrals as dissipative mechanisms in elastodynamics. We prove that if linear momentum is conserved in the domain, then the total energy loss of the system per unit scaling under the infinitesimal scaling transformation of the inhomogeneity is equal to the dynamic Mintegral, and if linear and angular momenta are conserved then the total energy loss of the system per unit rotation under the infinitesimal rotational transformation is equal to the dynamic L-integral.

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The high impact strength of polycarbonate has been studied and exploited for many applications. However, the interaction between processing-induced effects and the strain rate affects the mechanical behavior significantly. In this work, the effects of the processing-induced thermal history, generated by either injection molding or compression molding, were characterized. Polycarbonate samples manufactured with the two processes were experimentally compared using quasi-static and dynamic compression testing. The processing effects are further evaluated by combining a numerical calculation of the temperature history and a constitutive model to predict the yield strength of the glassy polymer. The constitutive modeling approach considers both the effect of the rate-dependent and stress-activated motion of the chain segments, and the strain-hardening effect due to molecular alignment. The results indicate that the thermal history has a significant effect at low strain rates, while its influence is negligible in the dynamic range. The modeling effort allows estimating the yield strength with different accuracy depending on the strain rate values.

This paper describes the architecture of microstrip (MS) interfaced packaging of a coplanar-waveguide (CPW)-based radio frequency microelectromechanical systems (RF MEMS) switch in a hermetic metalceramic RF package. The switch is integrated along with CPW to MS (CPW-MS) transitions within the package itself. This makes the MS interfaced packaged switch module readily mountable on MS based RF boards and subsystems. The CPW-MS transition for the package was designed as a separate off-chip entity on an alumina substrate and utilizes via hole. The integrated three-dimensional model of the package consisting of the RF MEMS switch and the transitions was simulated using high frequency structure simulator. The realized module shows an insertion loss of 0.2 and 1.1 dB at 100 MHz and 7 GHz, respectively. The measured isolation is better than 60 dB at 100 MHz and 30 dB at 7 GHz. The return loss is better than 15 dB up to 7 GHz. The estimated packaging and transitioning loss is 0.5 dB at 5 GHz. This packaging architecture is a planar solution for the MS interfaced packaging of CPW based RF MEMS switches for designers who do not have access to high-end technologies, such as zero-level packaging, through silicon via or low temperature co-fired ceramics. © 2015 Society of Photo-Optical Instrumentation Engineers (SPIE)1 Introduction Radio frequency microelectromechanical systems (RF MEMS) switches exhibit unprecedented low insertion loss and wideband performance. These switches are generally realized in a shunt or series configuration using microstrip (MS) line or coplanar waveguide (CPW) transmission lines. 1 Designers prefer CPW-based RF MEMS switches over MS ones as CPW transmission lines incorporate the availability of an adjacent ground path along with the signal line and support a higher frequency of operation. 1 On the other hand, realization of the majority of planar RF individual modules and their integration is carried out in MS transmission line technology. This is because of the inherent advantages of MS transmission lines, such as ease of interconnects, adjustments, compact size, ease of fabrication, and low cost. 2-6 Due to the different modes of electromagnetic signal propagation, CPWbased RF modules cannot be directly integrated to MS based RF modules. Likewise, CPW-based RF MEMS switches cannot be readily integrated on MS based RF boards or subsystems. A CPW to MS (CPW-MS) transition would be required at both ends of the CPW RF MEMS switch for the integration. 5,6 Reference 7 discusses a frequency tunable MS patch antenna using CPW based RF MEMS capacitors wherein CPW-MS transitions have been utilized.The published datasheets and references of commercially available surface mountable packaged RF MEMS switches, such as Omron and DelfMEMS, show CPW input-output RF